Physics · Article
Electric fields and superposition
Separate a source field from the force on a probe. Add signed vector contributions, locate a cancellation point and derive the field of a finite charged segment.
Previous article: Electric charge and Coulomb’s law
Back to PhysicsAfter reading, you can
- Define an electric field independently of the sign and presence of an ideal test charge.
- Calculate a prescribed electrostatic field using observation-minus-source vectors and signed source charges.
- Explain why a zero force, a zero field and a source singularity are different cases.
- Read a sampled vector diagram without confusing direction arrows, field lines, magnitudes and trajectories.
- Replace a sum by an appropriate charge integral, derive a finite-segment field and check its limits.
- State the fixed-source, continuum, material and time-dependence conditions under which the model applies.
Two sources and an empty observation point
Hold a positive source A and a negative source B at marked positions. Choose an observation point P without putting a third source there. Can we describe what these two sources would do to a small charge placed at P, before choosing that charge? The electric field supplies that description.
Use positive scales q₀ for charge and L₀ for length. A has charge +4q₀ at (−3, 0, 0)L₀; B has charge −q₀ at (3, 0, 0)L₀. Our first observation point is P = (0, 4, 0)L₀. Positions are three-component vectors even though this example is drawn in a plane.
The source list contains A and B only. P is a place, not a third charged object. If you followed the preceding Coulomb-force lesson, remove its recipient C from the source list for the present field calculation. We may later introduce a nonperturbing probe at P; its own field is excluded from the force attributed to A and B.
These are prescribed stationary point sources in vacuum. Supports keep their positions fixed. The model describes an electrostatic field, rather than an experiment in which finite charged objects move, exchange charge or rearrange their surface charge.
One field, different probe forces
At a chosen position, the electric field E is a vector specifying the electric force per unit charge on an ideal stationary probe. For a nonzero probe charge q, F = qE. A positive probe feels force along E; a negative probe feels force opposite E. The field direction follows the positive-probe convention regardless of which probe is actually used.
An operational definition considers probes small enough that changing the probe does not appreciably change the sources. In a prescribed-source mathematical model, E can be calculated at an empty point. It does not disappear because no probe is present, and it does not reverse when a negative probe replaces a positive one.
A zero-charge ideal probe has F = 0. Dividing that zero force by q = 0 cannot define E. Conversely, a nonzero probe can feel zero force where the source field cancels. Always identify which quantity is zero and why.
The SI field unit is N/C. In later potential work, the equivalent unit V/m will be useful. Here E₀ = kₑq₀/L₀² is a positive field scale and F₀ = q₀E₀ is a positive force scale; kₑ denotes the symbolic vacuum Coulomb constant. No numerical value of that constant is needed for our dimensionless comparisons.
A fixed field gives different signed probe forces
At the fixed observation P, changing η=q/q₀ changes F=ηq₀E. The source field does not reverse when the probe sign changes.
Seven signed probe cases at P
- Fx/F₀ at fixed P
- Fy/F₀ at fixed P
- These seven P cases preview the field calculated in the later P section. The complete table retains all 49 force cases at all seven control positions.
- Negative η reverses both force components. Zero η supplies zero force and is never a field definition obtained by dividing by zero.
- The straight joins follow the admitted linear probe rule at fixed sources; this plot is not a particle path.
Read every signed force case and its exact expressions in the complete tables.
Same prescribed source field at P, different ideal probes
All 49 retained probe-force cases, with the same A/B field
| Observation | η = q/q₀ | Fixed exact (Ex,Ey,Ez)/E₀ | Exact (Fx,Fy,Fz)/F₀ | Displayed (Fx,Fy,Fz)/F₀ | Source condition |
|---|---|---|---|---|---|
| Observation (0, 4, 0) L₀ | -2 | (3/25, 12/125, 0) | (-6/25, -24/125, 0) | (-0.24, -0.192, 0) | A and B remain fixed |
| Observation (0, 4, 0) L₀ | -1 | (3/25, 12/125, 0) | (-3/25, -12/125, 0) | (-0.12, -0.096, 0) | A and B remain fixed |
| Observation (0, 4, 0) L₀ | -1/2 | (3/25, 12/125, 0) | (-3/50, -6/125, 0) | (-0.06, -0.048, 0) | A and B remain fixed |
| Observation (0, 4, 0) L₀ | 0 | (3/25, 12/125, 0) | (0, 0, 0) | (0, 0, 0) | A and B remain fixed |
| Observation (0, 4, 0) L₀ | 1/2 | (3/25, 12/125, 0) | (3/50, 6/125, 0) | (0.06, 0.048, 0) | A and B remain fixed |
| Observation (0, 4, 0) L₀ | 1 | (3/25, 12/125, 0) | (3/25, 12/125, 0) | (0.12, 0.096, 0) | A and B remain fixed |
| Observation (0, 4, 0) L₀ | 2 | (3/25, 12/125, 0) | (6/25, 24/125, 0) | (0.24, 0.192, 0) | A and B remain fixed |
| Observation (0, -4, 0) L₀ | -2 | (3/25, -12/125, 0) | (-6/25, 24/125, 0) | (-0.24, 0.192, 0) | A and B remain fixed |
| Observation (0, -4, 0) L₀ | -1 | (3/25, -12/125, 0) | (-3/25, 12/125, 0) | (-0.12, 0.096, 0) | A and B remain fixed |
| Observation (0, -4, 0) L₀ | -1/2 | (3/25, -12/125, 0) | (-3/50, 6/125, 0) | (-0.06, 0.048, 0) | A and B remain fixed |
| Observation (0, -4, 0) L₀ | 0 | (3/25, -12/125, 0) | (0, 0, 0) | (0, 0, 0) | A and B remain fixed |
| Observation (0, -4, 0) L₀ | 1/2 | (3/25, -12/125, 0) | (3/50, -6/125, 0) | (0.06, -0.048, 0) | A and B remain fixed |
| Observation (0, -4, 0) L₀ | 1 | (3/25, -12/125, 0) | (3/25, -12/125, 0) | (0.12, -0.096, 0) | A and B remain fixed |
| Observation (0, -4, 0) L₀ | 2 | (3/25, -12/125, 0) | (6/25, -24/125, 0) | (0.24, -0.192, 0) | A and B remain fixed |
| Observation (0, 0, 0) L₀ | -2 | (5/9, 0, 0) | (-10/9, 0, 0) | (-1.11111111111, 0, 0) | A and B remain fixed |
| Observation (0, 0, 0) L₀ | -1 | (5/9, 0, 0) | (-5/9, 0, 0) | (-0.555555555556, 0, 0) | A and B remain fixed |
| Observation (0, 0, 0) L₀ | -1/2 | (5/9, 0, 0) | (-5/18, 0, 0) | (-0.277777777778, 0, 0) | A and B remain fixed |
| Observation (0, 0, 0) L₀ | 0 | (5/9, 0, 0) | (0, 0, 0) | (0, 0, 0) | A and B remain fixed |
| Observation (0, 0, 0) L₀ | 1/2 | (5/9, 0, 0) | (5/18, 0, 0) | (0.277777777778, 0, 0) | A and B remain fixed |
| Observation (0, 0, 0) L₀ | 1 | (5/9, 0, 0) | (5/9, 0, 0) | (0.555555555556, 0, 0) | A and B remain fixed |
| Observation (0, 0, 0) L₀ | 2 | (5/9, 0, 0) | (10/9, 0, 0) | (1.11111111111, 0, 0) | A and B remain fixed |
| Observation (-6, 0, 0) L₀ | -2 | (-35/81, 0, 0) | (70/81, 0, 0) | (0.864197530864, 0, 0) | A and B remain fixed |
| Observation (-6, 0, 0) L₀ | -1 | (-35/81, 0, 0) | (35/81, 0, 0) | (0.432098765432, 0, 0) | A and B remain fixed |
| Observation (-6, 0, 0) L₀ | -1/2 | (-35/81, 0, 0) | (35/162, 0, 0) | (0.216049382716, 0, 0) | A and B remain fixed |
| Observation (-6, 0, 0) L₀ | 0 | (-35/81, 0, 0) | (0, 0, 0) | (0, 0, 0) | A and B remain fixed |
| Observation (-6, 0, 0) L₀ | 1/2 | (-35/81, 0, 0) | (-35/162, 0, 0) | (-0.216049382716, 0, 0) | A and B remain fixed |
| Observation (-6, 0, 0) L₀ | 1 | (-35/81, 0, 0) | (-35/81, 0, 0) | (-0.432098765432, 0, 0) | A and B remain fixed |
| Observation (-6, 0, 0) L₀ | 2 | (-35/81, 0, 0) | (-70/81, 0, 0) | (-0.864197530864, 0, 0) | A and B remain fixed |
| Observation (6, 0, 0) L₀ | -2 | (-5/81, 0, 0) | (10/81, 0, 0) | (0.123456790123, 0, 0) | A and B remain fixed |
| Observation (6, 0, 0) L₀ | -1 | (-5/81, 0, 0) | (5/81, 0, 0) | (0.0617283950617, 0, 0) | A and B remain fixed |
| Observation (6, 0, 0) L₀ | -1/2 | (-5/81, 0, 0) | (5/162, 0, 0) | (0.0308641975309, 0, 0) | A and B remain fixed |
| Observation (6, 0, 0) L₀ | 0 | (-5/81, 0, 0) | (0, 0, 0) | (0, 0, 0) | A and B remain fixed |
| Observation (6, 0, 0) L₀ | 1/2 | (-5/81, 0, 0) | (-5/162, 0, 0) | (-0.0308641975309, 0, 0) | A and B remain fixed |
| Observation (6, 0, 0) L₀ | 1 | (-5/81, 0, 0) | (-5/81, 0, 0) | (-0.0617283950617, 0, 0) | A and B remain fixed |
| Observation (6, 0, 0) L₀ | 2 | (-5/81, 0, 0) | (-10/81, 0, 0) | (-0.123456790123, 0, 0) | A and B remain fixed |
| Observation (9, 0, 0) L₀ | -2 | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | A and B remain fixed |
| Observation (9, 0, 0) L₀ | -1 | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | A and B remain fixed |
| Observation (9, 0, 0) L₀ | -1/2 | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | A and B remain fixed |
| Observation (9, 0, 0) L₀ | 0 | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | A and B remain fixed |
| Observation (9, 0, 0) L₀ | 1/2 | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | A and B remain fixed |
| Observation (9, 0, 0) L₀ | 1 | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | A and B remain fixed |
| Observation (9, 0, 0) L₀ | 2 | (0, 0, 0) | (0, 0, 0) | (0, 0, 0) | A and B remain fixed |
| Observation (12, 0, 0) L₀ | -2 | (11/2025, 0, 0) | (-22/2025, 0, 0) | (-0.0108641975309, 0, 0) | A and B remain fixed |
| Observation (12, 0, 0) L₀ | -1 | (11/2025, 0, 0) | (-11/2025, 0, 0) | (-0.00543209876543, 0, 0) | A and B remain fixed |
| Observation (12, 0, 0) L₀ | -1/2 | (11/2025, 0, 0) | (-11/4050, 0, 0) | (-0.00271604938272, 0, 0) | A and B remain fixed |
| Observation (12, 0, 0) L₀ | 0 | (11/2025, 0, 0) | (0, 0, 0) | (0, 0, 0) | A and B remain fixed |
| Observation (12, 0, 0) L₀ | 1/2 | (11/2025, 0, 0) | (11/4050, 0, 0) | (0.00271604938272, 0, 0) | A and B remain fixed |
| Observation (12, 0, 0) L₀ | 1 | (11/2025, 0, 0) | (11/2025, 0, 0) | (0.00543209876543, 0, 0) | A and B remain fixed |
| Observation (12, 0, 0) L₀ | 2 | (11/2025, 0, 0) | (22/2025, 0, 0) | (0.0108641975309, 0, 0) | A and B remain fixed |
Every displayed and retained probe-force component
| Location and quantity | Dimensionless quantity | Exact expression | Displayed value (up to 12 significant digits) | Retained calculation digits (120 significant digits for nonzero values) | Exact-zero status |
|---|---|---|---|---|---|
| Observation (0, 4, 0) L₀; η=-2; x force component | Fx/F₀ | -6/25 | -0.24 | -2.40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, 4, 0) L₀; η=-2; y force component | Fy/F₀ | -24/125 | -0.192 | -1.92000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, 4, 0) L₀; η=-2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 4, 0) L₀; η=-1; x force component | Fx/F₀ | -3/25 | -0.12 | -1.20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, 4, 0) L₀; η=-1; y force component | Fy/F₀ | -12/125 | -0.096 | -9.60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, 4, 0) L₀; η=-1; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 4, 0) L₀; η=-1/2; x force component | Fx/F₀ | -3/50 | -0.06 | -6.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, 4, 0) L₀; η=-1/2; y force component | Fy/F₀ | -6/125 | -0.048 | -4.80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, 4, 0) L₀; η=-1/2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 4, 0) L₀; η=0; x force component | Fx/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 4, 0) L₀; η=0; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 4, 0) L₀; η=0; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 4, 0) L₀; η=1/2; x force component | Fx/F₀ | 3/50 | 0.06 | 6.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, 4, 0) L₀; η=1/2; y force component | Fy/F₀ | 6/125 | 0.048 | 4.80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, 4, 0) L₀; η=1/2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 4, 0) L₀; η=1; x force component | Fx/F₀ | 3/25 | 0.12 | 1.20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, 4, 0) L₀; η=1; y force component | Fy/F₀ | 12/125 | 0.096 | 9.60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, 4, 0) L₀; η=1; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 4, 0) L₀; η=2; x force component | Fx/F₀ | 6/25 | 0.24 | 2.40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, 4, 0) L₀; η=2; y force component | Fy/F₀ | 24/125 | 0.192 | 1.92000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, 4, 0) L₀; η=2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, -4, 0) L₀; η=-2; x force component | Fx/F₀ | -6/25 | -0.24 | -2.40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, -4, 0) L₀; η=-2; y force component | Fy/F₀ | 24/125 | 0.192 | 1.92000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, -4, 0) L₀; η=-2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, -4, 0) L₀; η=-1; x force component | Fx/F₀ | -3/25 | -0.12 | -1.20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, -4, 0) L₀; η=-1; y force component | Fy/F₀ | 12/125 | 0.096 | 9.60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, -4, 0) L₀; η=-1; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, -4, 0) L₀; η=-1/2; x force component | Fx/F₀ | -3/50 | -0.06 | -6.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, -4, 0) L₀; η=-1/2; y force component | Fy/F₀ | 6/125 | 0.048 | 4.80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, -4, 0) L₀; η=-1/2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, -4, 0) L₀; η=0; x force component | Fx/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, -4, 0) L₀; η=0; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, -4, 0) L₀; η=0; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, -4, 0) L₀; η=1/2; x force component | Fx/F₀ | 3/50 | 0.06 | 6.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, -4, 0) L₀; η=1/2; y force component | Fy/F₀ | -6/125 | -0.048 | -4.80000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, -4, 0) L₀; η=1/2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, -4, 0) L₀; η=1; x force component | Fx/F₀ | 3/25 | 0.12 | 1.20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, -4, 0) L₀; η=1; y force component | Fy/F₀ | -12/125 | -0.096 | -9.60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, -4, 0) L₀; η=1; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, -4, 0) L₀; η=2; x force component | Fx/F₀ | 6/25 | 0.24 | 2.40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, -4, 0) L₀; η=2; y force component | Fy/F₀ | -24/125 | -0.192 | -1.92000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, -4, 0) L₀; η=2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; η=-2; x force component | Fx/F₀ | -10/9 | -1.11111111111 | -1.11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111e+0 | Nonzero |
| Observation (0, 0, 0) L₀; η=-2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; η=-2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; η=-1; x force component | Fx/F₀ | -5/9 | -0.555555555556 | -5.55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555556e-1 | Nonzero |
| Observation (0, 0, 0) L₀; η=-1; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; η=-1; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; η=-1/2; x force component | Fx/F₀ | -5/18 | -0.277777777778 | -2.77777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778e-1 | Nonzero |
| Observation (0, 0, 0) L₀; η=-1/2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; η=-1/2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; η=0; x force component | Fx/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; η=0; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; η=0; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; η=1/2; x force component | Fx/F₀ | 5/18 | 0.277777777778 | 2.77777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778e-1 | Nonzero |
| Observation (0, 0, 0) L₀; η=1/2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; η=1/2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; η=1; x force component | Fx/F₀ | 5/9 | 0.555555555556 | 5.55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555556e-1 | Nonzero |
| Observation (0, 0, 0) L₀; η=1; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; η=1; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; η=2; x force component | Fx/F₀ | 10/9 | 1.11111111111 | 1.11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111e+0 | Nonzero |
| Observation (0, 0, 0) L₀; η=2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; η=2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; η=-2; x force component | Fx/F₀ | 70/81 | 0.864197530864 | 8.64197530864197530864197530864197530864197530864197530864197530864197530864197530864197530864197530864197530864197530864e-1 | Nonzero |
| Observation (-6, 0, 0) L₀; η=-2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; η=-2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; η=-1; x force component | Fx/F₀ | 35/81 | 0.432098765432 | 4.32098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432e-1 | Nonzero |
| Observation (-6, 0, 0) L₀; η=-1; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; η=-1; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; η=-1/2; x force component | Fx/F₀ | 35/162 | 0.216049382716 | 2.16049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716e-1 | Nonzero |
| Observation (-6, 0, 0) L₀; η=-1/2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; η=-1/2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; η=0; x force component | Fx/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; η=0; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; η=0; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; η=1/2; x force component | Fx/F₀ | -35/162 | -0.216049382716 | -2.16049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716049382716e-1 | Nonzero |
| Observation (-6, 0, 0) L₀; η=1/2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; η=1/2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; η=1; x force component | Fx/F₀ | -35/81 | -0.432098765432 | -4.32098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432e-1 | Nonzero |
| Observation (-6, 0, 0) L₀; η=1; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; η=1; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; η=2; x force component | Fx/F₀ | -70/81 | -0.864197530864 | -8.64197530864197530864197530864197530864197530864197530864197530864197530864197530864197530864197530864197530864197530864e-1 | Nonzero |
| Observation (-6, 0, 0) L₀; η=2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; η=2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; η=-2; x force component | Fx/F₀ | 10/81 | 0.123456790123 | 1.23456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123e-1 | Nonzero |
| Observation (6, 0, 0) L₀; η=-2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; η=-2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; η=-1; x force component | Fx/F₀ | 5/81 | 0.0617283950617 | 6.17283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617e-2 | Nonzero |
| Observation (6, 0, 0) L₀; η=-1; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; η=-1; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; η=-1/2; x force component | Fx/F₀ | 5/162 | 0.0308641975309 | 3.08641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975309e-2 | Nonzero |
| Observation (6, 0, 0) L₀; η=-1/2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; η=-1/2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; η=0; x force component | Fx/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; η=0; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; η=0; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; η=1/2; x force component | Fx/F₀ | -5/162 | -0.0308641975309 | -3.08641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975309e-2 | Nonzero |
| Observation (6, 0, 0) L₀; η=1/2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; η=1/2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; η=1; x force component | Fx/F₀ | -5/81 | -0.0617283950617 | -6.17283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617e-2 | Nonzero |
| Observation (6, 0, 0) L₀; η=1; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; η=1; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; η=2; x force component | Fx/F₀ | -10/81 | -0.123456790123 | -1.23456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123e-1 | Nonzero |
| Observation (6, 0, 0) L₀; η=2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; η=2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=-2; x force component | Fx/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=-2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=-2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=-1; x force component | Fx/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=-1; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=-1; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=-1/2; x force component | Fx/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=-1/2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=-1/2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=0; x force component | Fx/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=0; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=0; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=1/2; x force component | Fx/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=1/2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=1/2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=1; x force component | Fx/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=1; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=1; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=2; x force component | Fx/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; η=2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; η=-2; x force component | Fx/F₀ | -22/2025 | -0.0108641975309 | -1.08641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975309e-2 | Nonzero |
| Observation (12, 0, 0) L₀; η=-2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; η=-2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; η=-1; x force component | Fx/F₀ | -11/2025 | -0.00543209876543 | -5.43209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543e-3 | Nonzero |
| Observation (12, 0, 0) L₀; η=-1; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; η=-1; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; η=-1/2; x force component | Fx/F₀ | -11/4050 | -0.00271604938272 | -2.71604938271604938271604938271604938271604938271604938271604938271604938271604938271604938271604938271604938271604938272e-3 | Nonzero |
| Observation (12, 0, 0) L₀; η=-1/2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; η=-1/2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; η=0; x force component | Fx/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; η=0; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; η=0; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; η=1/2; x force component | Fx/F₀ | 11/4050 | 0.00271604938272 | 2.71604938271604938271604938271604938271604938271604938271604938271604938271604938271604938271604938271604938271604938272e-3 | Nonzero |
| Observation (12, 0, 0) L₀; η=1/2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; η=1/2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; η=1; x force component | Fx/F₀ | 11/2025 | 0.00543209876543 | 5.43209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543e-3 | Nonzero |
| Observation (12, 0, 0) L₀; η=1; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; η=1; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; η=2; x force component | Fx/F₀ | 22/2025 | 0.0108641975309 | 1.08641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975308641975309e-2 | Nonzero |
| Observation (12, 0, 0) L₀; η=2; y force component | Fy/F₀ | 0 | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; η=2; z force component | Fz/F₀ | 0 | 0 | 0 | Exactly zero |
The plot and long tables scroll locally; focus a region to use keyboard scrolling.
Build each vector before adding it
Let r denote the observation position and rⱼ the position of source j. The displacement from that source to the observation point is Rⱼ = r − rⱼ. For distinct positions, the source contribution is Eⱼ(r) = kₑqⱼRⱼ/|Rⱼ|³. Its magnitude is kₑ|qⱼ|/|Rⱼ|².
The displacement points away from the source. Multiplication by a positive source charge preserves that direction; multiplication by a negative source charge reverses it. Do not reverse the displacement a second time after inserting a negative qⱼ. The signed vector formula already supplies the direction.
For prescribed sources, superposition gives E(r) = ΣⱼEⱼ(r). Add x components to x components, y to y and z to z in one common coordinate system. Adding the individual magnitudes would give the magnitude of the result only when all nonzero contributions point in the same direction.
At r = rⱼ the ideal point-source kernel is undefined. Reject that location before dividing by a distance. A drawing mask, a missing arrow or a computer's finite plotting range cannot replace the singular formula with zero or with a softened finite law.
Calculate the field at P
At P, the dimensionless source-to-observation displacements are (3, 4, 0) from A and (−3, 4, 0) from B. Both distances are 5L₀. The equal distances simplify the calculation without making the two field contributions equal: the source charges differ in magnitude and sign.
A contributes E_A/E₀ = 4(3, 4, 0)/125 = (12, 16, 0)/125. B contributes E_B/E₀ = −(−3, 4, 0)/125 = (3, −4, 0)/125. Their sum is E(P)/E₀ = (15, 12, 0)/125 = (3/25, 12/125, 0).
Both x components point right. The positive source contributes upward y field, while the negative source contributes downward y field. The upward contribution is larger, so the result points right and up. Its magnitude is 3√41/125 times E₀, and its angle above the positive x axis is arctan(4/5).
For a probe q = ηq₀, the force is F/F₀ = η(15, 12, 0)/125. Changing η changes the force while the prescribed source field stays fixed. A negative η reverses both components together, rather than changing just one component.
From positions to the field at P
The first panel uses spatial coordinates. The second uses field-component coordinates: signed contributions add at one field-vector origin.
A and B are sources; P is a place
Signed field contributions at P
- Field from A
- Field from B (signed source)
- Total field at P
- Only A=+4q₀ and B=−q₀ produce this prescribed stationary vacuum field. P and an ideal probe are not extra sources.
- At P the field arrows have their actual component lengths in field-coordinate units. The spatial panel has different axes and different units.
- E₀=kₑq₀/L₀² is a field scale in N/C; F₀=q₀E₀ is a force scale in N. kₑ stays symbolic.
The complete controls, source contributions and retained calculation digits are available below.
Same prescribed source field at P, different ideal probes
Seven exact controls for A = +4q₀ and B = −q₀
Sources, observation point and coordinate convention
| Role | Signed charge/q₀ | Position/L₀ | Meaning |
|---|---|---|---|
| Prescribed source A | 4 | (-3, 0, 0) | Fixed stationary source; not a probe |
| Prescribed source B | -1 | (3, 0, 0) | Fixed stationary source; not a probe |
| Observation P | No source charge assigned | (0, 4, 0) | An unoccupied observation point |
Positive scales and units used by every native panel
| Symbol | Definition |
|---|---|
| q0 | arbitrary positive charge scale in C |
| L0 | arbitrary positive length scale in m |
| ke | symbolic Coulomb constant; no new numerical SI constant |
| E0 | ke q0/L0^2 in N/C |
| F0 | q0 E0 in N |
| R | position/L0 |
All seven retained point controls
| Observation position | Total (Ex,Ey,Ez)/E₀ | |E|/E₀ | Status |
|---|---|---|---|
| Observation (0, 4, 0) L₀ | (0.120, 0.096, 0) | 0.153674981698 | Nonzero field |
| Observation (0, -4, 0) L₀ | (0.120, -0.096, 0) | 0.153674981698 | Nonzero field |
| Observation (0, 0, 0) L₀ | (0.555555555556, 0, 0) | 0.555555555556 | Nonzero field |
| Observation (-6, 0, 0) L₀ | (-0.432098765432, 0, 0) | 0.432098765432 | Nonzero field |
| Observation (6, 0, 0) L₀ | (-0.0617283950617, 0, 0) | 0.0617283950617 | Nonzero field |
| Observation (9, 0, 0) L₀ | (0, 0, 0) | 0 | Exact null; no direction arrow |
| Observation (12, 0, 0) L₀ | (0.00543209876543, 0, 0) | 0.00543209876543 | Nonzero field |
Source-to-observer geometry and both signed contributions at every control
| Observation | Contribution | Displacement/L₀ | Squared distance/L₀² | (Ex,Ey,Ez)/E₀ |
|---|---|---|---|---|
| Observation (0, 4, 0) L₀ | Source A | (3, 4, 0) | 25 | (0.096, 0.128, 0) |
| Observation (0, 4, 0) L₀ | Source B | (-3, 4, 0) | 25 | (0.024, -0.032, 0) |
| Observation (0, -4, 0) L₀ | Source A | (3, -4, 0) | 25 | (0.096, -0.128, 0) |
| Observation (0, -4, 0) L₀ | Source B | (-3, -4, 0) | 25 | (0.024, 0.032, 0) |
| Observation (0, 0, 0) L₀ | Source A | (3, 0, 0) | 9 | (0.444444444444, 0, 0) |
| Observation (0, 0, 0) L₀ | Source B | (-3, 0, 0) | 9 | (0.111111111111, 0, 0) |
| Observation (-6, 0, 0) L₀ | Source A | (-3, 0, 0) | 9 | (-0.444444444444, 0, 0) |
| Observation (-6, 0, 0) L₀ | Source B | (-9, 0, 0) | 81 | (0.0123456790123, 0, 0) |
| Observation (6, 0, 0) L₀ | Source A | (9, 0, 0) | 81 | (0.0493827160494, 0, 0) |
| Observation (6, 0, 0) L₀ | Source B | (3, 0, 0) | 9 | (-0.111111111111, 0, 0) |
| Observation (9, 0, 0) L₀ | Source A | (12, 0, 0) | 144 | (0.0277777777778, 0, 0) |
| Observation (9, 0, 0) L₀ | Source B | (6, 0, 0) | 36 | (-0.0277777777778, 0, 0) |
| Observation (12, 0, 0) L₀ | Source A | (15, 0, 0) | 225 | (0.0177777777778, 0, 0) |
| Observation (12, 0, 0) L₀ | Source B | (9, 0, 0) | 81 | (-0.0123456790123, 0, 0) |
Every displayed and retained field value at all seven controls
| Location and quantity | Dimensionless quantity | Exact expression | Displayed value (up to 12 significant digits) | Retained calculation digits (120 significant digits for nonzero values) | Exact-zero status |
|---|---|---|---|---|---|
| Observation (0, 4, 0) L₀; field from A, x component | Ex/E₀ | (12)/(25)^(3/2) | 0.096 | 9.60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, 4, 0) L₀; field from A, y component | Ey/E₀ | (16)/(25)^(3/2) | 0.128 | 1.28000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, 4, 0) L₀; field from A, z component | Ez/E₀ | (0)/(25)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 4, 0) L₀; field from B, x component | Ex/E₀ | (3)/(25)^(3/2) | 0.024 | 2.40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, 4, 0) L₀; field from B, y component | Ey/E₀ | (-4)/(25)^(3/2) | -0.032 | -3.20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, 4, 0) L₀; field from B, z component | Ez/E₀ | (0)/(25)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 4, 0) L₀; total x field component | Ex/E₀ | (12)/(25)^(3/2) + (3)/(25)^(3/2) | 0.120 | 1.20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, 4, 0) L₀; total y field component | Ey/E₀ | (16)/(25)^(3/2) + (-4)/(25)^(3/2) | 0.096 | 9.60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, 4, 0) L₀; total z field component | Ez/E₀ | (0)/(25)^(3/2) + (0)/(25)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 4, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.153674981698 | 1.53674981698388368475717224190923518348490083182904453252702543040036386196725025782944503253996879116099483980091132398e-1 | Nonzero |
| Observation (0, -4, 0) L₀; field from A, x component | Ex/E₀ | (12)/(25)^(3/2) | 0.096 | 9.60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, -4, 0) L₀; field from A, y component | Ey/E₀ | (-16)/(25)^(3/2) | -0.128 | -1.28000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, -4, 0) L₀; field from A, z component | Ez/E₀ | (0)/(25)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, -4, 0) L₀; field from B, x component | Ex/E₀ | (3)/(25)^(3/2) | 0.024 | 2.40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, -4, 0) L₀; field from B, y component | Ey/E₀ | (4)/(25)^(3/2) | 0.032 | 3.20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, -4, 0) L₀; field from B, z component | Ez/E₀ | (0)/(25)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, -4, 0) L₀; total x field component | Ex/E₀ | (12)/(25)^(3/2) + (3)/(25)^(3/2) | 0.120 | 1.20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, -4, 0) L₀; total y field component | Ey/E₀ | (-16)/(25)^(3/2) + (4)/(25)^(3/2) | -0.096 | -9.60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, -4, 0) L₀; total z field component | Ez/E₀ | (0)/(25)^(3/2) + (0)/(25)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, -4, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.153674981698 | 1.53674981698388368475717224190923518348490083182904453252702543040036386196725025782944503253996879116099483980091132398e-1 | Nonzero |
| Observation (0, 0, 0) L₀; field from A, x component | Ex/E₀ | (12)/(9)^(3/2) | 0.444444444444 | 4.44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444e-1 | Nonzero |
| Observation (0, 0, 0) L₀; field from A, y component | Ey/E₀ | (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; field from A, z component | Ez/E₀ | (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; field from B, x component | Ex/E₀ | (3)/(9)^(3/2) | 0.111111111111 | 1.11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111e-1 | Nonzero |
| Observation (0, 0, 0) L₀; field from B, y component | Ey/E₀ | (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; field from B, z component | Ez/E₀ | (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; total x field component | Ex/E₀ | (12)/(9)^(3/2) + (3)/(9)^(3/2) | 0.555555555556 | 5.55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555556e-1 | Nonzero |
| Observation (0, 0, 0) L₀; total y field component | Ey/E₀ | (0)/(9)^(3/2) + (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; total z field component | Ez/E₀ | (0)/(9)^(3/2) + (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.555555555556 | 5.55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555556e-1 | Nonzero |
| Observation (-6, 0, 0) L₀; field from A, x component | Ex/E₀ | (-12)/(9)^(3/2) | -0.444444444444 | -4.44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444e-1 | Nonzero |
| Observation (-6, 0, 0) L₀; field from A, y component | Ey/E₀ | (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; field from A, z component | Ez/E₀ | (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; field from B, x component | Ex/E₀ | (9)/(81)^(3/2) | 0.0123456790123 | 1.23456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123e-2 | Nonzero |
| Observation (-6, 0, 0) L₀; field from B, y component | Ey/E₀ | (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; field from B, z component | Ez/E₀ | (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; total x field component | Ex/E₀ | (-12)/(9)^(3/2) + (9)/(81)^(3/2) | -0.432098765432 | -4.32098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432e-1 | Nonzero |
| Observation (-6, 0, 0) L₀; total y field component | Ey/E₀ | (0)/(9)^(3/2) + (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; total z field component | Ez/E₀ | (0)/(9)^(3/2) + (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.432098765432 | 4.32098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432e-1 | Nonzero |
| Observation (6, 0, 0) L₀; field from A, x component | Ex/E₀ | (36)/(81)^(3/2) | 0.0493827160494 | 4.93827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160494e-2 | Nonzero |
| Observation (6, 0, 0) L₀; field from A, y component | Ey/E₀ | (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; field from A, z component | Ez/E₀ | (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; field from B, x component | Ex/E₀ | (-3)/(9)^(3/2) | -0.111111111111 | -1.11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111e-1 | Nonzero |
| Observation (6, 0, 0) L₀; field from B, y component | Ey/E₀ | (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; field from B, z component | Ez/E₀ | (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; total x field component | Ex/E₀ | (36)/(81)^(3/2) + (-3)/(9)^(3/2) | -0.0617283950617 | -6.17283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617e-2 | Nonzero |
| Observation (6, 0, 0) L₀; total y field component | Ey/E₀ | (0)/(81)^(3/2) + (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; total z field component | Ez/E₀ | (0)/(81)^(3/2) + (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0617283950617 | 6.17283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617e-2 | Nonzero |
| Observation (9, 0, 0) L₀; field from A, x component | Ex/E₀ | (48)/(144)^(3/2) | 0.0277777777778 | 2.77777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778e-2 | Nonzero |
| Observation (9, 0, 0) L₀; field from A, y component | Ey/E₀ | (0)/(144)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; field from A, z component | Ez/E₀ | (0)/(144)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; field from B, x component | Ex/E₀ | (-6)/(36)^(3/2) | -0.0277777777778 | -2.77777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778e-2 | Nonzero |
| Observation (9, 0, 0) L₀; field from B, y component | Ey/E₀ | (0)/(36)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; field from B, z component | Ez/E₀ | (0)/(36)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; total x field component | Ex/E₀ | (48)/(144)^(3/2) + (-6)/(36)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; total y field component | Ey/E₀ | (0)/(144)^(3/2) + (0)/(36)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; total z field component | Ez/E₀ | (0)/(144)^(3/2) + (0)/(36)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; field from A, x component | Ex/E₀ | (60)/(225)^(3/2) | 0.0177777777778 | 1.77777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778e-2 | Nonzero |
| Observation (12, 0, 0) L₀; field from A, y component | Ey/E₀ | (0)/(225)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; field from A, z component | Ez/E₀ | (0)/(225)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; field from B, x component | Ex/E₀ | (-9)/(81)^(3/2) | -0.0123456790123 | -1.23456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123e-2 | Nonzero |
| Observation (12, 0, 0) L₀; field from B, y component | Ey/E₀ | (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; field from B, z component | Ez/E₀ | (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; total x field component | Ex/E₀ | (60)/(225)^(3/2) + (-9)/(81)^(3/2) | 0.00543209876543 | 5.43209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543e-3 | Nonzero |
| Observation (12, 0, 0) L₀; total y field component | Ey/E₀ | (0)/(225)^(3/2) + (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; total z field component | Ez/E₀ | (0)/(225)^(3/2) + (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.00543209876543 | 5.43209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543e-3 | Nonzero |
Use the local plot or table region to scroll horizontally on a narrow screen; each region is keyboard focusable.
| η = q/q₀ | Fₓ/F₀ | Fᵧ/F₀ | Direction relative to E |
|---|---|---|---|
| −2 | −6/25 | −24/125 | Opposite |
| −1 | −3/25 | −12/125 | Opposite |
| −1/2 | −3/50 | −6/125 | Opposite |
| 0 | 0 | 0 | No force direction |
| 1/2 | 3/50 | 6/125 | Same |
| 1 | 3/25 | 12/125 | Same |
| 2 | 6/25 | 24/125 | Same |
Use symmetry and several control points
Reflect an observation point across the x axis while keeping both sources fixed on that axis. Each source distance is unchanged, every x displacement is unchanged and every y displacement reverses. Thus Eₓ(x, −y, 0) = Eₓ(x, y, 0), while Eᵧ(x, −y, 0) = −Eᵧ(x, y, 0). This is a useful independent sign check.
At the midpoint, both sources contribute rightward field. Equal distances do not imply cancellation for opposite source signs: the positive source points away from A toward the midpoint, and the negative source points from the midpoint toward B. The total is 5E₀/9 to the right.
The following exact values are controls for the same two-source field. Their zero z components follow from observing in the sources' plane. They do not mean that the full field is a two-dimensional physical law. Off-plane observation points generally have a z component.
Keep exact fractions or expressions when checking an implementation. A rounded displayed number is useful for reading a scale, but it cannot by itself establish exact cancellation.
| Position/L₀ | Eₓ/E₀ | Eᵧ/E₀ | E_z/E₀ |
|---|---|---|---|
| (0, 4, 0) | 3/25 | 12/125 | 0 |
| (0, −4, 0) | 3/25 | −12/125 | 0 |
| (0, 0, 0) | 5/9 | 0 | 0 |
| (−6, 0, 0) | −35/81 | 0 | 0 |
| (6, 0, 0) | −5/81 | 0 | 0 |
| (9, 0, 0) | 0 | 0 | 0 |
| (12, 0, 0) | 11/2025 | 0 | 0 |
Where can these two contributions cancel?
Between the sources, both contributions point right, so no cancellation is possible there. On the left of A, the stronger positive source is also closer than the negative source; its leftward contribution dominates. Search to the right of B, where the stronger source is farther away.
For x > 3 in dimensionless coordinates, cancellation requires 4/(x + 3)² = 1/(x − 3)². Both distances are positive, so taking the positive square root gives 2/(x + 3) = 1/(x − 3). Solving yields x = 9. The field at (9, 0, 0)L₀ is exactly zero.
Do not solve the squared equation and accept every algebraic root without checking the region and vector directions. Magnitude equality is necessary for two nonzero vectors to cancel, but their directions must also be opposite.
This null is not a point-source position and not an assertion of a stable trap. For example, the table gives leftward field at x = 6 and rightward field at x = 12. A positive probe displaced slightly to either side of x = 9 along this axis is driven farther from the null. A zero instantaneous force does not establish restoring behavior in any direction, still less in all three directions.
Read the arrows without inventing a trajectory
A vector-field picture assigns a vector to each sampled observation position. The plane slice for this model uses x/L₀ = −6, −3, 0, 3, 6, 9, 12 and y/L₀ = −4, −2, 0, 2, 4, 6, 8, with z = 0. Two grid positions coincide with the ideal sources and are excluded. That leaves 47 finite field samples, including the exact null.
The proposed direction-only convention gives every nonzero arrow the same physical length, 11L₀/20, with equal length scales on the two spatial axes. These 46 arrows show direction only. Read actual magnitudes in the complete sample table; equal arrow lengths do not mean equal field strengths.
At the null there is no direction to normalize and therefore no arrow. The source drawing masks have radius L₀/2 only to keep the picture readable. They are neither source radii nor modifications to Coulomb's law. The unmodified source kernel applies at every retained sample outside those masks.
Sampled arrows are not field lines. A field line is a curve whose tangent follows the field direction where that direction is defined. Neither representation is generally a charged particle's trajectory: acceleration follows the force, while velocity and initial conditions also determine motion. The edge of the canvas likewise does not make the field outside it vanish.
A direction-only spatial slice
All 47 finite grid samples are retained. The 46 nonzero arrows have equal physical length 11L₀/20; their lengths do not encode field strength.
The z=0 slice, with equal spatial scales
- Nonzero direction arrow: full length 11L₀/20
- Source drawing mask: radius L₀/2
- Exact field null: no arrow
- The mask is a drawing convention, not a source radius or softened Coulomb law. Source positions are excluded before division.
- Use the complete magnitude table: equal nonzero arrow lengths do not mean equal |E|. Full displacement and endpoint digits are also available.
- Sampled arrows are not field lines or trajectories. A null does not establish a stable trap, and the canvas boundary does not set the outside field to zero.
All retained samples, both source contributions, source masks and arrow endpoints are listed below.
Seven exact controls for A = +4q₀ and B = −q₀
All 47 finite samples in the z=0 spatial slice
| Observation position | Total (Ex,Ey,Ez)/E₀ | |E|/E₀ | Status |
|---|---|---|---|
| Observation (-6, -4, 0) L₀ | (-0.0865792623854, -0.123813005505, 0) | 0.151081530993 | Nonzero field |
| Observation (-3, -4, 0) L₀ | (0.0160009671988, -0.239332688534, 0) | 0.239866977203 | Nonzero field |
| Observation (0, -4, 0) L₀ | (0.120, -0.096, 0) | 0.153674981698 | Nonzero field |
| Observation (3, -4, 0) L₀ | (0.0640038687952, 0.0198307541365, 0) | 0.0670056268561 | Nonzero field |
| Observation (6, -4, 0) L₀ | (0.0136829504586, 0.0152520220184, 0) | 0.0204901759119 | Nonzero field |
| Observation (9, -4, 0) L₀ | (0.00771611525246, 0.00276161731545, 0) | 0.00819542340494 | Nonzero field |
| Observation (12, -4, 0) L₀ | (0.00661635681857, -0.0000895640201278, 0) | 0.00661696299403 | Nonzero field |
| Observation (-6, -2, 0) L₀ | (-0.244530921532, -0.168124860421, 0) | 0.296751310488 | Nonzero field |
| Observation (-3, -2, 0) L₀ | (0.0237170824513, -0.992094305850, 0) | 0.992377756552 | Nonzero field |
| Observation (0, -2, 0) L₀ | (0.320019343976, -0.128007737590, 0) | 0.344671381756 | Nonzero field |
| Observation (3, -2, 0) L₀ | (0.0948683298051, 0.218377223398, 0) | 0.238093703611 | Nonzero field |
| Observation (6, -2, 0) L₀ | (-0.0180656541983, 0.0324607537308, 0) | 0.0371492717881 | Nonzero field |
| Observation (9, -2, 0) L₀ | (0.00294221278744, 0.00346247827730, 0) | 0.00454371785077 | Nonzero field |
| Observation (12, -2, 0) L₀ | (0.00582947081685, 0.000243586437684, 0) | 0.00583455776877 | Nonzero field |
| Observation (-6, 0, 0) L₀ | (-0.432098765432, 0, 0) | 0.432098765432 | Nonzero field |
| Observation (0, 0, 0) L₀ | (0.555555555556, 0, 0) | 0.555555555556 | Nonzero field |
| Observation (6, 0, 0) L₀ | (-0.0617283950617, 0, 0) | 0.0617283950617 | Nonzero field |
| Observation (9, 0, 0) L₀ | (0, 0, 0) | 0 | Exact null; no direction arrow |
| Observation (12, 0, 0) L₀ | (0.00543209876543, 0, 0) | 0.00543209876543 | Nonzero field |
| Observation (-6, 2, 0) L₀ | (-0.244530921532, 0.168124860421, 0) | 0.296751310488 | Nonzero field |
| Observation (-3, 2, 0) L₀ | (0.0237170824513, 0.992094305850, 0) | 0.992377756552 | Nonzero field |
| Observation (0, 2, 0) L₀ | (0.320019343976, 0.128007737590, 0) | 0.344671381756 | Nonzero field |
| Observation (3, 2, 0) L₀ | (0.0948683298051, -0.218377223398, 0) | 0.238093703611 | Nonzero field |
| Observation (6, 2, 0) L₀ | (-0.0180656541983, -0.0324607537308, 0) | 0.0371492717881 | Nonzero field |
| Observation (9, 2, 0) L₀ | (0.00294221278744, -0.00346247827730, 0) | 0.00454371785077 | Nonzero field |
| Observation (12, 2, 0) L₀ | (0.00582947081685, -0.000243586437684, 0) | 0.00583455776877 | Nonzero field |
| Observation (-6, 4, 0) L₀ | (-0.0865792623854, 0.123813005505, 0) | 0.151081530993 | Nonzero field |
| Observation (-3, 4, 0) L₀ | (0.0160009671988, 0.239332688534, 0) | 0.239866977203 | Nonzero field |
| Observation (0, 4, 0) L₀ | (0.120, 0.096, 0) | 0.153674981698 | Nonzero field |
| Observation (3, 4, 0) L₀ | (0.0640038687952, -0.0198307541365, 0) | 0.0670056268561 | Nonzero field |
| Observation (6, 4, 0) L₀ | (0.0136829504586, -0.0152520220184, 0) | 0.0204901759119 | Nonzero field |
| Observation (9, 4, 0) L₀ | (0.00771611525246, -0.00276161731545, 0) | 0.00819542340494 | Nonzero field |
| Observation (12, 4, 0) L₀ | (0.00661635681857, 0.0000895640201278, 0) | 0.00661696299403 | Nonzero field |
| Observation (-6, 6, 0) L₀ | (-0.0326407786227, 0.0747636118818, 0) | 0.0815782942376 | Nonzero field |
| Observation (-3, 6, 0) L₀ | (0.00982092751648, 0.101290183595, 0) | 0.101765180243 | Nonzero field |
| Observation (0, 6, 0) L₀ | (0.0496903995000, 0.0596284794000, 0) | 0.0776188853181 | Nonzero field |
| Observation (3, 6, 0) L₀ | (0.0392837100659, 0.0115059322881, 0) | 0.0409340488391 | Nonzero field |
| Observation (6, 6, 0) L₀ | (0.0185080840090, -0.000912050527341, 0) | 0.0185305426215 | Nonzero field |
| Observation (9, 6, 0) L₀ | (0.0100552322835, 0.000117152383519, 0) | 0.0100559147250 | Nonzero field |
| Observation (12, 6, 0) L₀ | (0.00711798685241, 0.000950783813699, 0) | 0.00718120649275 | Nonzero field |
| Observation (-6, 8, 0) L₀ | (-0.0140850936096, 0.0467238887818, 0) | 0.0488007340609 | Nonzero field |
| Observation (-3, 8, 0) L₀ | (0.006, 0.0545, 0) | 0.0548292804987 | Nonzero field |
| Observation (0, 8, 0) L₀ | (0.0240495507937, 0.0384792812700, 0) | 0.0453766016845 | Nonzero field |
| Observation (3, 8, 0) L₀ | (0.024, 0.016375, 0) | 0.0290540982479 | Nonzero field |
| Observation (6, 8, 0) L₀ | (0.0158082779429, 0.00550085122256, 0) | 0.0167380111032 | Nonzero field |
| Observation (9, 8, 0) L₀ | (0.0100009671988, 0.00266731146587, 0) | 0.0103505504862 | Nonzero field |
| Observation (12, 8, 0) L₀ | (0.00705795043033, 0.00193151239825, 0) | 0.00731747254327 | Nonzero field |
Both source contributions and distances at every retained plane sample
| Observation | Contribution | Displacement/L₀ | Squared distance/L₀² | (Ex,Ey,Ez)/E₀ |
|---|---|---|---|---|
| Observation (-6, -4, 0) L₀ | Source A | (-3, -4, 0) | 25 | (-0.096, -0.128, 0) |
| Observation (-6, -4, 0) L₀ | Source B | (-9, -4, 0) | 97 | (0.00942073761464, 0.00418699449540, 0) |
| Observation (-3, -4, 0) L₀ | Source A | (0, -4, 0) | 16 | (0, -0.25, 0) |
| Observation (-3, -4, 0) L₀ | Source B | (-6, -4, 0) | 52 | (0.0160009671988, 0.0106673114659, 0) |
| Observation (0, -4, 0) L₀ | Source A | (3, -4, 0) | 25 | (0.096, -0.128, 0) |
| Observation (0, -4, 0) L₀ | Source B | (-3, -4, 0) | 25 | (0.024, 0.032, 0) |
| Observation (3, -4, 0) L₀ | Source A | (6, -4, 0) | 52 | (0.0640038687952, -0.0426692458635, 0) |
| Observation (3, -4, 0) L₀ | Source B | (0, -4, 0) | 16 | (0, 0.0625, 0) |
| Observation (6, -4, 0) L₀ | Source A | (9, -4, 0) | 97 | (0.0376829504586, -0.0167479779816, 0) |
| Observation (6, -4, 0) L₀ | Source B | (3, -4, 0) | 25 | (-0.024, 0.032, 0) |
| Observation (9, -4, 0) L₀ | Source A | (12, -4, 0) | 160 | (0.0237170824513, -0.00790569415042, 0) |
| Observation (9, -4, 0) L₀ | Source B | (6, -4, 0) | 52 | (-0.0160009671988, 0.0106673114659, 0) |
| Observation (12, -4, 0) L₀ | Source A | (15, -4, 0) | 241 | (0.0160370944332, -0.00427655851552, 0) |
| Observation (12, -4, 0) L₀ | Source B | (9, -4, 0) | 97 | (-0.00942073761464, 0.00418699449540, 0) |
| Observation (-6, -2, 0) L₀ | Source A | (-3, -2, 0) | 13 | (-0.256015475181, -0.170676983454, 0) |
| Observation (-6, -2, 0) L₀ | Source B | (-9, -2, 0) | 85 | (0.0114845536492, 0.00255212303316, 0) |
| Observation (-3, -2, 0) L₀ | Source A | (0, -2, 0) | 4 | (0, -1, 0) |
| Observation (-3, -2, 0) L₀ | Source B | (-6, -2, 0) | 40 | (0.0237170824513, 0.00790569415042, 0) |
| Observation (0, -2, 0) L₀ | Source A | (3, -2, 0) | 13 | (0.256015475181, -0.170676983454, 0) |
| Observation (0, -2, 0) L₀ | Source B | (-3, -2, 0) | 13 | (0.0640038687952, 0.0426692458635, 0) |
| Observation (3, -2, 0) L₀ | Source A | (6, -2, 0) | 40 | (0.0948683298051, -0.0316227766017, 0) |
| Observation (3, -2, 0) L₀ | Source B | (0, -2, 0) | 4 | (0, 0.25, 0) |
| Observation (6, -2, 0) L₀ | Source A | (9, -2, 0) | 85 | (0.0459382145969, -0.0102084921326, 0) |
| Observation (6, -2, 0) L₀ | Source B | (3, -2, 0) | 13 | (-0.0640038687952, 0.0426692458635, 0) |
| Observation (9, -2, 0) L₀ | Source A | (12, -2, 0) | 148 | (0.0266592952387, -0.00444321587312, 0) |
| Observation (9, -2, 0) L₀ | Source B | (6, -2, 0) | 40 | (-0.0237170824513, 0.00790569415042, 0) |
| Observation (12, -2, 0) L₀ | Source A | (15, -2, 0) | 229 | (0.0173140244661, -0.00230853659548, 0) |
| Observation (12, -2, 0) L₀ | Source B | (9, -2, 0) | 85 | (-0.0114845536492, 0.00255212303316, 0) |
| Observation (-6, 0, 0) L₀ | Source A | (-3, 0, 0) | 9 | (-0.444444444444, 0, 0) |
| Observation (-6, 0, 0) L₀ | Source B | (-9, 0, 0) | 81 | (0.0123456790123, 0, 0) |
| Observation (0, 0, 0) L₀ | Source A | (3, 0, 0) | 9 | (0.444444444444, 0, 0) |
| Observation (0, 0, 0) L₀ | Source B | (-3, 0, 0) | 9 | (0.111111111111, 0, 0) |
| Observation (6, 0, 0) L₀ | Source A | (9, 0, 0) | 81 | (0.0493827160494, 0, 0) |
| Observation (6, 0, 0) L₀ | Source B | (3, 0, 0) | 9 | (-0.111111111111, 0, 0) |
| Observation (9, 0, 0) L₀ | Source A | (12, 0, 0) | 144 | (0.0277777777778, 0, 0) |
| Observation (9, 0, 0) L₀ | Source B | (6, 0, 0) | 36 | (-0.0277777777778, 0, 0) |
| Observation (12, 0, 0) L₀ | Source A | (15, 0, 0) | 225 | (0.0177777777778, 0, 0) |
| Observation (12, 0, 0) L₀ | Source B | (9, 0, 0) | 81 | (-0.0123456790123, 0, 0) |
| Observation (-6, 2, 0) L₀ | Source A | (-3, 2, 0) | 13 | (-0.256015475181, 0.170676983454, 0) |
| Observation (-6, 2, 0) L₀ | Source B | (-9, 2, 0) | 85 | (0.0114845536492, -0.00255212303316, 0) |
| Observation (-3, 2, 0) L₀ | Source A | (0, 2, 0) | 4 | (0, 1, 0) |
| Observation (-3, 2, 0) L₀ | Source B | (-6, 2, 0) | 40 | (0.0237170824513, -0.00790569415042, 0) |
| Observation (0, 2, 0) L₀ | Source A | (3, 2, 0) | 13 | (0.256015475181, 0.170676983454, 0) |
| Observation (0, 2, 0) L₀ | Source B | (-3, 2, 0) | 13 | (0.0640038687952, -0.0426692458635, 0) |
| Observation (3, 2, 0) L₀ | Source A | (6, 2, 0) | 40 | (0.0948683298051, 0.0316227766017, 0) |
| Observation (3, 2, 0) L₀ | Source B | (0, 2, 0) | 4 | (0, -0.25, 0) |
| Observation (6, 2, 0) L₀ | Source A | (9, 2, 0) | 85 | (0.0459382145969, 0.0102084921326, 0) |
| Observation (6, 2, 0) L₀ | Source B | (3, 2, 0) | 13 | (-0.0640038687952, -0.0426692458635, 0) |
| Observation (9, 2, 0) L₀ | Source A | (12, 2, 0) | 148 | (0.0266592952387, 0.00444321587312, 0) |
| Observation (9, 2, 0) L₀ | Source B | (6, 2, 0) | 40 | (-0.0237170824513, -0.00790569415042, 0) |
| Observation (12, 2, 0) L₀ | Source A | (15, 2, 0) | 229 | (0.0173140244661, 0.00230853659548, 0) |
| Observation (12, 2, 0) L₀ | Source B | (9, 2, 0) | 85 | (-0.0114845536492, -0.00255212303316, 0) |
| Observation (-6, 4, 0) L₀ | Source A | (-3, 4, 0) | 25 | (-0.096, 0.128, 0) |
| Observation (-6, 4, 0) L₀ | Source B | (-9, 4, 0) | 97 | (0.00942073761464, -0.00418699449540, 0) |
| Observation (-3, 4, 0) L₀ | Source A | (0, 4, 0) | 16 | (0, 0.25, 0) |
| Observation (-3, 4, 0) L₀ | Source B | (-6, 4, 0) | 52 | (0.0160009671988, -0.0106673114659, 0) |
| Observation (0, 4, 0) L₀ | Source A | (3, 4, 0) | 25 | (0.096, 0.128, 0) |
| Observation (0, 4, 0) L₀ | Source B | (-3, 4, 0) | 25 | (0.024, -0.032, 0) |
| Observation (3, 4, 0) L₀ | Source A | (6, 4, 0) | 52 | (0.0640038687952, 0.0426692458635, 0) |
| Observation (3, 4, 0) L₀ | Source B | (0, 4, 0) | 16 | (0, -0.0625, 0) |
| Observation (6, 4, 0) L₀ | Source A | (9, 4, 0) | 97 | (0.0376829504586, 0.0167479779816, 0) |
| Observation (6, 4, 0) L₀ | Source B | (3, 4, 0) | 25 | (-0.024, -0.032, 0) |
| Observation (9, 4, 0) L₀ | Source A | (12, 4, 0) | 160 | (0.0237170824513, 0.00790569415042, 0) |
| Observation (9, 4, 0) L₀ | Source B | (6, 4, 0) | 52 | (-0.0160009671988, -0.0106673114659, 0) |
| Observation (12, 4, 0) L₀ | Source A | (15, 4, 0) | 241 | (0.0160370944332, 0.00427655851552, 0) |
| Observation (12, 4, 0) L₀ | Source B | (9, 4, 0) | 97 | (-0.00942073761464, -0.00418699449540, 0) |
| Observation (-6, 6, 0) L₀ | Source A | (-3, 6, 0) | 45 | (-0.0397523196000, 0.0795046392000, 0) |
| Observation (-6, 6, 0) L₀ | Source B | (-9, 6, 0) | 117 | (0.00711154097725, -0.00474102731816, 0) |
| Observation (-3, 6, 0) L₀ | Source A | (0, 6, 0) | 36 | (0, 0.111111111111, 0) |
| Observation (-3, 6, 0) L₀ | Source B | (-6, 6, 0) | 72 | (0.00982092751648, -0.00982092751648, 0) |
| Observation (0, 6, 0) L₀ | Source A | (3, 6, 0) | 45 | (0.0397523196000, 0.0795046392000, 0) |
| Observation (0, 6, 0) L₀ | Source B | (-3, 6, 0) | 45 | (0.00993807990000, -0.0198761598000, 0) |
| Observation (3, 6, 0) L₀ | Source A | (6, 6, 0) | 72 | (0.0392837100659, 0.0392837100659, 0) |
| Observation (3, 6, 0) L₀ | Source B | (0, 6, 0) | 36 | (0, -0.0277777777778, 0) |
| Observation (6, 6, 0) L₀ | Source A | (9, 6, 0) | 117 | (0.0284461639090, 0.0189641092727, 0) |
| Observation (6, 6, 0) L₀ | Source B | (3, 6, 0) | 45 | (-0.00993807990000, -0.0198761598000, 0) |
| Observation (9, 6, 0) L₀ | Source A | (12, 6, 0) | 180 | (0.0198761598000, 0.00993807990000, 0) |
| Observation (9, 6, 0) L₀ | Source B | (6, 6, 0) | 72 | (-0.00982092751648, -0.00982092751648, 0) |
| Observation (12, 6, 0) L₀ | Source A | (15, 6, 0) | 261 | (0.0142295278297, 0.00569181113186, 0) |
| Observation (12, 6, 0) L₀ | Source B | (9, 6, 0) | 117 | (-0.00711154097725, -0.00474102731816, 0) |
| Observation (-6, 8, 0) L₀ | Source A | (-3, 8, 0) | 73 | (-0.0192396406350, 0.0513057083599, 0) |
| Observation (-6, 8, 0) L₀ | Source B | (-9, 8, 0) | 145 | (0.00515454702540, -0.00458181957814, 0) |
| Observation (-3, 8, 0) L₀ | Source A | (0, 8, 0) | 64 | (0, 0.0625, 0) |
| Observation (-3, 8, 0) L₀ | Source B | (-6, 8, 0) | 100 | (0.006, -0.008, 0) |
| Observation (0, 8, 0) L₀ | Source A | (3, 8, 0) | 73 | (0.0192396406350, 0.0513057083599, 0) |
| Observation (0, 8, 0) L₀ | Source B | (-3, 8, 0) | 73 | (0.00480991015875, -0.0128264270900, 0) |
| Observation (3, 8, 0) L₀ | Source A | (6, 8, 0) | 100 | (0.024, 0.032, 0) |
| Observation (3, 8, 0) L₀ | Source B | (0, 8, 0) | 64 | (0, -0.015625, 0) |
| Observation (6, 8, 0) L₀ | Source A | (9, 8, 0) | 145 | (0.0206181881016, 0.0183272783125, 0) |
| Observation (6, 8, 0) L₀ | Source B | (3, 8, 0) | 73 | (-0.00480991015875, -0.0128264270900, 0) |
| Observation (9, 8, 0) L₀ | Source A | (12, 8, 0) | 208 | (0.0160009671988, 0.0106673114659, 0) |
| Observation (9, 8, 0) L₀ | Source B | (6, 8, 0) | 100 | (-0.006, -0.008, 0) |
| Observation (12, 8, 0) L₀ | Source A | (15, 8, 0) | 289 | (0.0122124974557, 0.00651333197639, 0) |
| Observation (12, 8, 0) L₀ | Source B | (9, 8, 0) | 145 | (-0.00515454702540, -0.00458181957814, 0) |
The two excluded source positions
| Position/L₀ | Source at position | Field evaluation | Drawing convention |
|---|---|---|---|
| (-3, 0, 0) | Source A | Not evaluated | Drawing radius L₀/2 only; not a physical source radius |
| (3, 0, 0) | Source B | Not evaluated | Drawing radius L₀/2 only; not a physical source radius |
Every displayed and retained field value in the plane slice
| Location and quantity | Dimensionless quantity | Exact expression | Displayed value (up to 12 significant digits) | Retained calculation digits (120 significant digits for nonzero values) | Exact-zero status |
|---|---|---|---|---|---|
| Observation (-6, -4, 0) L₀; field from A, x component | Ex/E₀ | (-12)/(25)^(3/2) | -0.096 | -9.60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (-6, -4, 0) L₀; field from A, y component | Ey/E₀ | (-16)/(25)^(3/2) | -0.128 | -1.28000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (-6, -4, 0) L₀; field from A, z component | Ez/E₀ | (0)/(25)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, -4, 0) L₀; field from B, x component | Ex/E₀ | (9)/(97)^(3/2) | 0.00942073761464 | 9.42073761464182617660919361613971945321131114751672627755429809422127380735137715706651153757453840598819330320392632559e-3 | Nonzero |
| Observation (-6, -4, 0) L₀; field from B, y component | Ey/E₀ | (4)/(97)^(3/2) | 0.00418699449540 | 4.18699449539636718960408605161765309031613828778521167891302137520945502548950095869622735003312818043919702364618947804e-3 | Nonzero |
| Observation (-6, -4, 0) L₀; field from B, z component | Ez/E₀ | (0)/(97)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, -4, 0) L₀; total x field component | Ex/E₀ | (-12)/(25)^(3/2) + (9)/(97)^(3/2) | -0.0865792623854 | -8.65792623853581738233908063838602805467886888524832737224457019057787261926486228429334884624254615940118066967960736744e-2 | Nonzero |
| Observation (-6, -4, 0) L₀; total y field component | Ey/E₀ | (-16)/(25)^(3/2) + (4)/(97)^(3/2) | -0.123813005505 | -1.23813005504603632810395913948382346909683861712214788321086978624790544974510499041303772649966871819560802976353810522e-1 | Nonzero |
| Observation (-6, -4, 0) L₀; total z field component | Ez/E₀ | (0)/(25)^(3/2) + (0)/(97)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, -4, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.151081530993 | 1.51081530993287548886494626460783752667195495818497758382129206624336257848408582059897086671392966876808973999404323398e-1 | Nonzero |
| Observation (-3, -4, 0) L₀; field from A, x component | Ex/E₀ | (0)/(16)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, -4, 0) L₀; field from A, y component | Ey/E₀ | (-16)/(16)^(3/2) | -0.25 | -2.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (-3, -4, 0) L₀; field from A, z component | Ez/E₀ | (0)/(16)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, -4, 0) L₀; field from B, x component | Ex/E₀ | (6)/(52)^(3/2) | 0.0160009671988 | 1.60009671988046862120675500035672897022986534342244654410227206637300308356198688396654692988986274452966605711127080194e-2 | Nonzero |
| Observation (-3, -4, 0) L₀; field from B, y component | Ey/E₀ | (4)/(52)^(3/2) | 0.0106673114659 | 1.06673114658697908080450333357115264681991022894829769606818137758200205570799125597769795325990849635311070474084720129e-2 | Nonzero |
| Observation (-3, -4, 0) L₀; field from B, z component | Ez/E₀ | (0)/(52)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, -4, 0) L₀; total x field component | Ex/E₀ | (0)/(16)^(3/2) + (6)/(52)^(3/2) | 0.0160009671988 | 1.60009671988046862120675500035672897022986534342244654410227206637300308356198688396654692988986274452966605711127080194e-2 | Nonzero |
| Observation (-3, -4, 0) L₀; total y field component | Ey/E₀ | (-16)/(16)^(3/2) + (4)/(52)^(3/2) | -0.239332688534 | -2.39332688534130209191954966664288473531800897710517023039318186224179979442920087440223020467400915036468892952591527987e-1 | Nonzero |
| Observation (-3, -4, 0) L₀; total z field component | Ez/E₀ | (0)/(16)^(3/2) + (0)/(52)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, -4, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.239866977203 | 2.39866977202515738851957172872427261148843305217126523600159366747122705017148425311397264223904070135312305658784328593e-1 | Nonzero |
| Observation (0, -4, 0) L₀; field from A, x component | Ex/E₀ | (12)/(25)^(3/2) | 0.096 | 9.60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, -4, 0) L₀; field from A, y component | Ey/E₀ | (-16)/(25)^(3/2) | -0.128 | -1.28000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, -4, 0) L₀; field from A, z component | Ez/E₀ | (0)/(25)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, -4, 0) L₀; field from B, x component | Ex/E₀ | (3)/(25)^(3/2) | 0.024 | 2.40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, -4, 0) L₀; field from B, y component | Ey/E₀ | (4)/(25)^(3/2) | 0.032 | 3.20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, -4, 0) L₀; field from B, z component | Ez/E₀ | (0)/(25)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, -4, 0) L₀; total x field component | Ex/E₀ | (12)/(25)^(3/2) + (3)/(25)^(3/2) | 0.120 | 1.20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, -4, 0) L₀; total y field component | Ey/E₀ | (-16)/(25)^(3/2) + (4)/(25)^(3/2) | -0.096 | -9.60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, -4, 0) L₀; total z field component | Ez/E₀ | (0)/(25)^(3/2) + (0)/(25)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, -4, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.153674981698 | 1.53674981698388368475717224190923518348490083182904453252702543040036386196725025782944503253996879116099483980091132398e-1 | Nonzero |
| Observation (3, -4, 0) L₀; field from A, x component | Ex/E₀ | (24)/(52)^(3/2) | 0.0640038687952 | 6.40038687952187448482702000142691588091946137368978617640908826549201233424794753586618771955945097811866422844508320777e-2 | Nonzero |
| Observation (3, -4, 0) L₀; field from A, y component | Ey/E₀ | (-16)/(52)^(3/2) | -0.0426692458635 | -4.26692458634791632321801333428461058727964091579319078427272551032800822283196502391079181303963398541244281896338880518e-2 | Nonzero |
| Observation (3, -4, 0) L₀; field from A, z component | Ez/E₀ | (0)/(52)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, -4, 0) L₀; field from B, x component | Ex/E₀ | (0)/(16)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, -4, 0) L₀; field from B, y component | Ey/E₀ | (4)/(16)^(3/2) | 0.0625 | 6.25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (3, -4, 0) L₀; field from B, z component | Ez/E₀ | (0)/(16)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, -4, 0) L₀; total x field component | Ex/E₀ | (24)/(52)^(3/2) + (0)/(16)^(3/2) | 0.0640038687952 | 6.40038687952187448482702000142691588091946137368978617640908826549201233424794753586618771955945097811866422844508320777e-2 | Nonzero |
| Observation (3, -4, 0) L₀; total y field component | Ey/E₀ | (-16)/(52)^(3/2) + (4)/(16)^(3/2) | 0.0198307541365 | 1.98307541365208367678198666571538941272035908420680921572727448967199177716803497608920818696036601458755718103661119482e-2 | Nonzero |
| Observation (3, -4, 0) L₀; total z field component | Ez/E₀ | (0)/(52)^(3/2) + (0)/(16)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, -4, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0670056268561 | 6.70056268560985411174905860175357897514136637557512038214894843404682652648750580204337263536568875696446270491928368594e-2 | Nonzero |
| Observation (6, -4, 0) L₀; field from A, x component | Ex/E₀ | (36)/(97)^(3/2) | 0.0376829504586 | 3.76829504585673047064367744645588778128452445900669051102171923768850952294055086282660461502981536239527732128157053024e-2 | Nonzero |
| Observation (6, -4, 0) L₀; field from A, y component | Ey/E₀ | (-16)/(97)^(3/2) | -0.0167479779816 | -1.67479779815854687584163442064706123612645531511408467156520855008378201019580038347849094001325127217567880945847579122e-2 | Nonzero |
| Observation (6, -4, 0) L₀; field from A, z component | Ez/E₀ | (0)/(97)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, -4, 0) L₀; field from B, x component | Ex/E₀ | (-3)/(25)^(3/2) | -0.024 | -2.40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (6, -4, 0) L₀; field from B, y component | Ey/E₀ | (4)/(25)^(3/2) | 0.032 | 3.20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (6, -4, 0) L₀; field from B, z component | Ez/E₀ | (0)/(25)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, -4, 0) L₀; total x field component | Ex/E₀ | (36)/(97)^(3/2) + (-3)/(25)^(3/2) | 0.0136829504586 | 1.36829504585673047064367744645588778128452445900669051102171923768850952294055086282660461502981536239527732128157053024e-2 | Nonzero |
| Observation (6, -4, 0) L₀; total y field component | Ey/E₀ | (-16)/(97)^(3/2) + (4)/(25)^(3/2) | 0.0152520220184 | 1.52520220184145312415836557935293876387354468488591532843479144991621798980419961652150905998674872782432119054152420878e-2 | Nonzero |
| Observation (6, -4, 0) L₀; total z field component | Ez/E₀ | (0)/(97)^(3/2) + (0)/(25)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, -4, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0204901759119 | 2.04901759119293284246349398649338884931279669004185613095248721403511312824776214767360973466622167252188290317123798133e-2 | Nonzero |
| Observation (9, -4, 0) L₀; field from A, x component | Ex/E₀ | (48)/(160)^(3/2) | 0.0237170824513 | 2.37170824512628449899917015832453890028966635449391262014312863959444582897942866600818608128447522139051046311463004136e-2 | Nonzero |
| Observation (9, -4, 0) L₀; field from A, y component | Ey/E₀ | (-16)/(160)^(3/2) | -0.00790569415042 | -7.90569415042094832999723386108179633429888784831304206714376213198148609659809555336062027094825073796836821038210013787e-3 | Nonzero |
| Observation (9, -4, 0) L₀; field from A, z component | Ez/E₀ | (0)/(160)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, -4, 0) L₀; field from B, x component | Ex/E₀ | (-6)/(52)^(3/2) | -0.0160009671988 | -1.60009671988046862120675500035672897022986534342244654410227206637300308356198688396654692988986274452966605711127080194e-2 | Nonzero |
| Observation (9, -4, 0) L₀; field from B, y component | Ey/E₀ | (4)/(52)^(3/2) | 0.0106673114659 | 1.06673114658697908080450333357115264681991022894829769606818137758200205570799125597769795325990849635311070474084720129e-2 | Nonzero |
| Observation (9, -4, 0) L₀; field from B, z component | Ez/E₀ | (0)/(52)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, -4, 0) L₀; total x field component | Ex/E₀ | (48)/(160)^(3/2) + (-6)/(52)^(3/2) | 0.00771611525246 | 7.71611525245815877792415157967809930059801011071466076040856573221442745417441782041639151394612476860844406003359239419e-3 | Nonzero |
| Observation (9, -4, 0) L₀; total y field component | Ey/E₀ | (-16)/(160)^(3/2) + (4)/(52)^(3/2) | 0.00276161731545 | 2.76161731544884247804779947462973013390021444116993489353805164383853446048181700641635926165083422556273883702637187508e-3 | Nonzero |
| Observation (9, -4, 0) L₀; total z field component | Ez/E₀ | (0)/(160)^(3/2) + (0)/(52)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, -4, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.00819542340494 | 8.19542340493792345686211621658612611256871992229489484400535421821465727206368176715042625194445323154908091816843864960e-3 | Nonzero |
| Observation (12, -4, 0) L₀; field from A, x component | Ex/E₀ | (60)/(241)^(3/2) | 0.0160370944332 | 1.60370944332157060610483239963220130882241243023749707398496691597554140785749555572947185786997069645151481450049773084e-2 | Nonzero |
| Observation (12, -4, 0) L₀; field from A, y component | Ey/E₀ | (-16)/(241)^(3/2) | -0.00427655851552 | -4.27655851552418828294621973235253682352643314729999219729324510926811042095332148194525828765325519053737283866799394891e-3 | Nonzero |
| Observation (12, -4, 0) L₀; field from A, z component | Ez/E₀ | (0)/(241)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, -4, 0) L₀; field from B, x component | Ex/E₀ | (-9)/(97)^(3/2) | -0.00942073761464 | -9.42073761464182617660919361613971945321131114751672627755429809422127380735137715706651153757453840598819330320392632559e-3 | Nonzero |
| Observation (12, -4, 0) L₀; field from B, y component | Ey/E₀ | (4)/(97)^(3/2) | 0.00418699449540 | 4.18699449539636718960408605161765309031613828778521167891302137520945502548950095869622735003312818043919702364618947804e-3 | Nonzero |
| Observation (12, -4, 0) L₀; field from B, z component | Ez/E₀ | (0)/(97)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, -4, 0) L₀; total x field component | Ex/E₀ | (60)/(241)^(3/2) + (-9)/(97)^(3/2) | 0.00661635681857 | 6.61635681857387988443913038018229363501281315485824446229537106553414027122357840022820704112516855852695484180105098282e-3 | Nonzero |
| Observation (12, -4, 0) L₀; total y field component | Ey/E₀ | (-16)/(241)^(3/2) + (4)/(97)^(3/2) | -0.0000895640201278 | -8.95640201278210933421336807348837332102948595147805183802237340586553954638205232490309376201270100981758150218044708701e-5 | Nonzero |
| Observation (12, -4, 0) L₀; total z field component | Ez/E₀ | (0)/(241)^(3/2) + (0)/(97)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, -4, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.00661696299403 | 6.61696299403212092941239916272598534601715741684182441970673913374672352813307235790252487713016254826070656382628499210e-3 | Nonzero |
| Observation (-6, -2, 0) L₀; field from A, x component | Ex/E₀ | (-12)/(13)^(3/2) | -0.256015475181 | -2.56015475180874979393080800057076635236778454947591447056363530619680493369917901434647508782378039124746569137803328311e-1 | Nonzero |
| Observation (-6, -2, 0) L₀; field from A, y component | Ey/E₀ | (-8)/(13)^(3/2) | -0.170676983454 | -1.70676983453916652928720533371384423491185636631727631370909020413120328913278600956431672521585359416497712758535552207e-1 | Nonzero |
| Observation (-6, -2, 0) L₀; field from A, z component | Ez/E₀ | (0)/(13)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, -2, 0) L₀; field from B, x component | Ex/E₀ | (9)/(85)^(3/2) | 0.0114845536492 | 1.14845536492229738117675388976975970124873696108653530895598297368836040472272497089150237809189654096142641217868297796e-2 | Nonzero |
| Observation (-6, -2, 0) L₀; field from B, y component | Ey/E₀ | (2)/(85)^(3/2) | 0.00255212303316 | 2.55212303316066084705945308837724378055274880241452290879107327486302312160605549087000528464865897991428091595262883990e-3 | Nonzero |
| Observation (-6, -2, 0) L₀; field from B, z component | Ez/E₀ | (0)/(85)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, -2, 0) L₀; total x field component | Ex/E₀ | (-12)/(13)^(3/2) + (9)/(85)^(3/2) | -0.244530921532 | -2.44530921531652005581313261159379038224291085336726093966803700882796889322690651725732485001459073715132305016016498531e-1 | Nonzero |
| Observation (-6, -2, 0) L₀; total y field component | Ey/E₀ | (-8)/(13)^(3/2) + (2)/(85)^(3/2) | -0.168124860421 | -1.68124860420755992081661080283007179710632887829313108462117947138257305791672545465561667236936700436583431842582923367e-1 | Nonzero |
| Observation (-6, -2, 0) L₀; total z field component | Ez/E₀ | (0)/(13)^(3/2) + (0)/(85)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, -2, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.296751310488 | 2.96751310488458728117273737559915904441209792474968301839139013668528735189765252028023303600620446128462285108955801997e-1 | Nonzero |
| Observation (-3, -2, 0) L₀; field from A, x component | Ex/E₀ | (0)/(4)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, -2, 0) L₀; field from A, y component | Ey/E₀ | (-8)/(4)^(3/2) | -1 | -1.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+0 | Nonzero |
| Observation (-3, -2, 0) L₀; field from A, z component | Ez/E₀ | (0)/(4)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, -2, 0) L₀; field from B, x component | Ex/E₀ | (6)/(40)^(3/2) | 0.0237170824513 | 2.37170824512628449899917015832453890028966635449391262014312863959444582897942866600818608128447522139051046311463004136e-2 | Nonzero |
| Observation (-3, -2, 0) L₀; field from B, y component | Ey/E₀ | (2)/(40)^(3/2) | 0.00790569415042 | 7.90569415042094832999723386108179633429888784831304206714376213198148609659809555336062027094825073796836821038210013787e-3 | Nonzero |
| Observation (-3, -2, 0) L₀; field from B, z component | Ez/E₀ | (0)/(40)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, -2, 0) L₀; total x field component | Ex/E₀ | (0)/(4)^(3/2) + (6)/(40)^(3/2) | 0.0237170824513 | 2.37170824512628449899917015832453890028966635449391262014312863959444582897942866600818608128447522139051046311463004136e-2 | Nonzero |
| Observation (-3, -2, 0) L₀; total y field component | Ey/E₀ | (-8)/(4)^(3/2) + (2)/(40)^(3/2) | -0.992094305850 | -9.92094305849579051670002766138918203665701112151686957932856237868018513903401904446639379729051749262031631789617899862e-1 | Nonzero |
| Observation (-3, -2, 0) L₀; total z field component | Ez/E₀ | (0)/(4)^(3/2) + (0)/(40)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, -2, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.992377756552 | 9.92377756551988675890531565867974827601878681394727798188814823457478204270586460522596251017143651606344651914098044795e-1 | Nonzero |
| Observation (0, -2, 0) L₀; field from A, x component | Ex/E₀ | (12)/(13)^(3/2) | 0.256015475181 | 2.56015475180874979393080800057076635236778454947591447056363530619680493369917901434647508782378039124746569137803328311e-1 | Nonzero |
| Observation (0, -2, 0) L₀; field from A, y component | Ey/E₀ | (-8)/(13)^(3/2) | -0.170676983454 | -1.70676983453916652928720533371384423491185636631727631370909020413120328913278600956431672521585359416497712758535552207e-1 | Nonzero |
| Observation (0, -2, 0) L₀; field from A, z component | Ez/E₀ | (0)/(13)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, -2, 0) L₀; field from B, x component | Ex/E₀ | (3)/(13)^(3/2) | 0.0640038687952 | 6.40038687952187448482702000142691588091946137368978617640908826549201233424794753586618771955945097811866422844508320777e-2 | Nonzero |
| Observation (0, -2, 0) L₀; field from B, y component | Ey/E₀ | (2)/(13)^(3/2) | 0.0426692458635 | 4.26692458634791632321801333428461058727964091579319078427272551032800822283196502391079181303963398541244281896338880518e-2 | Nonzero |
| Observation (0, -2, 0) L₀; field from B, z component | Ez/E₀ | (0)/(13)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, -2, 0) L₀; total x field component | Ex/E₀ | (12)/(13)^(3/2) + (3)/(13)^(3/2) | 0.320019343976 | 3.20019343976093724241351000071345794045973068684489308820454413274600616712397376793309385977972548905933211422254160388e-1 | Nonzero |
| Observation (0, -2, 0) L₀; total y field component | Ey/E₀ | (-8)/(13)^(3/2) + (2)/(13)^(3/2) | -0.128007737590 | -1.28007737590437489696540400028538317618389227473795723528181765309840246684958950717323754391189019562373284568901664155e-1 | Nonzero |
| Observation (0, -2, 0) L₀; total z field component | Ez/E₀ | (0)/(13)^(3/2) + (0)/(13)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, -2, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.344671381756 | 3.44671381756466252992215712058678049124469495066442522466941913450320180846466836800037237475254433491796783476748446516e-1 | Nonzero |
| Observation (3, -2, 0) L₀; field from A, x component | Ex/E₀ | (24)/(40)^(3/2) | 0.0948683298051 | 9.48683298050513799599668063329815560115866541797565048057251455837778331591771466403274432513790088556204185245852016545e-2 | Nonzero |
| Observation (3, -2, 0) L₀; field from A, y component | Ey/E₀ | (-8)/(40)^(3/2) | -0.0316227766017 | -3.16227766016837933199889354443271853371955513932521682685750485279259443863923822134424810837930029518734728415284005515e-2 | Nonzero |
| Observation (3, -2, 0) L₀; field from A, z component | Ez/E₀ | (0)/(40)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, -2, 0) L₀; field from B, x component | Ex/E₀ | (0)/(4)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, -2, 0) L₀; field from B, y component | Ey/E₀ | (2)/(4)^(3/2) | 0.25 | 2.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (3, -2, 0) L₀; field from B, z component | Ez/E₀ | (0)/(4)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, -2, 0) L₀; total x field component | Ex/E₀ | (24)/(40)^(3/2) + (0)/(4)^(3/2) | 0.0948683298051 | 9.48683298050513799599668063329815560115866541797565048057251455837778331591771466403274432513790088556204185245852016545e-2 | Nonzero |
| Observation (3, -2, 0) L₀; total y field component | Ey/E₀ | (-8)/(40)^(3/2) + (2)/(4)^(3/2) | 0.218377223398 | 2.18377223398316206680011064555672814662804448606747831731424951472074055613607617786557518916206997048126527158471599449e-1 | Nonzero |
| Observation (3, -2, 0) L₀; total z field component | Ez/E₀ | (0)/(40)^(3/2) + (0)/(4)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, -2, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.238093703611 | 2.38093703610906316087660254589009741560720388852157812615244580307732405414643714547009419275801274685638507722980100215e-1 | Nonzero |
| Observation (6, -2, 0) L₀; field from A, x component | Ex/E₀ | (36)/(85)^(3/2) | 0.0459382145969 | 4.59382145968918952470701555907903880499494784434614123582393189475344161889089988356600951236758616384570564871473191183e-2 | Nonzero |
| Observation (6, -2, 0) L₀; field from A, y component | Ey/E₀ | (-8)/(85)^(3/2) | -0.0102084921326 | -1.02084921326426433882378123535089751222109952096580916351642930994520924864242219634800211385946359196571236638105153596e-2 | Nonzero |
| Observation (6, -2, 0) L₀; field from A, z component | Ez/E₀ | (0)/(85)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, -2, 0) L₀; field from B, x component | Ex/E₀ | (-3)/(13)^(3/2) | -0.0640038687952 | -6.40038687952187448482702000142691588091946137368978617640908826549201233424794753586618771955945097811866422844508320777e-2 | Nonzero |
| Observation (6, -2, 0) L₀; field from B, y component | Ey/E₀ | (2)/(13)^(3/2) | 0.0426692458635 | 4.26692458634791632321801333428461058727964091579319078427272551032800822283196502391079181303963398541244281896338880518e-2 | Nonzero |
| Observation (6, -2, 0) L₀; field from B, z component | Ez/E₀ | (0)/(13)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, -2, 0) L₀; total x field component | Ex/E₀ | (36)/(85)^(3/2) + (-3)/(13)^(3/2) | -0.0180656541983 | -1.80656541983268496012000444234787707592451352934364494058515637073857071535704765230017820719186481427295857973035129594e-2 | Nonzero |
| Observation (6, -2, 0) L₀; total y field component | Ey/E₀ | (-8)/(85)^(3/2) + (2)/(13)^(3/2) | 0.0324607537308 | 3.24607537308365198439423209893371307505854139482738162075629620038279897418954282756278969918017039344673045258233726922e-2 | Nonzero |
| Observation (6, -2, 0) L₀; total z field component | Ez/E₀ | (0)/(85)^(3/2) + (0)/(13)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, -2, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0371492717881 | 3.71492717881190985955296521128705547348317237737931654979594069943509142825373236207893759166118348507347464286517534340e-2 | Nonzero |
| Observation (9, -2, 0) L₀; field from A, x component | Ex/E₀ | (48)/(148)^(3/2) | 0.0266592952387 | 2.66592952387065873878729769694758235007376337244108598382139651416493764440565824973107367185880876410413517935944389937e-2 | Nonzero |
| Observation (9, -2, 0) L₀; field from A, y component | Ey/E₀ | (-8)/(148)^(3/2) | -0.00444321587312 | -4.44321587311776456464549616157930391678960562073514330636899419027489607400943041621845611976468127350689196559907316562e-3 | Nonzero |
| Observation (9, -2, 0) L₀; field from A, z component | Ez/E₀ | (0)/(148)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, -2, 0) L₀; field from B, x component | Ex/E₀ | (-6)/(40)^(3/2) | -0.0237170824513 | -2.37170824512628449899917015832453890028966635449391262014312863959444582897942866600818608128447522139051046311463004136e-2 | Nonzero |
| Observation (9, -2, 0) L₀; field from B, y component | Ey/E₀ | (2)/(40)^(3/2) | 0.00790569415042 | 7.90569415042094832999723386108179633429888784831304206714376213198148609659809555336062027094825073796836821038210013787e-3 | Nonzero |
| Observation (9, -2, 0) L₀; field from B, z component | Ez/E₀ | (0)/(40)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, -2, 0) L₀; total x field component | Ex/E₀ | (48)/(148)^(3/2) + (-6)/(40)^(3/2) | 0.00294221278744 | 2.94221278744374239788127538623043449784097017947173363678267874570491815426229583722887590574333542713624716244813858010e-3 | Nonzero |
| Observation (9, -2, 0) L₀; total y field component | Ey/E₀ | (-8)/(148)^(3/2) + (2)/(40)^(3/2) | 0.00346247827730 | 3.46247827730318376535173769950249241750928222757789876077476794170659002258866513714216415118356946446147624478302697225e-3 | Nonzero |
| Observation (9, -2, 0) L₀; total z field component | Ez/E₀ | (0)/(148)^(3/2) + (0)/(40)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, -2, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.00454371785077 | 4.54371785076867417229676157422758257128194572185607440526498585631204619769476374650369099498322720107194911173700878465e-3 | Nonzero |
| Observation (12, -2, 0) L₀; field from A, x component | Ex/E₀ | (60)/(229)^(3/2) | 0.0173140244661 | 1.73140244660722212702181827760810036556032975921725026398660242859397926471848554823084556027712206607104378042295117944e-2 | Nonzero |
| Observation (12, -2, 0) L₀; field from A, y component | Ey/E₀ | (-8)/(229)^(3/2) | -0.00230853659548 | -2.30853659547629616936242437014413382074710634562300035198213657145863901962464739764112741370282942142805837389726823925e-3 | Nonzero |
| Observation (12, -2, 0) L₀; field from A, z component | Ez/E₀ | (0)/(229)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, -2, 0) L₀; field from B, x component | Ex/E₀ | (-9)/(85)^(3/2) | -0.0114845536492 | -1.14845536492229738117675388976975970124873696108653530895598297368836040472272497089150237809189654096142641217868297796e-2 | Nonzero |
| Observation (12, -2, 0) L₀; field from B, y component | Ey/E₀ | (2)/(85)^(3/2) | 0.00255212303316 | 2.55212303316066084705945308837724378055274880241452290879107327486302312160605549087000528464865897991428091595262883990e-3 | Nonzero |
| Observation (12, -2, 0) L₀; field from B, z component | Ez/E₀ | (0)/(85)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, -2, 0) L₀; total x field component | Ex/E₀ | (60)/(229)^(3/2) + (-9)/(85)^(3/2) | 0.00582947081685 | 5.82947081684924745845064387838340664311592798130714955030619454905618859995760577339343182185225525109617368244268201484e-3 | Nonzero |
| Observation (12, -2, 0) L₀; total y field component | Ey/E₀ | (-8)/(229)^(3/2) + (2)/(85)^(3/2) | 0.000243586437684 | 2.43586437684364677697028718233109959805642456791522556808936703404384101981408093228877870945829558486222542055360600649e-4 | Nonzero |
| Observation (12, -2, 0) L₀; total z field component | Ez/E₀ | (0)/(229)^(3/2) + (0)/(85)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, -2, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.00583455776877 | 5.83455776877055106961227147967249549735094298093157861225727428823108326947495165745862493156121816922037319885990485954e-3 | Nonzero |
| Observation (-6, 0, 0) L₀; field from A, x component | Ex/E₀ | (-12)/(9)^(3/2) | -0.444444444444 | -4.44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444e-1 | Nonzero |
| Observation (-6, 0, 0) L₀; field from A, y component | Ey/E₀ | (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; field from A, z component | Ez/E₀ | (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; field from B, x component | Ex/E₀ | (9)/(81)^(3/2) | 0.0123456790123 | 1.23456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123e-2 | Nonzero |
| Observation (-6, 0, 0) L₀; field from B, y component | Ey/E₀ | (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; field from B, z component | Ez/E₀ | (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; total x field component | Ex/E₀ | (-12)/(9)^(3/2) + (9)/(81)^(3/2) | -0.432098765432 | -4.32098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432e-1 | Nonzero |
| Observation (-6, 0, 0) L₀; total y field component | Ey/E₀ | (0)/(9)^(3/2) + (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; total z field component | Ez/E₀ | (0)/(9)^(3/2) + (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 0, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.432098765432 | 4.32098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432098765432e-1 | Nonzero |
| Observation (0, 0, 0) L₀; field from A, x component | Ex/E₀ | (12)/(9)^(3/2) | 0.444444444444 | 4.44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444e-1 | Nonzero |
| Observation (0, 0, 0) L₀; field from A, y component | Ey/E₀ | (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; field from A, z component | Ez/E₀ | (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; field from B, x component | Ex/E₀ | (3)/(9)^(3/2) | 0.111111111111 | 1.11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111e-1 | Nonzero |
| Observation (0, 0, 0) L₀; field from B, y component | Ey/E₀ | (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; field from B, z component | Ez/E₀ | (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; total x field component | Ex/E₀ | (12)/(9)^(3/2) + (3)/(9)^(3/2) | 0.555555555556 | 5.55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555556e-1 | Nonzero |
| Observation (0, 0, 0) L₀; total y field component | Ey/E₀ | (0)/(9)^(3/2) + (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; total z field component | Ez/E₀ | (0)/(9)^(3/2) + (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 0, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.555555555556 | 5.55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555556e-1 | Nonzero |
| Observation (6, 0, 0) L₀; field from A, x component | Ex/E₀ | (36)/(81)^(3/2) | 0.0493827160494 | 4.93827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160493827160494e-2 | Nonzero |
| Observation (6, 0, 0) L₀; field from A, y component | Ey/E₀ | (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; field from A, z component | Ez/E₀ | (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; field from B, x component | Ex/E₀ | (-3)/(9)^(3/2) | -0.111111111111 | -1.11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111e-1 | Nonzero |
| Observation (6, 0, 0) L₀; field from B, y component | Ey/E₀ | (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; field from B, z component | Ez/E₀ | (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; total x field component | Ex/E₀ | (36)/(81)^(3/2) + (-3)/(9)^(3/2) | -0.0617283950617 | -6.17283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617e-2 | Nonzero |
| Observation (6, 0, 0) L₀; total y field component | Ey/E₀ | (0)/(81)^(3/2) + (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; total z field component | Ez/E₀ | (0)/(81)^(3/2) + (0)/(9)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 0, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0617283950617 | 6.17283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617283950617e-2 | Nonzero |
| Observation (9, 0, 0) L₀; field from A, x component | Ex/E₀ | (48)/(144)^(3/2) | 0.0277777777778 | 2.77777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778e-2 | Nonzero |
| Observation (9, 0, 0) L₀; field from A, y component | Ey/E₀ | (0)/(144)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; field from A, z component | Ez/E₀ | (0)/(144)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; field from B, x component | Ex/E₀ | (-6)/(36)^(3/2) | -0.0277777777778 | -2.77777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778e-2 | Nonzero |
| Observation (9, 0, 0) L₀; field from B, y component | Ey/E₀ | (0)/(36)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; field from B, z component | Ez/E₀ | (0)/(36)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; total x field component | Ex/E₀ | (48)/(144)^(3/2) + (-6)/(36)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; total y field component | Ey/E₀ | (0)/(144)^(3/2) + (0)/(36)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; total z field component | Ez/E₀ | (0)/(144)^(3/2) + (0)/(36)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 0, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; field from A, x component | Ex/E₀ | (60)/(225)^(3/2) | 0.0177777777778 | 1.77777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778e-2 | Nonzero |
| Observation (12, 0, 0) L₀; field from A, y component | Ey/E₀ | (0)/(225)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; field from A, z component | Ez/E₀ | (0)/(225)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; field from B, x component | Ex/E₀ | (-9)/(81)^(3/2) | -0.0123456790123 | -1.23456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123456790123e-2 | Nonzero |
| Observation (12, 0, 0) L₀; field from B, y component | Ey/E₀ | (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; field from B, z component | Ez/E₀ | (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; total x field component | Ex/E₀ | (60)/(225)^(3/2) + (-9)/(81)^(3/2) | 0.00543209876543 | 5.43209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543e-3 | Nonzero |
| Observation (12, 0, 0) L₀; total y field component | Ey/E₀ | (0)/(225)^(3/2) + (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; total z field component | Ez/E₀ | (0)/(225)^(3/2) + (0)/(81)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 0, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.00543209876543 | 5.43209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543209876543e-3 | Nonzero |
| Observation (-6, 2, 0) L₀; field from A, x component | Ex/E₀ | (-12)/(13)^(3/2) | -0.256015475181 | -2.56015475180874979393080800057076635236778454947591447056363530619680493369917901434647508782378039124746569137803328311e-1 | Nonzero |
| Observation (-6, 2, 0) L₀; field from A, y component | Ey/E₀ | (8)/(13)^(3/2) | 0.170676983454 | 1.70676983453916652928720533371384423491185636631727631370909020413120328913278600956431672521585359416497712758535552207e-1 | Nonzero |
| Observation (-6, 2, 0) L₀; field from A, z component | Ez/E₀ | (0)/(13)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 2, 0) L₀; field from B, x component | Ex/E₀ | (9)/(85)^(3/2) | 0.0114845536492 | 1.14845536492229738117675388976975970124873696108653530895598297368836040472272497089150237809189654096142641217868297796e-2 | Nonzero |
| Observation (-6, 2, 0) L₀; field from B, y component | Ey/E₀ | (-2)/(85)^(3/2) | -0.00255212303316 | -2.55212303316066084705945308837724378055274880241452290879107327486302312160605549087000528464865897991428091595262883990e-3 | Nonzero |
| Observation (-6, 2, 0) L₀; field from B, z component | Ez/E₀ | (0)/(85)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 2, 0) L₀; total x field component | Ex/E₀ | (-12)/(13)^(3/2) + (9)/(85)^(3/2) | -0.244530921532 | -2.44530921531652005581313261159379038224291085336726093966803700882796889322690651725732485001459073715132305016016498531e-1 | Nonzero |
| Observation (-6, 2, 0) L₀; total y field component | Ey/E₀ | (8)/(13)^(3/2) + (-2)/(85)^(3/2) | 0.168124860421 | 1.68124860420755992081661080283007179710632887829313108462117947138257305791672545465561667236936700436583431842582923367e-1 | Nonzero |
| Observation (-6, 2, 0) L₀; total z field component | Ez/E₀ | (0)/(13)^(3/2) + (0)/(85)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 2, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.296751310488 | 2.96751310488458728117273737559915904441209792474968301839139013668528735189765252028023303600620446128462285108955801997e-1 | Nonzero |
| Observation (-3, 2, 0) L₀; field from A, x component | Ex/E₀ | (0)/(4)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, 2, 0) L₀; field from A, y component | Ey/E₀ | (8)/(4)^(3/2) | 1 | 1.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+0 | Nonzero |
| Observation (-3, 2, 0) L₀; field from A, z component | Ez/E₀ | (0)/(4)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, 2, 0) L₀; field from B, x component | Ex/E₀ | (6)/(40)^(3/2) | 0.0237170824513 | 2.37170824512628449899917015832453890028966635449391262014312863959444582897942866600818608128447522139051046311463004136e-2 | Nonzero |
| Observation (-3, 2, 0) L₀; field from B, y component | Ey/E₀ | (-2)/(40)^(3/2) | -0.00790569415042 | -7.90569415042094832999723386108179633429888784831304206714376213198148609659809555336062027094825073796836821038210013787e-3 | Nonzero |
| Observation (-3, 2, 0) L₀; field from B, z component | Ez/E₀ | (0)/(40)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, 2, 0) L₀; total x field component | Ex/E₀ | (0)/(4)^(3/2) + (6)/(40)^(3/2) | 0.0237170824513 | 2.37170824512628449899917015832453890028966635449391262014312863959444582897942866600818608128447522139051046311463004136e-2 | Nonzero |
| Observation (-3, 2, 0) L₀; total y field component | Ey/E₀ | (8)/(4)^(3/2) + (-2)/(40)^(3/2) | 0.992094305850 | 9.92094305849579051670002766138918203665701112151686957932856237868018513903401904446639379729051749262031631789617899862e-1 | Nonzero |
| Observation (-3, 2, 0) L₀; total z field component | Ez/E₀ | (0)/(4)^(3/2) + (0)/(40)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, 2, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.992377756552 | 9.92377756551988675890531565867974827601878681394727798188814823457478204270586460522596251017143651606344651914098044795e-1 | Nonzero |
| Observation (0, 2, 0) L₀; field from A, x component | Ex/E₀ | (12)/(13)^(3/2) | 0.256015475181 | 2.56015475180874979393080800057076635236778454947591447056363530619680493369917901434647508782378039124746569137803328311e-1 | Nonzero |
| Observation (0, 2, 0) L₀; field from A, y component | Ey/E₀ | (8)/(13)^(3/2) | 0.170676983454 | 1.70676983453916652928720533371384423491185636631727631370909020413120328913278600956431672521585359416497712758535552207e-1 | Nonzero |
| Observation (0, 2, 0) L₀; field from A, z component | Ez/E₀ | (0)/(13)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 2, 0) L₀; field from B, x component | Ex/E₀ | (3)/(13)^(3/2) | 0.0640038687952 | 6.40038687952187448482702000142691588091946137368978617640908826549201233424794753586618771955945097811866422844508320777e-2 | Nonzero |
| Observation (0, 2, 0) L₀; field from B, y component | Ey/E₀ | (-2)/(13)^(3/2) | -0.0426692458635 | -4.26692458634791632321801333428461058727964091579319078427272551032800822283196502391079181303963398541244281896338880518e-2 | Nonzero |
| Observation (0, 2, 0) L₀; field from B, z component | Ez/E₀ | (0)/(13)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 2, 0) L₀; total x field component | Ex/E₀ | (12)/(13)^(3/2) + (3)/(13)^(3/2) | 0.320019343976 | 3.20019343976093724241351000071345794045973068684489308820454413274600616712397376793309385977972548905933211422254160388e-1 | Nonzero |
| Observation (0, 2, 0) L₀; total y field component | Ey/E₀ | (8)/(13)^(3/2) + (-2)/(13)^(3/2) | 0.128007737590 | 1.28007737590437489696540400028538317618389227473795723528181765309840246684958950717323754391189019562373284568901664155e-1 | Nonzero |
| Observation (0, 2, 0) L₀; total z field component | Ez/E₀ | (0)/(13)^(3/2) + (0)/(13)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 2, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.344671381756 | 3.44671381756466252992215712058678049124469495066442522466941913450320180846466836800037237475254433491796783476748446516e-1 | Nonzero |
| Observation (3, 2, 0) L₀; field from A, x component | Ex/E₀ | (24)/(40)^(3/2) | 0.0948683298051 | 9.48683298050513799599668063329815560115866541797565048057251455837778331591771466403274432513790088556204185245852016545e-2 | Nonzero |
| Observation (3, 2, 0) L₀; field from A, y component | Ey/E₀ | (8)/(40)^(3/2) | 0.0316227766017 | 3.16227766016837933199889354443271853371955513932521682685750485279259443863923822134424810837930029518734728415284005515e-2 | Nonzero |
| Observation (3, 2, 0) L₀; field from A, z component | Ez/E₀ | (0)/(40)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, 2, 0) L₀; field from B, x component | Ex/E₀ | (0)/(4)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, 2, 0) L₀; field from B, y component | Ey/E₀ | (-2)/(4)^(3/2) | -0.25 | -2.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (3, 2, 0) L₀; field from B, z component | Ez/E₀ | (0)/(4)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, 2, 0) L₀; total x field component | Ex/E₀ | (24)/(40)^(3/2) + (0)/(4)^(3/2) | 0.0948683298051 | 9.48683298050513799599668063329815560115866541797565048057251455837778331591771466403274432513790088556204185245852016545e-2 | Nonzero |
| Observation (3, 2, 0) L₀; total y field component | Ey/E₀ | (8)/(40)^(3/2) + (-2)/(4)^(3/2) | -0.218377223398 | -2.18377223398316206680011064555672814662804448606747831731424951472074055613607617786557518916206997048126527158471599449e-1 | Nonzero |
| Observation (3, 2, 0) L₀; total z field component | Ez/E₀ | (0)/(40)^(3/2) + (0)/(4)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, 2, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.238093703611 | 2.38093703610906316087660254589009741560720388852157812615244580307732405414643714547009419275801274685638507722980100215e-1 | Nonzero |
| Observation (6, 2, 0) L₀; field from A, x component | Ex/E₀ | (36)/(85)^(3/2) | 0.0459382145969 | 4.59382145968918952470701555907903880499494784434614123582393189475344161889089988356600951236758616384570564871473191183e-2 | Nonzero |
| Observation (6, 2, 0) L₀; field from A, y component | Ey/E₀ | (8)/(85)^(3/2) | 0.0102084921326 | 1.02084921326426433882378123535089751222109952096580916351642930994520924864242219634800211385946359196571236638105153596e-2 | Nonzero |
| Observation (6, 2, 0) L₀; field from A, z component | Ez/E₀ | (0)/(85)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 2, 0) L₀; field from B, x component | Ex/E₀ | (-3)/(13)^(3/2) | -0.0640038687952 | -6.40038687952187448482702000142691588091946137368978617640908826549201233424794753586618771955945097811866422844508320777e-2 | Nonzero |
| Observation (6, 2, 0) L₀; field from B, y component | Ey/E₀ | (-2)/(13)^(3/2) | -0.0426692458635 | -4.26692458634791632321801333428461058727964091579319078427272551032800822283196502391079181303963398541244281896338880518e-2 | Nonzero |
| Observation (6, 2, 0) L₀; field from B, z component | Ez/E₀ | (0)/(13)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 2, 0) L₀; total x field component | Ex/E₀ | (36)/(85)^(3/2) + (-3)/(13)^(3/2) | -0.0180656541983 | -1.80656541983268496012000444234787707592451352934364494058515637073857071535704765230017820719186481427295857973035129594e-2 | Nonzero |
| Observation (6, 2, 0) L₀; total y field component | Ey/E₀ | (8)/(85)^(3/2) + (-2)/(13)^(3/2) | -0.0324607537308 | -3.24607537308365198439423209893371307505854139482738162075629620038279897418954282756278969918017039344673045258233726922e-2 | Nonzero |
| Observation (6, 2, 0) L₀; total z field component | Ez/E₀ | (0)/(85)^(3/2) + (0)/(13)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 2, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0371492717881 | 3.71492717881190985955296521128705547348317237737931654979594069943509142825373236207893759166118348507347464286517534340e-2 | Nonzero |
| Observation (9, 2, 0) L₀; field from A, x component | Ex/E₀ | (48)/(148)^(3/2) | 0.0266592952387 | 2.66592952387065873878729769694758235007376337244108598382139651416493764440565824973107367185880876410413517935944389937e-2 | Nonzero |
| Observation (9, 2, 0) L₀; field from A, y component | Ey/E₀ | (8)/(148)^(3/2) | 0.00444321587312 | 4.44321587311776456464549616157930391678960562073514330636899419027489607400943041621845611976468127350689196559907316562e-3 | Nonzero |
| Observation (9, 2, 0) L₀; field from A, z component | Ez/E₀ | (0)/(148)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 2, 0) L₀; field from B, x component | Ex/E₀ | (-6)/(40)^(3/2) | -0.0237170824513 | -2.37170824512628449899917015832453890028966635449391262014312863959444582897942866600818608128447522139051046311463004136e-2 | Nonzero |
| Observation (9, 2, 0) L₀; field from B, y component | Ey/E₀ | (-2)/(40)^(3/2) | -0.00790569415042 | -7.90569415042094832999723386108179633429888784831304206714376213198148609659809555336062027094825073796836821038210013787e-3 | Nonzero |
| Observation (9, 2, 0) L₀; field from B, z component | Ez/E₀ | (0)/(40)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 2, 0) L₀; total x field component | Ex/E₀ | (48)/(148)^(3/2) + (-6)/(40)^(3/2) | 0.00294221278744 | 2.94221278744374239788127538623043449784097017947173363678267874570491815426229583722887590574333542713624716244813858010e-3 | Nonzero |
| Observation (9, 2, 0) L₀; total y field component | Ey/E₀ | (8)/(148)^(3/2) + (-2)/(40)^(3/2) | -0.00346247827730 | -3.46247827730318376535173769950249241750928222757789876077476794170659002258866513714216415118356946446147624478302697225e-3 | Nonzero |
| Observation (9, 2, 0) L₀; total z field component | Ez/E₀ | (0)/(148)^(3/2) + (0)/(40)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 2, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.00454371785077 | 4.54371785076867417229676157422758257128194572185607440526498585631204619769476374650369099498322720107194911173700878465e-3 | Nonzero |
| Observation (12, 2, 0) L₀; field from A, x component | Ex/E₀ | (60)/(229)^(3/2) | 0.0173140244661 | 1.73140244660722212702181827760810036556032975921725026398660242859397926471848554823084556027712206607104378042295117944e-2 | Nonzero |
| Observation (12, 2, 0) L₀; field from A, y component | Ey/E₀ | (8)/(229)^(3/2) | 0.00230853659548 | 2.30853659547629616936242437014413382074710634562300035198213657145863901962464739764112741370282942142805837389726823925e-3 | Nonzero |
| Observation (12, 2, 0) L₀; field from A, z component | Ez/E₀ | (0)/(229)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 2, 0) L₀; field from B, x component | Ex/E₀ | (-9)/(85)^(3/2) | -0.0114845536492 | -1.14845536492229738117675388976975970124873696108653530895598297368836040472272497089150237809189654096142641217868297796e-2 | Nonzero |
| Observation (12, 2, 0) L₀; field from B, y component | Ey/E₀ | (-2)/(85)^(3/2) | -0.00255212303316 | -2.55212303316066084705945308837724378055274880241452290879107327486302312160605549087000528464865897991428091595262883990e-3 | Nonzero |
| Observation (12, 2, 0) L₀; field from B, z component | Ez/E₀ | (0)/(85)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 2, 0) L₀; total x field component | Ex/E₀ | (60)/(229)^(3/2) + (-9)/(85)^(3/2) | 0.00582947081685 | 5.82947081684924745845064387838340664311592798130714955030619454905618859995760577339343182185225525109617368244268201484e-3 | Nonzero |
| Observation (12, 2, 0) L₀; total y field component | Ey/E₀ | (8)/(229)^(3/2) + (-2)/(85)^(3/2) | -0.000243586437684 | -2.43586437684364677697028718233109959805642456791522556808936703404384101981408093228877870945829558486222542055360600649e-4 | Nonzero |
| Observation (12, 2, 0) L₀; total z field component | Ez/E₀ | (0)/(229)^(3/2) + (0)/(85)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 2, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.00583455776877 | 5.83455776877055106961227147967249549735094298093157861225727428823108326947495165745862493156121816922037319885990485954e-3 | Nonzero |
| Observation (-6, 4, 0) L₀; field from A, x component | Ex/E₀ | (-12)/(25)^(3/2) | -0.096 | -9.60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (-6, 4, 0) L₀; field from A, y component | Ey/E₀ | (16)/(25)^(3/2) | 0.128 | 1.28000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (-6, 4, 0) L₀; field from A, z component | Ez/E₀ | (0)/(25)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 4, 0) L₀; field from B, x component | Ex/E₀ | (9)/(97)^(3/2) | 0.00942073761464 | 9.42073761464182617660919361613971945321131114751672627755429809422127380735137715706651153757453840598819330320392632559e-3 | Nonzero |
| Observation (-6, 4, 0) L₀; field from B, y component | Ey/E₀ | (-4)/(97)^(3/2) | -0.00418699449540 | -4.18699449539636718960408605161765309031613828778521167891302137520945502548950095869622735003312818043919702364618947804e-3 | Nonzero |
| Observation (-6, 4, 0) L₀; field from B, z component | Ez/E₀ | (0)/(97)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 4, 0) L₀; total x field component | Ex/E₀ | (-12)/(25)^(3/2) + (9)/(97)^(3/2) | -0.0865792623854 | -8.65792623853581738233908063838602805467886888524832737224457019057787261926486228429334884624254615940118066967960736744e-2 | Nonzero |
| Observation (-6, 4, 0) L₀; total y field component | Ey/E₀ | (16)/(25)^(3/2) + (-4)/(97)^(3/2) | 0.123813005505 | 1.23813005504603632810395913948382346909683861712214788321086978624790544974510499041303772649966871819560802976353810522e-1 | Nonzero |
| Observation (-6, 4, 0) L₀; total z field component | Ez/E₀ | (0)/(25)^(3/2) + (0)/(97)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 4, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.151081530993 | 1.51081530993287548886494626460783752667195495818497758382129206624336257848408582059897086671392966876808973999404323398e-1 | Nonzero |
| Observation (-3, 4, 0) L₀; field from A, x component | Ex/E₀ | (0)/(16)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, 4, 0) L₀; field from A, y component | Ey/E₀ | (16)/(16)^(3/2) | 0.25 | 2.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (-3, 4, 0) L₀; field from A, z component | Ez/E₀ | (0)/(16)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, 4, 0) L₀; field from B, x component | Ex/E₀ | (6)/(52)^(3/2) | 0.0160009671988 | 1.60009671988046862120675500035672897022986534342244654410227206637300308356198688396654692988986274452966605711127080194e-2 | Nonzero |
| Observation (-3, 4, 0) L₀; field from B, y component | Ey/E₀ | (-4)/(52)^(3/2) | -0.0106673114659 | -1.06673114658697908080450333357115264681991022894829769606818137758200205570799125597769795325990849635311070474084720129e-2 | Nonzero |
| Observation (-3, 4, 0) L₀; field from B, z component | Ez/E₀ | (0)/(52)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, 4, 0) L₀; total x field component | Ex/E₀ | (0)/(16)^(3/2) + (6)/(52)^(3/2) | 0.0160009671988 | 1.60009671988046862120675500035672897022986534342244654410227206637300308356198688396654692988986274452966605711127080194e-2 | Nonzero |
| Observation (-3, 4, 0) L₀; total y field component | Ey/E₀ | (16)/(16)^(3/2) + (-4)/(52)^(3/2) | 0.239332688534 | 2.39332688534130209191954966664288473531800897710517023039318186224179979442920087440223020467400915036468892952591527987e-1 | Nonzero |
| Observation (-3, 4, 0) L₀; total z field component | Ez/E₀ | (0)/(16)^(3/2) + (0)/(52)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, 4, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.239866977203 | 2.39866977202515738851957172872427261148843305217126523600159366747122705017148425311397264223904070135312305658784328593e-1 | Nonzero |
| Observation (0, 4, 0) L₀; field from A, x component | Ex/E₀ | (12)/(25)^(3/2) | 0.096 | 9.60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, 4, 0) L₀; field from A, y component | Ey/E₀ | (16)/(25)^(3/2) | 0.128 | 1.28000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, 4, 0) L₀; field from A, z component | Ez/E₀ | (0)/(25)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 4, 0) L₀; field from B, x component | Ex/E₀ | (3)/(25)^(3/2) | 0.024 | 2.40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, 4, 0) L₀; field from B, y component | Ey/E₀ | (-4)/(25)^(3/2) | -0.032 | -3.20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, 4, 0) L₀; field from B, z component | Ez/E₀ | (0)/(25)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 4, 0) L₀; total x field component | Ex/E₀ | (12)/(25)^(3/2) + (3)/(25)^(3/2) | 0.120 | 1.20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Observation (0, 4, 0) L₀; total y field component | Ey/E₀ | (16)/(25)^(3/2) + (-4)/(25)^(3/2) | 0.096 | 9.60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (0, 4, 0) L₀; total z field component | Ez/E₀ | (0)/(25)^(3/2) + (0)/(25)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 4, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.153674981698 | 1.53674981698388368475717224190923518348490083182904453252702543040036386196725025782944503253996879116099483980091132398e-1 | Nonzero |
| Observation (3, 4, 0) L₀; field from A, x component | Ex/E₀ | (24)/(52)^(3/2) | 0.0640038687952 | 6.40038687952187448482702000142691588091946137368978617640908826549201233424794753586618771955945097811866422844508320777e-2 | Nonzero |
| Observation (3, 4, 0) L₀; field from A, y component | Ey/E₀ | (16)/(52)^(3/2) | 0.0426692458635 | 4.26692458634791632321801333428461058727964091579319078427272551032800822283196502391079181303963398541244281896338880518e-2 | Nonzero |
| Observation (3, 4, 0) L₀; field from A, z component | Ez/E₀ | (0)/(52)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, 4, 0) L₀; field from B, x component | Ex/E₀ | (0)/(16)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, 4, 0) L₀; field from B, y component | Ey/E₀ | (-4)/(16)^(3/2) | -0.0625 | -6.25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (3, 4, 0) L₀; field from B, z component | Ez/E₀ | (0)/(16)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, 4, 0) L₀; total x field component | Ex/E₀ | (24)/(52)^(3/2) + (0)/(16)^(3/2) | 0.0640038687952 | 6.40038687952187448482702000142691588091946137368978617640908826549201233424794753586618771955945097811866422844508320777e-2 | Nonzero |
| Observation (3, 4, 0) L₀; total y field component | Ey/E₀ | (16)/(52)^(3/2) + (-4)/(16)^(3/2) | -0.0198307541365 | -1.98307541365208367678198666571538941272035908420680921572727448967199177716803497608920818696036601458755718103661119482e-2 | Nonzero |
| Observation (3, 4, 0) L₀; total z field component | Ez/E₀ | (0)/(52)^(3/2) + (0)/(16)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, 4, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0670056268561 | 6.70056268560985411174905860175357897514136637557512038214894843404682652648750580204337263536568875696446270491928368594e-2 | Nonzero |
| Observation (6, 4, 0) L₀; field from A, x component | Ex/E₀ | (36)/(97)^(3/2) | 0.0376829504586 | 3.76829504585673047064367744645588778128452445900669051102171923768850952294055086282660461502981536239527732128157053024e-2 | Nonzero |
| Observation (6, 4, 0) L₀; field from A, y component | Ey/E₀ | (16)/(97)^(3/2) | 0.0167479779816 | 1.67479779815854687584163442064706123612645531511408467156520855008378201019580038347849094001325127217567880945847579122e-2 | Nonzero |
| Observation (6, 4, 0) L₀; field from A, z component | Ez/E₀ | (0)/(97)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 4, 0) L₀; field from B, x component | Ex/E₀ | (-3)/(25)^(3/2) | -0.024 | -2.40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (6, 4, 0) L₀; field from B, y component | Ey/E₀ | (-4)/(25)^(3/2) | -0.032 | -3.20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (6, 4, 0) L₀; field from B, z component | Ez/E₀ | (0)/(25)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 4, 0) L₀; total x field component | Ex/E₀ | (36)/(97)^(3/2) + (-3)/(25)^(3/2) | 0.0136829504586 | 1.36829504585673047064367744645588778128452445900669051102171923768850952294055086282660461502981536239527732128157053024e-2 | Nonzero |
| Observation (6, 4, 0) L₀; total y field component | Ey/E₀ | (16)/(97)^(3/2) + (-4)/(25)^(3/2) | -0.0152520220184 | -1.52520220184145312415836557935293876387354468488591532843479144991621798980419961652150905998674872782432119054152420878e-2 | Nonzero |
| Observation (6, 4, 0) L₀; total z field component | Ez/E₀ | (0)/(97)^(3/2) + (0)/(25)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 4, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0204901759119 | 2.04901759119293284246349398649338884931279669004185613095248721403511312824776214767360973466622167252188290317123798133e-2 | Nonzero |
| Observation (9, 4, 0) L₀; field from A, x component | Ex/E₀ | (48)/(160)^(3/2) | 0.0237170824513 | 2.37170824512628449899917015832453890028966635449391262014312863959444582897942866600818608128447522139051046311463004136e-2 | Nonzero |
| Observation (9, 4, 0) L₀; field from A, y component | Ey/E₀ | (16)/(160)^(3/2) | 0.00790569415042 | 7.90569415042094832999723386108179633429888784831304206714376213198148609659809555336062027094825073796836821038210013787e-3 | Nonzero |
| Observation (9, 4, 0) L₀; field from A, z component | Ez/E₀ | (0)/(160)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 4, 0) L₀; field from B, x component | Ex/E₀ | (-6)/(52)^(3/2) | -0.0160009671988 | -1.60009671988046862120675500035672897022986534342244654410227206637300308356198688396654692988986274452966605711127080194e-2 | Nonzero |
| Observation (9, 4, 0) L₀; field from B, y component | Ey/E₀ | (-4)/(52)^(3/2) | -0.0106673114659 | -1.06673114658697908080450333357115264681991022894829769606818137758200205570799125597769795325990849635311070474084720129e-2 | Nonzero |
| Observation (9, 4, 0) L₀; field from B, z component | Ez/E₀ | (0)/(52)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 4, 0) L₀; total x field component | Ex/E₀ | (48)/(160)^(3/2) + (-6)/(52)^(3/2) | 0.00771611525246 | 7.71611525245815877792415157967809930059801011071466076040856573221442745417441782041639151394612476860844406003359239419e-3 | Nonzero |
| Observation (9, 4, 0) L₀; total y field component | Ey/E₀ | (16)/(160)^(3/2) + (-4)/(52)^(3/2) | -0.00276161731545 | -2.76161731544884247804779947462973013390021444116993489353805164383853446048181700641635926165083422556273883702637187508e-3 | Nonzero |
| Observation (9, 4, 0) L₀; total z field component | Ez/E₀ | (0)/(160)^(3/2) + (0)/(52)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 4, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.00819542340494 | 8.19542340493792345686211621658612611256871992229489484400535421821465727206368176715042625194445323154908091816843864960e-3 | Nonzero |
| Observation (12, 4, 0) L₀; field from A, x component | Ex/E₀ | (60)/(241)^(3/2) | 0.0160370944332 | 1.60370944332157060610483239963220130882241243023749707398496691597554140785749555572947185786997069645151481450049773084e-2 | Nonzero |
| Observation (12, 4, 0) L₀; field from A, y component | Ey/E₀ | (16)/(241)^(3/2) | 0.00427655851552 | 4.27655851552418828294621973235253682352643314729999219729324510926811042095332148194525828765325519053737283866799394891e-3 | Nonzero |
| Observation (12, 4, 0) L₀; field from A, z component | Ez/E₀ | (0)/(241)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 4, 0) L₀; field from B, x component | Ex/E₀ | (-9)/(97)^(3/2) | -0.00942073761464 | -9.42073761464182617660919361613971945321131114751672627755429809422127380735137715706651153757453840598819330320392632559e-3 | Nonzero |
| Observation (12, 4, 0) L₀; field from B, y component | Ey/E₀ | (-4)/(97)^(3/2) | -0.00418699449540 | -4.18699449539636718960408605161765309031613828778521167891302137520945502548950095869622735003312818043919702364618947804e-3 | Nonzero |
| Observation (12, 4, 0) L₀; field from B, z component | Ez/E₀ | (0)/(97)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 4, 0) L₀; total x field component | Ex/E₀ | (60)/(241)^(3/2) + (-9)/(97)^(3/2) | 0.00661635681857 | 6.61635681857387988443913038018229363501281315485824446229537106553414027122357840022820704112516855852695484180105098282e-3 | Nonzero |
| Observation (12, 4, 0) L₀; total y field component | Ey/E₀ | (16)/(241)^(3/2) + (-4)/(97)^(3/2) | 0.0000895640201278 | 8.95640201278210933421336807348837332102948595147805183802237340586553954638205232490309376201270100981758150218044708701e-5 | Nonzero |
| Observation (12, 4, 0) L₀; total z field component | Ez/E₀ | (0)/(241)^(3/2) + (0)/(97)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 4, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.00661696299403 | 6.61696299403212092941239916272598534601715741684182441970673913374672352813307235790252487713016254826070656382628499210e-3 | Nonzero |
| Observation (-6, 6, 0) L₀; field from A, x component | Ex/E₀ | (-12)/(45)^(3/2) | -0.0397523196000 | -3.97523195999962612694964207774449108522776597264271239870381732517425942335609759895895894822894626661245897982359783734e-2 | Nonzero |
| Observation (-6, 6, 0) L₀; field from A, y component | Ey/E₀ | (24)/(45)^(3/2) | 0.0795046392000 | 7.95046391999925225389928415548898217045553194528542479740763465034851884671219519791791789645789253322491795964719567468e-2 | Nonzero |
| Observation (-6, 6, 0) L₀; field from A, z component | Ez/E₀ | (0)/(45)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 6, 0) L₀; field from B, x component | Ex/E₀ | (9)/(117)^(3/2) | 0.00711154097725 | 7.11154097724652720536335555714101764546606819298865130712120918388001370471994170651798635506605664235407136493898134196e-3 | Nonzero |
| Observation (-6, 6, 0) L₀; field from B, y component | Ey/E₀ | (-6)/(117)^(3/2) | -0.00474102731816 | -4.74102731816435147024223703809401176364404546199243420474747278925334246981329447101199090337737109490271424329265422798e-3 | Nonzero |
| Observation (-6, 6, 0) L₀; field from B, z component | Ez/E₀ | (0)/(117)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 6, 0) L₀; total x field component | Ex/E₀ | (-12)/(45)^(3/2) + (9)/(117)^(3/2) | -0.0326407786227 | -3.26407786227497340641330652203038932068115915334384726799169640678625805288410342830716031272234060237705184332969970314e-2 | Nonzero |
| Observation (-6, 6, 0) L₀; total y field component | Ey/E₀ | (24)/(45)^(3/2) + (-6)/(117)^(3/2) | 0.0747636118818 | 7.47636118818281710687506045167958099409112739908618137693288737142318459973086575081671880612015542373464653531793025188e-2 | Nonzero |
| Observation (-6, 6, 0) L₀; total z field component | Ez/E₀ | (0)/(45)^(3/2) + (0)/(117)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 6, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0815782942376 | 8.15782942375972611570521151798158478945043142019491396587727086888367460004700286390665980285192351169076765536565401644e-2 | Nonzero |
| Observation (-3, 6, 0) L₀; field from A, x component | Ex/E₀ | (0)/(36)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, 6, 0) L₀; field from A, y component | Ey/E₀ | (24)/(36)^(3/2) | 0.111111111111 | 1.11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111e-1 | Nonzero |
| Observation (-3, 6, 0) L₀; field from A, z component | Ez/E₀ | (0)/(36)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, 6, 0) L₀; field from B, x component | Ex/E₀ | (6)/(72)^(3/2) | 0.00982092751648 | 9.82092751647982672778950502923401443451161024567325050817138706938008665598685443646102454394195536621537393215911317378e-3 | Nonzero |
| Observation (-3, 6, 0) L₀; field from B, y component | Ey/E₀ | (-6)/(72)^(3/2) | -0.00982092751648 | -9.82092751647982672778950502923401443451161024567325050817138706938008665598685443646102454394195536621537393215911317378e-3 | Nonzero |
| Observation (-3, 6, 0) L₀; field from B, z component | Ez/E₀ | (0)/(72)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, 6, 0) L₀; total x field component | Ex/E₀ | (0)/(36)^(3/2) + (6)/(72)^(3/2) | 0.00982092751648 | 9.82092751647982672778950502923401443451161024567325050817138706938008665598685443646102454394195536621537393215911317378e-3 | Nonzero |
| Observation (-3, 6, 0) L₀; total y field component | Ey/E₀ | (24)/(36)^(3/2) + (-6)/(72)^(3/2) | 0.101290183595 | 1.01290183594631284383321606081877096676599500865437860602939724041731024455124256674650086567169155744895737178951997937e-1 | Nonzero |
| Observation (-3, 6, 0) L₀; total z field component | Ez/E₀ | (0)/(36)^(3/2) + (0)/(72)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, 6, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.101765180243 | 1.01765180243136518488830480217043426107854400368943023421924125442421615183344462433402244172891193529307650993606313600e-1 | Nonzero |
| Observation (0, 6, 0) L₀; field from A, x component | Ex/E₀ | (12)/(45)^(3/2) | 0.0397523196000 | 3.97523195999962612694964207774449108522776597264271239870381732517425942335609759895895894822894626661245897982359783734e-2 | Nonzero |
| Observation (0, 6, 0) L₀; field from A, y component | Ey/E₀ | (24)/(45)^(3/2) | 0.0795046392000 | 7.95046391999925225389928415548898217045553194528542479740763465034851884671219519791791789645789253322491795964719567468e-2 | Nonzero |
| Observation (0, 6, 0) L₀; field from A, z component | Ez/E₀ | (0)/(45)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 6, 0) L₀; field from B, x component | Ex/E₀ | (3)/(45)^(3/2) | 0.00993807990000 | 9.93807989999906531737410519436122771306941493160678099675954331293564855839024399739739737057236566653114744955899459335e-3 | Nonzero |
| Observation (0, 6, 0) L₀; field from B, y component | Ey/E₀ | (-6)/(45)^(3/2) | -0.0198761598000 | -1.98761597999981306347482103887224554261388298632135619935190866258712971167804879947947947411447313330622948991179891867e-2 | Nonzero |
| Observation (0, 6, 0) L₀; field from B, z component | Ez/E₀ | (0)/(45)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 6, 0) L₀; total x field component | Ex/E₀ | (12)/(45)^(3/2) + (3)/(45)^(3/2) | 0.0496903995000 | 4.96903994999953265868705259718061385653470746580339049837977165646782427919512199869869868528618283326557372477949729668e-2 | Nonzero |
| Observation (0, 6, 0) L₀; total y field component | Ey/E₀ | (24)/(45)^(3/2) + (-6)/(45)^(3/2) | 0.0596284794000 | 5.96284793999943919042446311661673662784164895896406859805572598776138913503414639843843842234341939991868846973539675601e-2 | Nonzero |
| Observation (0, 6, 0) L₀; total z field component | Ez/E₀ | (0)/(45)^(3/2) + (0)/(45)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 6, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0776188853181 | 7.76188853181021362058713050263862433455446853319924956344670044881591948802632174059421369529943851248307004942399196705e-2 | Nonzero |
| Observation (3, 6, 0) L₀; field from A, x component | Ex/E₀ | (24)/(72)^(3/2) | 0.0392837100659 | 3.92837100659193069111580201169360577380464409826930020326855482775203466239474177458440981757678214648614957286364526951e-2 | Nonzero |
| Observation (3, 6, 0) L₀; field from A, y component | Ey/E₀ | (24)/(72)^(3/2) | 0.0392837100659 | 3.92837100659193069111580201169360577380464409826930020326855482775203466239474177458440981757678214648614957286364526951e-2 | Nonzero |
| Observation (3, 6, 0) L₀; field from A, z component | Ez/E₀ | (0)/(72)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, 6, 0) L₀; field from B, x component | Ex/E₀ | (0)/(36)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, 6, 0) L₀; field from B, y component | Ey/E₀ | (-6)/(36)^(3/2) | -0.0277777777778 | -2.77777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778e-2 | Nonzero |
| Observation (3, 6, 0) L₀; field from B, z component | Ez/E₀ | (0)/(36)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, 6, 0) L₀; total x field component | Ex/E₀ | (24)/(72)^(3/2) + (0)/(36)^(3/2) | 0.0392837100659 | 3.92837100659193069111580201169360577380464409826930020326855482775203466239474177458440981757678214648614957286364526951e-2 | Nonzero |
| Observation (3, 6, 0) L₀; total y field component | Ey/E₀ | (24)/(72)^(3/2) + (-6)/(36)^(3/2) | 0.0115059322881 | 1.15059322881415291333802423391582799602686632049152242549077704997425688461696399680663203979900436870837179508586749174e-2 | Nonzero |
| Observation (3, 6, 0) L₀; total z field component | Ez/E₀ | (0)/(72)^(3/2) + (0)/(36)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, 6, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0409340488391 | 4.09340488391083498098613648500254583542032455937331396238011077959780315924711713212939257854683943955383996955359701191e-2 | Nonzero |
| Observation (6, 6, 0) L₀; field from A, x component | Ex/E₀ | (36)/(117)^(3/2) | 0.0284461639090 | 2.84461639089861088214534222285640705818642727719546052284848367355200548188797668260719454202642265694162854597559253679e-2 | Nonzero |
| Observation (6, 6, 0) L₀; field from A, y component | Ey/E₀ | (24)/(117)^(3/2) | 0.0189641092727 | 1.89641092726574058809689481523760470545761818479697368189898911570133698792531778840479636135094843796108569731706169119e-2 | Nonzero |
| Observation (6, 6, 0) L₀; field from A, z component | Ez/E₀ | (0)/(117)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 6, 0) L₀; field from B, x component | Ex/E₀ | (-3)/(45)^(3/2) | -0.00993807990000 | -9.93807989999906531737410519436122771306941493160678099675954331293564855839024399739739737057236566653114744955899459335e-3 | Nonzero |
| Observation (6, 6, 0) L₀; field from B, y component | Ey/E₀ | (-6)/(45)^(3/2) | -0.0198761598000 | -1.98761597999981306347482103887224554261388298632135619935190866258712971167804879947947947411447313330622948991179891867e-2 | Nonzero |
| Observation (6, 6, 0) L₀; field from B, z component | Ez/E₀ | (0)/(45)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 6, 0) L₀; total x field component | Ex/E₀ | (36)/(117)^(3/2) + (-3)/(45)^(3/2) | 0.0185080840090 | 1.85080840089870435040793170342028428687948578403478242317252934225844062604895228286745480496918609028851380101969307745e-2 | Nonzero |
| Observation (6, 6, 0) L₀; total y field component | Ey/E₀ | (24)/(117)^(3/2) + (-6)/(45)^(3/2) | -0.000912050527341 | -9.12050527340724753779262236346408371562648015243825174529195468857927237527310110746831127635246953451437925947372274799e-4 | Nonzero |
| Observation (6, 6, 0) L₀; total z field component | Ez/E₀ | (0)/(117)^(3/2) + (0)/(45)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 6, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0185305426215 | 1.85305426215247244271025989824852980429241484938576525684383742313354124319796989462010655593774303542147366899178384919e-2 | Nonzero |
| Observation (9, 6, 0) L₀; field from A, x component | Ex/E₀ | (48)/(180)^(3/2) | 0.0198761598000 | 1.98761597999981306347482103887224554261388298632135619935190866258712971167804879947947947411447313330622948991179891867e-2 | Nonzero |
| Observation (9, 6, 0) L₀; field from A, y component | Ey/E₀ | (24)/(180)^(3/2) | 0.00993807990000 | 9.93807989999906531737410519436122771306941493160678099675954331293564855839024399739739737057236566653114744955899459335e-3 | Nonzero |
| Observation (9, 6, 0) L₀; field from A, z component | Ez/E₀ | (0)/(180)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 6, 0) L₀; field from B, x component | Ex/E₀ | (-6)/(72)^(3/2) | -0.00982092751648 | -9.82092751647982672778950502923401443451161024567325050817138706938008665598685443646102454394195536621537393215911317378e-3 | Nonzero |
| Observation (9, 6, 0) L₀; field from B, y component | Ey/E₀ | (-6)/(72)^(3/2) | -0.00982092751648 | -9.82092751647982672778950502923401443451161024567325050817138706938008665598685443646102454394195536621537393215911317378e-3 | Nonzero |
| Observation (9, 6, 0) L₀; field from B, z component | Ez/E₀ | (0)/(72)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 6, 0) L₀; total x field component | Ex/E₀ | (48)/(180)^(3/2) + (-6)/(72)^(3/2) | 0.0100552322835 | 1.00552322835183039069587053594884409916272196175403114853476995564912104607936335583337701972027759668469209669588760129e-2 | Nonzero |
| Observation (9, 6, 0) L₀; total y field component | Ey/E₀ | (24)/(180)^(3/2) + (-6)/(72)^(3/2) | 0.000117152383519 | 1.17152383519238589584600165127213278557804685933530488588156243555561902403389560936372826630410300315773517399881419568e-4 | Nonzero |
| Observation (9, 6, 0) L₀; total z field component | Ez/E₀ | (0)/(180)^(3/2) + (0)/(72)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 6, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0100559147250 | 1.00559147250000565629837042192003756049996942103849518386982625630191420711013318686167749403948833246881227517798515322e-2 | Nonzero |
| Observation (12, 6, 0) L₀; field from A, x component | Ex/E₀ | (60)/(261)^(3/2) | 0.0142295278297 | 1.42295278296591466012702087238481425717931567225387470938839705906107701488377822509621714405597449713798515571249722833e-2 | Nonzero |
| Observation (12, 6, 0) L₀; field from A, y component | Ey/E₀ | (24)/(261)^(3/2) | 0.00569181113186 | 5.69181113186365864050808348953925702871726268901549883755358823624430805953511290038486857622389798855194062284998891331e-3 | Nonzero |
| Observation (12, 6, 0) L₀; field from A, z component | Ez/E₀ | (0)/(261)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 6, 0) L₀; field from B, x component | Ex/E₀ | (-9)/(117)^(3/2) | -0.00711154097725 | -7.11154097724652720536335555714101764546606819298865130712120918388001370471994170651798635506605664235407136493898134196e-3 | Nonzero |
| Observation (12, 6, 0) L₀; field from B, y component | Ey/E₀ | (-6)/(117)^(3/2) | -0.00474102731816 | -4.74102731816435147024223703809401176364404546199243420474747278925334246981329447101199090337737109490271424329265422798e-3 | Nonzero |
| Observation (12, 6, 0) L₀; field from B, z component | Ez/E₀ | (0)/(117)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 6, 0) L₀; total x field component | Ex/E₀ | (60)/(261)^(3/2) + (-9)/(117)^(3/2) | 0.00711798685241 | 7.11798685241261939590685316670712492632708852955009578676276140673075644411784054444418508549368832902578019218599094132e-3 | Nonzero |
| Observation (12, 6, 0) L₀; total y field component | Ey/E₀ | (24)/(261)^(3/2) + (-6)/(117)^(3/2) | 0.000950783813699 | 9.50783813699307170265846451445245265073217227023064632806115446990965589721818429372877672846526893649226379557334685336e-4 | Nonzero |
| Observation (12, 6, 0) L₀; total z field component | Ez/E₀ | (0)/(261)^(3/2) + (0)/(117)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 6, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.00718120649275 | 7.18120649274977384138661353585981393826588052711171787713969289650950321528357316084537417566747980556670036819785828093e-3 | Nonzero |
| Observation (-6, 8, 0) L₀; field from A, x component | Ex/E₀ | (-12)/(73)^(3/2) | -0.0192396406350 | -1.92396406349803666756351623034108608022393439584160981240202317592906334831915144629333203905580996725853991053599644238e-2 | Nonzero |
| Observation (-6, 8, 0) L₀; field from A, y component | Ey/E₀ | (32)/(73)^(3/2) | 0.0513057083599 | 5.13057083599476444683604328090956288059715838891095949973872846914416892885107052344888543748215991268943976142932384633e-2 | Nonzero |
| Observation (-6, 8, 0) L₀; field from A, z component | Ez/E₀ | (0)/(73)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 8, 0) L₀; field from B, x component | Ex/E₀ | (9)/(145)^(3/2) | 0.00515454702540 | 5.15454702540454978935334931145814375609170852059379336830686801049885557108643324266929723154428274936487978236821904479e-3 | Nonzero |
| Observation (-6, 8, 0) L₀; field from B, y component | Ey/E₀ | (-8)/(145)^(3/2) | -0.00458181957814 | -4.58181957813737759053631049907390556097040757386114966071721600933231606318794066015048642803936244387989313988286137315e-3 | Nonzero |
| Observation (-6, 8, 0) L₀; field from B, z component | Ez/E₀ | (0)/(145)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 8, 0) L₀; total x field component | Ex/E₀ | (-12)/(73)^(3/2) + (9)/(145)^(3/2) | -0.0140850936096 | -1.40850936095758168862818129919527170461476354378223047557133637487917779121050812202640231590138169232205193229917453790e-2 | Nonzero |
| Observation (-6, 8, 0) L₀; total y field component | Ey/E₀ | (32)/(73)^(3/2) + (-8)/(145)^(3/2) | 0.0467238887818 | 4.67238887818102668778241223100217232450011763152484453366700686821093732253227645743383679467822366830145044744103770902e-2 | Nonzero |
| Observation (-6, 8, 0) L₀; total z field component | Ez/E₀ | (0)/(73)^(3/2) + (0)/(145)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-6, 8, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0488007340609 | 4.88007340609287230760226690637658564858151859770991624349083761087528755466086406001028587020273773724608115921399611674e-2 | Nonzero |
| Observation (-3, 8, 0) L₀; field from A, x component | Ex/E₀ | (0)/(64)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, 8, 0) L₀; field from A, y component | Ey/E₀ | (32)/(64)^(3/2) | 0.0625 | 6.25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (-3, 8, 0) L₀; field from A, z component | Ez/E₀ | (0)/(64)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, 8, 0) L₀; field from B, x component | Ex/E₀ | (6)/(100)^(3/2) | 0.006 | 6.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-3 | Nonzero |
| Observation (-3, 8, 0) L₀; field from B, y component | Ey/E₀ | (-8)/(100)^(3/2) | -0.008 | -8.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-3 | Nonzero |
| Observation (-3, 8, 0) L₀; field from B, z component | Ez/E₀ | (0)/(100)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, 8, 0) L₀; total x field component | Ex/E₀ | (0)/(64)^(3/2) + (6)/(100)^(3/2) | 0.006 | 6.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-3 | Nonzero |
| Observation (-3, 8, 0) L₀; total y field component | Ey/E₀ | (32)/(64)^(3/2) + (-8)/(100)^(3/2) | 0.0545 | 5.45000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (-3, 8, 0) L₀; total z field component | Ez/E₀ | (0)/(64)^(3/2) + (0)/(100)^(3/2) | 0 | 0 | Exactly zero |
| Observation (-3, 8, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0548292804987 | 5.48292804986532720413701792403189091254299851456306317307016981619703442949532198940198613930196139608745333416395260886e-2 | Nonzero |
| Observation (0, 8, 0) L₀; field from A, x component | Ex/E₀ | (12)/(73)^(3/2) | 0.0192396406350 | 1.92396406349803666756351623034108608022393439584160981240202317592906334831915144629333203905580996725853991053599644238e-2 | Nonzero |
| Observation (0, 8, 0) L₀; field from A, y component | Ey/E₀ | (32)/(73)^(3/2) | 0.0513057083599 | 5.13057083599476444683604328090956288059715838891095949973872846914416892885107052344888543748215991268943976142932384633e-2 | Nonzero |
| Observation (0, 8, 0) L₀; field from A, z component | Ez/E₀ | (0)/(73)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 8, 0) L₀; field from B, x component | Ex/E₀ | (3)/(73)^(3/2) | 0.00480991015875 | 4.80991015874509166890879057585271520055983598960402453100505793982265837079787861573333009763952491814634977633999110594e-3 | Nonzero |
| Observation (0, 8, 0) L₀; field from B, y component | Ey/E₀ | (-8)/(73)^(3/2) | -0.0128264270900 | -1.28264270899869111170901082022739072014928959722773987493468211728604223221276763086222135937053997817235994035733096158e-2 | Nonzero |
| Observation (0, 8, 0) L₀; field from B, z component | Ez/E₀ | (0)/(73)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 8, 0) L₀; total x field component | Ex/E₀ | (12)/(73)^(3/2) + (3)/(73)^(3/2) | 0.0240495507937 | 2.40495507937254583445439528792635760027991799480201226550252896991132918539893930786666504881976245907317488816999555297e-2 | Nonzero |
| Observation (0, 8, 0) L₀; total y field component | Ey/E₀ | (32)/(73)^(3/2) + (-8)/(73)^(3/2) | 0.0384792812700 | 3.84792812699607333512703246068217216044786879168321962480404635185812669663830289258666407811161993451707982107199288475e-2 | Nonzero |
| Observation (0, 8, 0) L₀; total z field component | Ez/E₀ | (0)/(73)^(3/2) + (0)/(73)^(3/2) | 0 | 0 | Exactly zero |
| Observation (0, 8, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0453766016845 | 4.53766016844885788491908560953726946223649428177052059834085263194441858394853628191175267471524696347458430325183991959e-2 | Nonzero |
| Observation (3, 8, 0) L₀; field from A, x component | Ex/E₀ | (24)/(100)^(3/2) | 0.024 | 2.40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (3, 8, 0) L₀; field from A, y component | Ey/E₀ | (32)/(100)^(3/2) | 0.032 | 3.20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (3, 8, 0) L₀; field from A, z component | Ez/E₀ | (0)/(100)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, 8, 0) L₀; field from B, x component | Ex/E₀ | (0)/(64)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, 8, 0) L₀; field from B, y component | Ey/E₀ | (-8)/(64)^(3/2) | -0.015625 | -1.56250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (3, 8, 0) L₀; field from B, z component | Ez/E₀ | (0)/(64)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, 8, 0) L₀; total x field component | Ex/E₀ | (24)/(100)^(3/2) + (0)/(64)^(3/2) | 0.024 | 2.40000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (3, 8, 0) L₀; total y field component | Ey/E₀ | (32)/(100)^(3/2) + (-8)/(64)^(3/2) | 0.016375 | 1.63750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-2 | Nonzero |
| Observation (3, 8, 0) L₀; total z field component | Ez/E₀ | (0)/(100)^(3/2) + (0)/(64)^(3/2) | 0 | 0 | Exactly zero |
| Observation (3, 8, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0290540982479 | 2.90540982479236481293252452415924739032422556076035316993183942337841233245691072313551018194730437618276066795540808108e-2 | Nonzero |
| Observation (6, 8, 0) L₀; field from A, x component | Ex/E₀ | (36)/(145)^(3/2) | 0.0206181881016 | 2.06181881016181991574133972458325750243668340823751734732274720419954222843457329706771889261771309974595191294728761792e-2 | Nonzero |
| Observation (6, 8, 0) L₀; field from A, y component | Ey/E₀ | (32)/(145)^(3/2) | 0.0183272783125 | 1.83272783125495103621452419962956222438816302954445986428688640373292642527517626406019457121574497755195725595314454926e-2 | Nonzero |
| Observation (6, 8, 0) L₀; field from A, z component | Ez/E₀ | (0)/(145)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 8, 0) L₀; field from B, x component | Ex/E₀ | (-3)/(73)^(3/2) | -0.00480991015875 | -4.80991015874509166890879057585271520055983598960402453100505793982265837079787861573333009763952491814634977633999110594e-3 | Nonzero |
| Observation (6, 8, 0) L₀; field from B, y component | Ey/E₀ | (-8)/(73)^(3/2) | -0.0128264270900 | -1.28264270899869111170901082022739072014928959722773987493468211728604223221276763086222135937053997817235994035733096158e-2 | Nonzero |
| Observation (6, 8, 0) L₀; field from B, z component | Ez/E₀ | (0)/(73)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 8, 0) L₀; total x field component | Ex/E₀ | (36)/(145)^(3/2) + (-3)/(73)^(3/2) | 0.0158082779429 | 1.58082779428731074885046066699798598238069980927711489422224141021727639135478543549438588285376060793131693531328850732e-2 | Nonzero |
| Observation (6, 8, 0) L₀; total y field component | Ey/E₀ | (32)/(145)^(3/2) + (-8)/(73)^(3/2) | 0.00550085122256 | 5.50085122256259924505513379402171504238873432316719989352204286446884193062408633197973211845204999379597315595813587676e-3 | Nonzero |
| Observation (6, 8, 0) L₀; total z field component | Ez/E₀ | (0)/(145)^(3/2) + (0)/(73)^(3/2) | 0 | 0 | Exactly zero |
| Observation (6, 8, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0167380111032 | 1.67380111032313767503415457659621404482593689561527184171061643383837510111968793646253639485810811215606218154354867559e-2 | Nonzero |
| Observation (9, 8, 0) L₀; field from A, x component | Ex/E₀ | (48)/(208)^(3/2) | 0.0160009671988 | 1.60009671988046862120675500035672897022986534342244654410227206637300308356198688396654692988986274452966605711127080194e-2 | Nonzero |
| Observation (9, 8, 0) L₀; field from A, y component | Ey/E₀ | (32)/(208)^(3/2) | 0.0106673114659 | 1.06673114658697908080450333357115264681991022894829769606818137758200205570799125597769795325990849635311070474084720129e-2 | Nonzero |
| Observation (9, 8, 0) L₀; field from A, z component | Ez/E₀ | (0)/(208)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 8, 0) L₀; field from B, x component | Ex/E₀ | (-6)/(100)^(3/2) | -0.006 | -6.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-3 | Nonzero |
| Observation (9, 8, 0) L₀; field from B, y component | Ey/E₀ | (-8)/(100)^(3/2) | -0.008 | -8.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-3 | Nonzero |
| Observation (9, 8, 0) L₀; field from B, z component | Ez/E₀ | (0)/(100)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 8, 0) L₀; total x field component | Ex/E₀ | (48)/(208)^(3/2) + (-6)/(100)^(3/2) | 0.0100009671988 | 1.00009671988046862120675500035672897022986534342244654410227206637300308356198688396654692988986274452966605711127080194e-2 | Nonzero |
| Observation (9, 8, 0) L₀; total y field component | Ey/E₀ | (32)/(208)^(3/2) + (-8)/(100)^(3/2) | 0.00266731146587 | 2.66731146586979080804503333571152646819910228948297696068181377582002055707991255977697953259908496353110704740847201295e-3 | Nonzero |
| Observation (9, 8, 0) L₀; total z field component | Ez/E₀ | (0)/(208)^(3/2) + (0)/(100)^(3/2) | 0 | 0 | Exactly zero |
| Observation (9, 8, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.0103505504862 | 1.03505504862073739001712354921159608795175324532466381613745209041936958940788340553292258238872427272849958014983118620e-2 | Nonzero |
| Observation (12, 8, 0) L₀; field from A, x component | Ex/E₀ | (60)/(289)^(3/2) | 0.0122124974557 | 1.22124974557296967229798493791980460004070832485243232240993283126399348666802361082841441074699776104213311622226745369e-2 | Nonzero |
| Observation (12, 8, 0) L₀; field from A, y component | Ey/E₀ | (32)/(289)^(3/2) | 0.00651333197639 | 6.51333197638917158558925300223895786688377773254630571951964176674129859556279259108487685731732139222470995318542641970e-3 | Nonzero |
| Observation (12, 8, 0) L₀; field from A, z component | Ez/E₀ | (0)/(289)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 8, 0) L₀; field from B, x component | Ex/E₀ | (-9)/(145)^(3/2) | -0.00515454702540 | -5.15454702540454978935334931145814375609170852059379336830686801049885557108643324266929723154428274936487978236821904479e-3 | Nonzero |
| Observation (12, 8, 0) L₀; field from B, y component | Ey/E₀ | (-8)/(145)^(3/2) | -0.00458181957814 | -4.58181957813737759053631049907390556097040757386114966071721600933231606318794066015048642803936244387989313988286137315e-3 | Nonzero |
| Observation (12, 8, 0) L₀; field from B, z component | Ez/E₀ | (0)/(145)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 8, 0) L₀; total x field component | Ex/E₀ | (60)/(289)^(3/2) + (-9)/(145)^(3/2) | 0.00705795043033 | 7.05795043032514693362650006773990224431537472793052985579246030214107929559380286561484687592569486105645137985445549215e-3 | Nonzero |
| Observation (12, 8, 0) L₀; total y field component | Ey/E₀ | (32)/(289)^(3/2) + (-8)/(145)^(3/2) | 0.00193151239825 | 1.93151239825179399505294250316505230591337015868515605880242575740898253237485193093439042927795894834481681330256504655e-3 | Nonzero |
| Observation (12, 8, 0) L₀; total z field component | Ez/E₀ | (0)/(289)^(3/2) + (0)/(145)^(3/2) | 0 | 0 | Exactly zero |
| Observation (12, 8, 0) L₀; total field magnitude | |E|/E₀ | sqrt(Ex^2+Ey^2+Ez^2) | 0.00731747254327 | 7.31747254327116171315667931691739191856361789678610035991104335001050499571626846266718326972910822193451608318495609626e-3 | Nonzero |
All 46 direction-only arrows: full displacements and endpoints
| Observation | Geometric quantity | Component unit | Retained calculation digits | Meaning |
|---|---|---|---|---|
| Observation (-6, -4, 0) L₀ | Direction-only arrow displacement | x/L₀ | -3.15184748253991798754292221192121602883188250144096032397836885298001043736579556764760155467266035670645228146491951269e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, -4, 0) L₀ | Direction-only arrow displacement | y/L₀ | -4.50731155422018518542957076999446266648924672428409307639016378947463387385033224094572056200012014010500549978713599610e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, -4, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, -4, 0) L₀ | Arrow endpoint position | x/L₀ | -6.31518474825399179875429222119212160288318825014409603239783688529800104373657955676476015546726603567064522814649195127e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, -4, 0) L₀ | Arrow endpoint position | y/L₀ | -4.45073115542201851854295707699944626664892467242840930763901637894746338738503322409457205620001201401050054997871359961e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, -4, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-3, -4, 0) L₀ | Direction-only arrow displacement | x/L₀ | 3.66892185909877590435564766575332499850184248802147541766311646234510959895380029839830429098004960215847325290180612478e-2 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-3, -4, 0) L₀ | Direction-only arrow displacement | y/L₀ | -5.48774909447564592459035307409483409961541202743009964366599664672980849860023769794021197907912875474862384042270801356e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-3, -4, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-3, -4, 0) L₀ | Arrow endpoint position | x/L₀ | -2.96331078140901224095644352334246675001498157511978524582336883537654890401046199701601695709019950397841526747098193875e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-3, -4, 0) L₀ | Arrow endpoint position | y/L₀ | -4.54877490944756459245903530740948340996154120274300996436659966467298084986002376979402119790791287547486238404227080136e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-3, -4, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, -4, 0) L₀ | Direction-only arrow displacement | x/L₀ | 4.29477845193666680191282892809999670181247691822141510614768285935061038659546565958432300760662009724871525350864445219e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, -4, 0) L₀ | Direction-only arrow displacement | y/L₀ | -3.43582276154933344153026314247999736144998153457713208491814628748048830927637252766745840608529607779897220280691556175e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, -4, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, -4, 0) L₀ | Arrow endpoint position | x/L₀ | 4.29477845193666680191282892809999670181247691822141510614768285935061038659546565958432300760662009724871525350864445219e-1 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, -4, 0) L₀ | Arrow endpoint position | y/L₀ | -4.34358227615493334415302631424799973614499815345771320849181462874804883092763725276674584060852960777989722028069155618e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, -4, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (3, -4, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.25360771759817890554586663121136170524412624103325535282244155120897918889163211074527871679115253457091948842250960693e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (3, -4, 0) L₀ | Direction-only arrow displacement | y/L₀ | 1.62776102348988971053566995445301949712674043622494845357527059092076058367884047166273932413576090571915661916962426487e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (3, -4, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (3, -4, 0) L₀ | Arrow endpoint position | x/L₀ | 3.52536077175981789055458666312113617052441262410332553528224415512089791888916321107452787167911525345709194884225096069e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (3, -4, 0) L₀ | Arrow endpoint position | y/L₀ | -3.83722389765101102894643300455469805028732595637750515464247294090792394163211595283372606758642390942808433808303757351e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (3, -4, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, -4, 0) L₀ | Direction-only arrow displacement | x/L₀ | 3.67279557996894458946080396983135630416172144125092218386965831954109783252645569244380563558798003486912181255124540239e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, -4, 0) L₀ | Direction-only arrow displacement | y/L₀ | 4.09396783423619291497713043110156620599860849198315804493797631883496906779941985048591189407577679979273244080903869955e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, -4, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, -4, 0) L₀ | Arrow endpoint position | x/L₀ | 6.36727955799689445894608039698313563041617214412509221838696583195410978325264556924438056355879800348691218125512454024e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, -4, 0) L₀ | Arrow endpoint position | y/L₀ | -3.59060321657638070850228695688984337940013915080168419550620236811650309322005801495140881059242232002072675591909613005e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, -4, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (9, -4, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.17833329550120129623532902795870785653515935016477427330492799099585818521503178786689952472734413094512450064954492431e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (9, -4, 0) L₀ | Direction-only arrow displacement | y/L₀ | 1.85333868483439050432820535283820351190320304967156134407240019827353021560461701055211431886612729362403515124665523442e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (9, -4, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (9, -4, 0) L₀ | Arrow endpoint position | x/L₀ | 9.51783332955012012962353290279587078565351593501647742733049279909958581852150317878668995247273441309451245006495449243e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (9, -4, 0) L₀ | Arrow endpoint position | y/L₀ | -3.81466613151656094956717946471617964880967969503284386559275998017264697843953829894478856811338727063759648487533447656e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (9, -4, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, -4, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.49949614875837560665934536777357155908582809725976932036926533017540821254780323232696198710467269181949093728859658833e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, -4, 0) L₀ | Direction-only arrow displacement | y/L₀ | -7.44453476840201230878601042059642726841533928353482630204133090892672668060664280473670672700151068271974071926612482943e-3 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, -4, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, -4, 0) L₀ | Arrow endpoint position | x/L₀ | 1.25499496148758375606659345367773571559085828097259769320369265330175408212547803232326961987104672691819490937288596588e+1 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, -4, 0) L₀ | Arrow endpoint position | y/L₀ | -4.00744453476840201230878601042059642726841533928353482630204133090892672668060664280473670672700151068271974071926612483e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, -4, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, -2, 0) L₀ | Direction-only arrow displacement | x/L₀ | -4.53214533816319153966127029910039024020257208503797810587519478760387052864700936626979536135821247411711245307674862378e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, -2, 0) L₀ | Direction-only arrow displacement | y/L₀ | -3.11603251487619271996016121615161042980766840192476289826950567312722498622540355826638698742021264556994098315052350961e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, -2, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, -2, 0) L₀ | Arrow endpoint position | x/L₀ | -6.45321453381631915396612702991003902402025720850379781058751947876038705286470093662697953613582124741171124530767486238e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, -2, 0) L₀ | Arrow endpoint position | y/L₀ | -2.31160325148761927199601612161516104298076684019247628982695056731272249862254035582663869874202126455699409831505235096e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, -2, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-3, -2, 0) L₀ | Direction-only arrow displacement | x/L₀ | 1.31445865871855573908152358780992981909182496375384760842321078813853391755347286912688340038236180579846221608936973185e-2 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-3, -2, 0) L₀ | Direction-only arrow displacement | y/L₀ | -5.49842904695015575810725982939940521065217155955133335514711279290043226445144344567352273216192630754833914613468219919e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-3, -2, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-3, -2, 0) L₀ | Arrow endpoint position | x/L₀ | -2.98685541341281444260918476412190070180908175036246152391576789211861466082446527130873116599617638194201537783910630268e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-3, -2, 0) L₀ | Arrow endpoint position | y/L₀ | -2.54984290469501557581072598293994052106521715595513333551471127929004322644514434456735227321619263075483391461346821992e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-3, -2, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, -2, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.10662179986892623653084615577100216545226911880109286331760994570544013716415910531404927573087847660394422756322442816e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, -2, 0) L₀ | Direction-only arrow displacement | y/L₀ | -2.04264871994757049461233846230840086618090764752043714532704397828217605486566364212561971029235139064157769102528977126e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, -2, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, -2, 0) L₀ | Arrow endpoint position | x/L₀ | 5.10662179986892623653084615577100216545226911880109286331760994570544013716415910531404927573087847660394422756322442816e-1 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, -2, 0) L₀ | Arrow endpoint position | y/L₀ | -2.20426487199475704946123384623084008661809076475204371453270439782821760548656636421256197102923513906415776910252897713e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, -2, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (3, -2, 0) L₀ | Direction-only arrow displacement | x/L₀ | 2.19147254217386073512882657238948613192469866945194950313659979930329124388998589204173824596258844253844732845202313958e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (3, -2, 0) L₀ | Direction-only arrow displacement | y/L₀ | 5.04454637176605168945223882864419864765065877775346356759795578497847798914772221534990856287685586809897622575183507225e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (3, -2, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (3, -2, 0) L₀ | Arrow endpoint position | x/L₀ | 3.21914725421738607351288265723894861319246986694519495031365997993032912438899858920417382459625884425384473284520231396e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (3, -2, 0) L₀ | Arrow endpoint position | y/L₀ | -1.49554536282339483105477611713558013523493412222465364324020442150215220108522777846500914371231441319010237742481649278e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (3, -2, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, -2, 0) L₀ | Direction-only arrow displacement | x/L₀ | -2.67464457062587324369055794874123333620678319127774113273988874230215886208552721898515834688087899640253524313610766492e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, -2, 0) L₀ | Direction-only arrow displacement | y/L₀ | 4.80585855189492007110020804203982302058663609131884026971215991050146184409484735572368752765607686795169449956205963834e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, -2, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, -2, 0) L₀ | Arrow endpoint position | x/L₀ | 5.73253554293741267563094420512587666637932168087222588672601112576978411379144727810148416531191210035974647568638923351e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, -2, 0) L₀ | Arrow endpoint position | y/L₀ | -1.51941414481050799288997919579601769794133639086811597302878400894985381559051526442763124723439231320483055004379403617e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, -2, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (9, -2, 0) L₀ | Direction-only arrow displacement | x/L₀ | 3.56143820158265276673361263222341200476455946128517972052235820553213665171443148753578220123173146339192301601334615682e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (9, -2, 0) L₀ | Direction-only arrow displacement | y/L₀ | 4.19120005920830745971439963149844883111072145240148479950729056186589499246233664711225155712483545894427694863481927721e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (9, -2, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (9, -2, 0) L₀ | Arrow endpoint position | x/L₀ | 9.35614382015826527667336126322234120047645594612851797205223582055321366517144314875357822012317314633919230160133461568e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (9, -2, 0) L₀ | Arrow endpoint position | y/L₀ | -1.58087999407916925402856003685015511688892785475985152004927094381341050075376633528877484428751645410557230513651807228e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (9, -2, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, -2, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.49520473758663882564762278793904599028313773244991571555560669589287611748929206462151915665222699367297260138611535007e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, -2, 0) L₀ | Direction-only arrow displacement | y/L₀ | 2.29619014903731183658111957973789486889343936189163873938783508212781990327433195458886093009098923558787466037538806806e-2 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, -2, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, -2, 0) L₀ | Arrow endpoint position | x/L₀ | 1.25495204737586638825647622787939045990283137732449915715555606695892876117489292064621519156652226993672972601386115350e+1 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, -2, 0) L₀ | Arrow endpoint position | y/L₀ | -1.97703809850962688163418880420262105131106560638108361260612164917872180096725668045411139069909010764412125339624611932e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, -2, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, 0, 0) L₀ | Direction-only arrow displacement | x/L₀ | -5.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, 0, 0) L₀ | Direction-only arrow displacement | y/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, 0, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, 0, 0) L₀ | Arrow endpoint position | x/L₀ | -6.55000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, 0, 0) L₀ | Arrow endpoint position | y/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, 0, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, 0, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, 0, 0) L₀ | Direction-only arrow displacement | y/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, 0, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, 0, 0) L₀ | Arrow endpoint position | x/L₀ | 5.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, 0, 0) L₀ | Arrow endpoint position | y/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, 0, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, 0, 0) L₀ | Direction-only arrow displacement | x/L₀ | -5.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, 0, 0) L₀ | Direction-only arrow displacement | y/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, 0, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, 0, 0) L₀ | Arrow endpoint position | x/L₀ | 5.45000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, 0, 0) L₀ | Arrow endpoint position | y/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, 0, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, 0, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, 0, 0) L₀ | Direction-only arrow displacement | y/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, 0, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, 0, 0) L₀ | Arrow endpoint position | x/L₀ | 1.25500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+1 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, 0, 0) L₀ | Arrow endpoint position | y/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, 0, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, 2, 0) L₀ | Direction-only arrow displacement | x/L₀ | -4.53214533816319153966127029910039024020257208503797810587519478760387052864700936626979536135821247411711245307674862378e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, 2, 0) L₀ | Direction-only arrow displacement | y/L₀ | 3.11603251487619271996016121615161042980766840192476289826950567312722498622540355826638698742021264556994098315052350961e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, 2, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, 2, 0) L₀ | Arrow endpoint position | x/L₀ | -6.45321453381631915396612702991003902402025720850379781058751947876038705286470093662697953613582124741171124530767486238e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, 2, 0) L₀ | Arrow endpoint position | y/L₀ | 2.31160325148761927199601612161516104298076684019247628982695056731272249862254035582663869874202126455699409831505235096e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, 2, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-3, 2, 0) L₀ | Direction-only arrow displacement | x/L₀ | 1.31445865871855573908152358780992981909182496375384760842321078813853391755347286912688340038236180579846221608936973185e-2 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-3, 2, 0) L₀ | Direction-only arrow displacement | y/L₀ | 5.49842904695015575810725982939940521065217155955133335514711279290043226445144344567352273216192630754833914613468219919e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-3, 2, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-3, 2, 0) L₀ | Arrow endpoint position | x/L₀ | -2.98685541341281444260918476412190070180908175036246152391576789211861466082446527130873116599617638194201537783910630268e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-3, 2, 0) L₀ | Arrow endpoint position | y/L₀ | 2.54984290469501557581072598293994052106521715595513333551471127929004322644514434456735227321619263075483391461346821992e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-3, 2, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, 2, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.10662179986892623653084615577100216545226911880109286331760994570544013716415910531404927573087847660394422756322442816e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, 2, 0) L₀ | Direction-only arrow displacement | y/L₀ | 2.04264871994757049461233846230840086618090764752043714532704397828217605486566364212561971029235139064157769102528977126e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, 2, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, 2, 0) L₀ | Arrow endpoint position | x/L₀ | 5.10662179986892623653084615577100216545226911880109286331760994570544013716415910531404927573087847660394422756322442816e-1 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, 2, 0) L₀ | Arrow endpoint position | y/L₀ | 2.20426487199475704946123384623084008661809076475204371453270439782821760548656636421256197102923513906415776910252897713e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, 2, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (3, 2, 0) L₀ | Direction-only arrow displacement | x/L₀ | 2.19147254217386073512882657238948613192469866945194950313659979930329124388998589204173824596258844253844732845202313958e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (3, 2, 0) L₀ | Direction-only arrow displacement | y/L₀ | -5.04454637176605168945223882864419864765065877775346356759795578497847798914772221534990856287685586809897622575183507225e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (3, 2, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (3, 2, 0) L₀ | Arrow endpoint position | x/L₀ | 3.21914725421738607351288265723894861319246986694519495031365997993032912438899858920417382459625884425384473284520231396e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (3, 2, 0) L₀ | Arrow endpoint position | y/L₀ | 1.49554536282339483105477611713558013523493412222465364324020442150215220108522777846500914371231441319010237742481649278e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (3, 2, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, 2, 0) L₀ | Direction-only arrow displacement | x/L₀ | -2.67464457062587324369055794874123333620678319127774113273988874230215886208552721898515834688087899640253524313610766492e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, 2, 0) L₀ | Direction-only arrow displacement | y/L₀ | -4.80585855189492007110020804203982302058663609131884026971215991050146184409484735572368752765607686795169449956205963834e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, 2, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, 2, 0) L₀ | Arrow endpoint position | x/L₀ | 5.73253554293741267563094420512587666637932168087222588672601112576978411379144727810148416531191210035974647568638923351e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, 2, 0) L₀ | Arrow endpoint position | y/L₀ | 1.51941414481050799288997919579601769794133639086811597302878400894985381559051526442763124723439231320483055004379403617e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, 2, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (9, 2, 0) L₀ | Direction-only arrow displacement | x/L₀ | 3.56143820158265276673361263222341200476455946128517972052235820553213665171443148753578220123173146339192301601334615682e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (9, 2, 0) L₀ | Direction-only arrow displacement | y/L₀ | -4.19120005920830745971439963149844883111072145240148479950729056186589499246233664711225155712483545894427694863481927721e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (9, 2, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (9, 2, 0) L₀ | Arrow endpoint position | x/L₀ | 9.35614382015826527667336126322234120047645594612851797205223582055321366517144314875357822012317314633919230160133461568e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (9, 2, 0) L₀ | Arrow endpoint position | y/L₀ | 1.58087999407916925402856003685015511688892785475985152004927094381341050075376633528877484428751645410557230513651807228e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (9, 2, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, 2, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.49520473758663882564762278793904599028313773244991571555560669589287611748929206462151915665222699367297260138611535007e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, 2, 0) L₀ | Direction-only arrow displacement | y/L₀ | -2.29619014903731183658111957973789486889343936189163873938783508212781990327433195458886093009098923558787466037538806806e-2 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, 2, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, 2, 0) L₀ | Arrow endpoint position | x/L₀ | 1.25495204737586638825647622787939045990283137732449915715555606695892876117489292064621519156652226993672972601386115350e+1 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, 2, 0) L₀ | Arrow endpoint position | y/L₀ | 1.97703809850962688163418880420262105131106560638108361260612164917872180096725668045411139069909010764412125339624611932e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, 2, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, 4, 0) L₀ | Direction-only arrow displacement | x/L₀ | -3.15184748253991798754292221192121602883188250144096032397836885298001043736579556764760155467266035670645228146491951269e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, 4, 0) L₀ | Direction-only arrow displacement | y/L₀ | 4.50731155422018518542957076999446266648924672428409307639016378947463387385033224094572056200012014010500549978713599610e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, 4, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, 4, 0) L₀ | Arrow endpoint position | x/L₀ | -6.31518474825399179875429222119212160288318825014409603239783688529800104373657955676476015546726603567064522814649195127e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, 4, 0) L₀ | Arrow endpoint position | y/L₀ | 4.45073115542201851854295707699944626664892467242840930763901637894746338738503322409457205620001201401050054997871359961e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, 4, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-3, 4, 0) L₀ | Direction-only arrow displacement | x/L₀ | 3.66892185909877590435564766575332499850184248802147541766311646234510959895380029839830429098004960215847325290180612478e-2 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-3, 4, 0) L₀ | Direction-only arrow displacement | y/L₀ | 5.48774909447564592459035307409483409961541202743009964366599664672980849860023769794021197907912875474862384042270801356e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-3, 4, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-3, 4, 0) L₀ | Arrow endpoint position | x/L₀ | -2.96331078140901224095644352334246675001498157511978524582336883537654890401046199701601695709019950397841526747098193875e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-3, 4, 0) L₀ | Arrow endpoint position | y/L₀ | 4.54877490944756459245903530740948340996154120274300996436659966467298084986002376979402119790791287547486238404227080136e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-3, 4, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, 4, 0) L₀ | Direction-only arrow displacement | x/L₀ | 4.29477845193666680191282892809999670181247691822141510614768285935061038659546565958432300760662009724871525350864445219e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, 4, 0) L₀ | Direction-only arrow displacement | y/L₀ | 3.43582276154933344153026314247999736144998153457713208491814628748048830927637252766745840608529607779897220280691556175e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, 4, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, 4, 0) L₀ | Arrow endpoint position | x/L₀ | 4.29477845193666680191282892809999670181247691822141510614768285935061038659546565958432300760662009724871525350864445219e-1 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, 4, 0) L₀ | Arrow endpoint position | y/L₀ | 4.34358227615493334415302631424799973614499815345771320849181462874804883092763725276674584060852960777989722028069155618e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, 4, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (3, 4, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.25360771759817890554586663121136170524412624103325535282244155120897918889163211074527871679115253457091948842250960693e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (3, 4, 0) L₀ | Direction-only arrow displacement | y/L₀ | -1.62776102348988971053566995445301949712674043622494845357527059092076058367884047166273932413576090571915661916962426487e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (3, 4, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (3, 4, 0) L₀ | Arrow endpoint position | x/L₀ | 3.52536077175981789055458666312113617052441262410332553528224415512089791888916321107452787167911525345709194884225096069e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (3, 4, 0) L₀ | Arrow endpoint position | y/L₀ | 3.83722389765101102894643300455469805028732595637750515464247294090792394163211595283372606758642390942808433808303757351e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (3, 4, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, 4, 0) L₀ | Direction-only arrow displacement | x/L₀ | 3.67279557996894458946080396983135630416172144125092218386965831954109783252645569244380563558798003486912181255124540239e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, 4, 0) L₀ | Direction-only arrow displacement | y/L₀ | -4.09396783423619291497713043110156620599860849198315804493797631883496906779941985048591189407577679979273244080903869955e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, 4, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, 4, 0) L₀ | Arrow endpoint position | x/L₀ | 6.36727955799689445894608039698313563041617214412509221838696583195410978325264556924438056355879800348691218125512454024e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, 4, 0) L₀ | Arrow endpoint position | y/L₀ | 3.59060321657638070850228695688984337940013915080168419550620236811650309322005801495140881059242232002072675591909613005e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, 4, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (9, 4, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.17833329550120129623532902795870785653515935016477427330492799099585818521503178786689952472734413094512450064954492431e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (9, 4, 0) L₀ | Direction-only arrow displacement | y/L₀ | -1.85333868483439050432820535283820351190320304967156134407240019827353021560461701055211431886612729362403515124665523442e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (9, 4, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (9, 4, 0) L₀ | Arrow endpoint position | x/L₀ | 9.51783332955012012962353290279587078565351593501647742733049279909958581852150317878668995247273441309451245006495449243e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (9, 4, 0) L₀ | Arrow endpoint position | y/L₀ | 3.81466613151656094956717946471617964880967969503284386559275998017264697843953829894478856811338727063759648487533447656e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (9, 4, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, 4, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.49949614875837560665934536777357155908582809725976932036926533017540821254780323232696198710467269181949093728859658833e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, 4, 0) L₀ | Direction-only arrow displacement | y/L₀ | 7.44453476840201230878601042059642726841533928353482630204133090892672668060664280473670672700151068271974071926612482943e-3 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, 4, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, 4, 0) L₀ | Arrow endpoint position | x/L₀ | 1.25499496148758375606659345367773571559085828097259769320369265330175408212547803232326961987104672691819490937288596588e+1 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, 4, 0) L₀ | Arrow endpoint position | y/L₀ | 4.00744453476840201230878601042059642726841533928353482630204133090892672668060664280473670672700151068271974071926612483e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, 4, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, 6, 0) L₀ | Direction-only arrow displacement | x/L₀ | -2.20063785474918132347552774796197302264500383193052433902341099037728649534231394876975348598373352551983994538959379190e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, 6, 0) L₀ | Direction-only arrow displacement | y/L₀ | 5.04055483377027861924116755101971516499719851539653427917912216851257028501146281512908137134005991654841689978384601580e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, 6, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, 6, 0) L₀ | Arrow endpoint position | x/L₀ | -6.22006378547491813234755277479619730226450038319305243390234109903772864953423139487697534859837335255198399453895937919e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, 6, 0) L₀ | Arrow endpoint position | y/L₀ | 6.50405548337702786192411675510197151649971985153965342791791221685125702850114628151290813713400599165484168997838460158e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, 6, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-3, 6, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.30781758668206729677831593503057687615197953038381543444169935111662235655414328848234346540008154618195876876114975927e-2 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-3, 6, 0) L₀ | Direction-only arrow displacement | y/L₀ | 5.47432833548236176218951310335824935737600325246506977596366669713271381149425168779164728264215099756604582447600069181e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-3, 6, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-3, 6, 0) L₀ | Arrow endpoint position | x/L₀ | -2.94692182413317932703221684064969423123848020469616184565558300648883377643445856711517656534599918453818041231238850241e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-3, 6, 0) L₀ | Arrow endpoint position | y/L₀ | 6.54743283354823617621895131033582493573760032524650697759636666971327138114942516877916472826421509975660458244760006918e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-3, 6, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, 6, 0) L₀ | Direction-only arrow displacement | x/L₀ | 3.52101419815463927604208811857992276841194084029238509434220005582371481468459006551966244159578089536843926155292952612e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, 6, 0) L₀ | Direction-only arrow displacement | y/L₀ | 4.22521703778556713125050574229590732209432900835086211321064006698845777762150807862359492991493707444212711386351543134e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, 6, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, 6, 0) L₀ | Arrow endpoint position | x/L₀ | 3.52101419815463927604208811857992276841194084029238509434220005582371481468459006551966244159578089536843926155292952612e-1 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, 6, 0) L₀ | Arrow endpoint position | y/L₀ | 6.42252170377855671312505057422959073220943290083508621132106400669884577776215080786235949299149370744421271138635154313e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, 6, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (3, 6, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.27825640243367009028563911073655476987904193440192107522617345496155554086487681099661241796571969903813387172923228351e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (3, 6, 0) L₀ | Direction-only arrow displacement | y/L₀ | 1.54596550743151140170087341838092471110097663512932031603318020425620327345706770227472798967488340135955969509431495339e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (3, 6, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (3, 6, 0) L₀ | Arrow endpoint position | x/L₀ | 3.52782564024336700902856391107365547698790419344019210752261734549615555408648768109966124179657196990381338717292322835e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (3, 6, 0) L₀ | Arrow endpoint position | y/L₀ | 6.15459655074315114017008734183809247111009766351293203160331802042562032734570677022747279896748834013595596950943149534e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (3, 6, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, 6, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.49333412024244968132867417378880809168119347055363222710006307399338980842069702351122949271373115043030897800687304972e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, 6, 0) L₀ | Direction-only arrow displacement | y/L₀ | -2.70703238584453189931490724039272192123000124658290938234225991941438366647563606441551279955258497449853444841659035460e-2 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, 6, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, 6, 0) L₀ | Arrow endpoint position | x/L₀ | 6.54933341202424496813286741737888080916811934705536322271000630739933898084206970235112294927137311504303089780068730497e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, 6, 0) L₀ | Arrow endpoint position | y/L₀ | 5.97292967614155468100685092759607278078769998753417090617657740080585616333524363935584487200447415025501465551583409645e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, 6, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (9, 6, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.49962674423438494432687883195773768917638872126936793624063928620853316778322636200559053864456575168587903171925741326e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (9, 6, 0) L₀ | Direction-only arrow displacement | y/L₀ | 6.40755343473548219067555567035921556504575996558722940732034341106045017152085144606814452804649975644961490382379380187e-3 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (9, 6, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (9, 6, 0) L₀ | Arrow endpoint position | x/L₀ | 9.54996267442343849443268788319577376891763887212693679362406392862085331677832263620055905386445657516858790317192574133e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (9, 6, 0) L₀ | Arrow endpoint position | y/L₀ | 6.00640755343473548219067555567035921556504575996558722940732034341106045017152085144606814452804649975644961490382379380e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (9, 6, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, 6, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.45158083503024187557054106111435566083671304975239617625488511080573409793780906430621662921803040072941285984813499653e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, 6, 0) L₀ | Direction-only arrow displacement | y/L₀ | 7.28193929616946694613839280074431874610985211764246262158227023136045906559992460955493069582878285166685048912905479623e-2 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, 6, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, 6, 0) L₀ | Arrow endpoint position | x/L₀ | 1.25451580835030241875570541061114355660836713049752396176254885110805734097937809064306216629218030400729412859848134997e+1 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, 6, 0) L₀ | Arrow endpoint position | y/L₀ | 6.07281939296169466946138392800744318746109852117642462621582270231360459065599924609554930695828782851666850489129054796e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, 6, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, 8, 0) L₀ | Direction-only arrow displacement | x/L₀ | -1.58743544217893481718873442074313727628758071339703450299699934099359952931303655530880967688218920275901467354016660148e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, 8, 0) L₀ | Direction-only arrow displacement | y/L₀ | 5.26593284394267315410700671657783137223600365101553897182023198541282183385019235810824111234550598945397331220737824382e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, 8, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-6, 8, 0) L₀ | Arrow endpoint position | x/L₀ | -6.15874354421789348171887344207431372762875807133970345029969993409935995293130365553088096768821892027590146735401666015e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, 8, 0) L₀ | Arrow endpoint position | y/L₀ | 8.52659328439426731541070067165778313722360036510155389718202319854128218338501923581082411123455059894539733122073782438e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-6, 8, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-3, 8, 0) L₀ | Direction-only arrow displacement | x/L₀ | 6.01868193415570221160986582929072432811372809914614834798555023482751388518405407568450869345412810215005272440450515069e-2 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-3, 8, 0) L₀ | Direction-only arrow displacement | y/L₀ | 5.46696942352476284221229479493907459803663635672441808275354146330165844570884911874676206322083302611963122466742551187e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-3, 8, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (-3, 8, 0) L₀ | Arrow endpoint position | x/L₀ | -2.93981318065844297788390134170709275671886271900853851652014449765172486114815945924315491306545871897849947275595494849e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-3, 8, 0) L₀ | Arrow endpoint position | y/L₀ | 8.54669694235247628422122947949390745980366363567244180827535414633016584457088491187467620632208330261196312246674255119e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (-3, 8, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, 8, 0) L₀ | Direction-only arrow displacement | x/L₀ | 2.91499417001748994170020404926542269344999575751590827323856168367360258442236793943683418134253441432261636845784406249e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, 8, 0) L₀ | Direction-only arrow displacement | y/L₀ | 4.66399067202798390672032647882467630951999321202545323718169869387776413507578870309893469014805506291618618953255049999e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, 8, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (0, 8, 0) L₀ | Arrow endpoint position | x/L₀ | 2.91499417001748994170020404926542269344999575751590827323856168367360258442236793943683418134253441432261636845784406249e-1 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, 8, 0) L₀ | Arrow endpoint position | y/L₀ | 8.46639906720279839067203264788246763095199932120254532371816986938777641350757887030989346901480550629161861895325505000e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (0, 8, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (3, 8, 0) L₀ | Direction-only arrow displacement | x/L₀ | 4.54324890325699175190263159279913409596650764225885489673006560827410039511262966942134012347817258121091385893332484385e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (3, 8, 0) L₀ | Direction-only arrow displacement | y/L₀ | 3.09982086628471833072523301383690920089381511008286453891478434731201641541538795153226852174812816738869643500138309659e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (3, 8, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (3, 8, 0) L₀ | Arrow endpoint position | x/L₀ | 3.45432489032569917519026315927991340959665076422588548967300656082741003951126296694213401234781725812109138589333248439e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (3, 8, 0) L₀ | Arrow endpoint position | y/L₀ | 8.30998208662847183307252330138369092008938151100828645389147843473120164154153879515322685217481281673886964350013830966e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (3, 8, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, 8, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.19449581850359259046712244942074107518194718875564833417386686972120279431517502965543767866896548538516470259572192768e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, 8, 0) L₀ | Direction-only arrow displacement | y/L₀ | 1.80754341346167718136536403704435777721392462037813529542331819263112555901664982183564946518622870429830037415221040940e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, 8, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (6, 8, 0) L₀ | Arrow endpoint position | x/L₀ | 6.51944958185035925904671224494207410751819471887556483341738668697212027943151750296554376786689654853851647025957219277e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, 8, 0) L₀ | Arrow endpoint position | y/L₀ | 8.18075434134616771813653640370443577772139246203781352954233181926311255590166498218356494651862287042983003741522104094e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (6, 8, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (9, 8, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.31424098329099626665176865250280124782094841149441988558430642353054864321064531267448547445110279518714204918842062048e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (9, 8, 0) L₀ | Direction-only arrow displacement | y/L₀ | 1.41733650609526922557958675140554615111647604463656816729141649258821445734709581876018985113005903713636924989968794821e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (9, 8, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (9, 8, 0) L₀ | Arrow endpoint position | x/L₀ | 9.53142409832909962666517686525028012478209484114944198855843064235305486432106453126744854744511027951871420491884206205e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (9, 8, 0) L₀ | Arrow endpoint position | y/L₀ | 8.14173365060952692255795867514055461511164760446365681672914164925882144573470958187601898511300590371363692498996879482e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (9, 8, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, 8, 0) L₀ | Direction-only arrow displacement | x/L₀ | 5.30493652517826911900596788571096512747118688609319308151283702289681729626179573070165005592257018558102498100834178309e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, 8, 0) L₀ | Direction-only arrow displacement | y/L₀ | 1.45177424685434878862345062181803904015967934707357356441163839370377512885915517479939791393170537684375483184394354077e-1 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, 8, 0) L₀ | Direction-only arrow displacement | z/L₀ | 0 | Full arrow length is 11L₀/20; does not encode |E| |
| Observation (12, 8, 0) L₀ | Arrow endpoint position | x/L₀ | 1.25304936525178269119005967885710965127471186886093193081512837022896817296261795730701650055922570185581024981008341783e+1 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, 8, 0) L₀ | Arrow endpoint position | y/L₀ | 8.14517742468543487886234506218180390401596793470735735644116383937037751288591551747993979139317053768437548318439435408e+0 | Endpoint is observation position plus admitted arrow displacement |
| Observation (12, 8, 0) L₀ | Arrow endpoint position | z/L₀ | 0 | Endpoint is observation position plus admitted arrow displacement |
The spatial plot retains one equal-scale transform; scroll its own region on narrow screens.
What must stay fixed when you superpose?
Superposition is a statement about adding field contributions for specified sources. If E_A is calculated from one prescribed distribution and E_B from another, their sum gives the field of their combined prescribed distribution in this vacuum electrostatic model.
A different experiment can change the inputs. Bringing a conductor or a polarizable body into the arrangement may rearrange charge. The field remains a vector sum of contributions from the actual total charge distribution, but that distribution may no longer equal the two separate distributions you first calculated. Adding results from incompatible source configurations answers the wrong question.
Likewise, inserting a finite probe can disturb the sources. The ideal nonperturbing-probe limit separates field description from that disturbance. In a real measurement, source response and uncertainty require an explicit model rather than a declaration that every probe is harmless.
In a linear material model, response equations can sometimes be superposed together with the field equations. That needs stated constitutive assumptions and boundary conditions. Do not replace the vacuum constant in an arbitrary nonuniform material arrangement and infer that the original point-source picture has been justified.
When charge is spread out
A line, surface or volume description replaces separate point-source charges by a signed charge measure dq. With observation position r fixed and source position r′ varying, the electrostatic expression is E(r) = kₑ∫(r − r′)dq/|r − r′|³, wherever that integral is defined with its stated source model.
For a thin line use dq = λ dl, where λ is charge per length in C/m. For a surface use dq = σ dA, with σ in C/m². For a volume use dq = ρ dV, with ρ in C/m³. These densities can be negative and can vary with position. The differential element and density must describe the same geometric support.
The integration variable labels sources, not the observation point. Integrate all components in one fixed coordinate system and apply any symmetry before claiming a component vanishes. Cancellation of opposite transverse components can leave longitudinal components that add.
A continuous density is a model at an appropriate observation scale. It need not resolve individual microscopic charges. Near a discrete charge, on a singular ideal line, or at an ideal surface boundary, existence, one-sided limits and the meaning of the field need separate care. There is no universal instruction to integrate through a singularity and call the result finite.
A finite charged segment, derived component by component
Now set aside A and B. Consider a separate prescribed thin straight segment from x′ = −L₀ to x′ = L₀, with constant λ = q₀/L₀. Its total charge is 2q₀. Uniform charge is an assigned source model; we are not claiming that an isolated conducting wire automatically has this equilibrium distribution.
Observe at (0, h, 0)L₀ with h > 0, and label a source point by u = x′/L₀, so −1 ≤ u ≤ 1 and dq = q₀ du. The dimensionless vector contribution is d(E/E₀) = (−u, h, 0)du/(u² + h²)^(3/2).
The x integrand is odd in u, so symmetric source pairs cancel Eₓ. Their y contributions are equal and positive, so those add. The z component vanishes because every source-to-observation displacement has zero z component. This symmetry argument sets components, not the magnitude of the remaining component.
For the y integral, an antiderivative is u/[h√(u² + h²)]. Differentiating with respect to u gives h/(u² + h²)^(3/2), exactly the y kernel for fixed positive h. Evaluating at the endpoints therefore gives E/E₀ = (0, 2/[h√(1 + h²)], 0).
This result comes from an exact integral in the stated ideal model. A plotted set of samples is not a numerical quadrature study and supplies no claim about convergence of a numerical integration method.
A separate finite segment: geometry, field and limits
Set A and B aside. The prescribed uniform segment has total charge 2q₀. Its exact positive-y field is read directly from the admitted analytic controls and samples.
The separate source, illustrated at h=1
All 71 field evaluations and six exact controls
- All 71 retained analytic samples (joined for reading)
- All six exact controls
Ratios to the near and far forms
- Exact field / (2/h²): far total-charge form
- Exact field / (2/h): local infinite-line form
- The x contributions cancel by odd symmetry and Ez=0. For h>0, Ey/E₀=2/[h√(1+h²)] follows from the exact integral.
- All 71 samples lie in 1/2≤h≤4. Joining them is not a numerical quadrature or convergence claim. The six controls and both ratio families remain complete in the tables.
- The limits hEy/E₀→2 as h→0+ and h²Ey/E₀→2 as h→∞ have stated regimes. h=0 is excluded. Uniform density is prescribed, not a conductor-equilibrium result.
The complete source definition, 77 control/sample rows and retained field/ratio digits are available below.
Exact positive y-field controls for the separate uniform segment
The separate prescribed segment and its observation domain
| Quantity | Meaning |
|---|---|
| Source support | u=x′/L₀ in [−1,1] at (u,0,0)L₀ |
| Density and charge measure | λ=q₀/L₀; dq=q₀ du; total charge=2q₀ |
| Observation | (0,h,0)L₀ with h>0; separate from A and B |
| Exact field | E/E₀=(0,2/[h√(1+h²)],0) |
| Source condition | Prescribed uniform charge; no conductor-equilibrium claim |
All six controls and all 71 analytic samples
| Kind | h = H/L₀ | Ex/E₀ | Ey/E₀ | Ez/E₀ | Ratio to 2/h² | Ratio to 2/h |
|---|---|---|---|---|---|---|
| Exact control | 1/2 | 0 | 3.57770876400 | 0 | 0.447213595500 | 0.894427191000 |
| Exact control | 3/4 | 0 | 2.13333333333 | 0 | 0.6 | 0.8 |
| Exact control | 1 | 0 | 1.41421356237 | 0 | 0.707106781187 | 0.707106781187 |
| Exact control | 4/3 | 0 | 0.900000000000 | 0 | 0.800000000000 | 0.600000000000 |
| Exact control | 2 | 0 | 0.447213595500 | 0 | 0.894427191000 | 0.447213595500 |
| Exact control | 4 | 0 | 0.121267812518 | 0 | 0.970142500145 | 0.242535625036 |
| Analytic sample | 1/2 | 0 | 3.57770876400 | 0 | 0.447213595500 | 0.894427191000 |
| Analytic sample | 11/20 | 0 | 3.18623966792 | 0 | 0.481918749772 | 0.876215908677 |
| Analytic sample | 3/5 | 0 | 2.85830975238 | 0 | 0.514495755428 | 0.857492925713 |
| Analytic sample | 13/20 | 0 | 2.57982651169 | 0 | 0.544988350595 | 0.838443616301 |
| Analytic sample | 7/10 | 0 | 2.34066263005 | 0 | 0.573462344363 | 0.819231920519 |
| Analytic sample | 3/4 | 0 | 2.13333333333 | 0 | 0.6 | 0.8 |
| Analytic sample | 4/5 | 0 | 1.95217202361 | 0 | 0.624695047554 | 0.780868809443 |
| Analytic sample | 17/20 | 0 | 1.79279839473 | 0 | 0.647648420096 | 0.761939317759 |
| Analytic sample | 9/10 | 0 | 1.65176476944 | 0 | 0.668964731622 | 0.743294146247 |
| Analytic sample | 19/20 | 0 | 1.52631459704 | 0 | 0.688749461915 | 0.724999433594 |
| Analytic sample | 1 | 0 | 1.41421356237 | 0 | 0.707106781187 | 0.707106781187 |
| Analytic sample | 21/20 | 0 | 1.31362889984 | 0 | 0.724137931034 | 0.689655172414 |
| Analytic sample | 11/10 | 0 | 1.22304144363 | 0 | 0.739940073396 | 0.672672793996 |
| Analytic sample | 23/20 | 0 | 1.14118037378 | 0 | 0.754605522164 | 0.656178714925 |
| Analytic sample | 6/5 | 0 | 1.06697399944 | 0 | 0.768221279597 | 0.640184399664 |
| Analytic sample | 5/4 | 0 | 0.999512076087 | 0 | 0.780868809443 | 0.624695047554 |
| Analytic sample | 13/10 | 0 | 0.938016555153 | 0 | 0.792623989105 | 0.609710760850 |
| Analytic sample | 27/20 | 0 | 0.881818593520 | 0 | 0.803557193345 | 0.595227550626 |
| Analytic sample | 7/5 | 0 | 0.830340276742 | 0 | 0.813733471207 | 0.581238193719 |
| Analytic sample | 29/20 | 0 | 0.783079939040 | 0 | 0.823212785915 | 0.567732955804 |
| Analytic sample | 3/2 | 0 | 0.739600261634 | 0 | 0.832050294338 | 0.554700196225 |
| Analytic sample | 31/20 | 0 | 0.699518541706 | 0 | 0.840296648224 | 0.542126869822 |
| Analytic sample | 8/5 | 0 | 0.662498675004 | 0 | 0.847998304005 | 0.529998940003 |
| Analytic sample | 33/20 | 0 | 0.628244504356 | 0 | 0.855197831554 | 0.518301716093 |
| Analytic sample | 17/10 | 0 | 0.596494266545 | 0 | 0.861934215158 | 0.507020126563 |
| Analytic sample | 7/4 | 0 | 0.567015929551 | 0 | 0.868243142124 | 0.496138938357 |
| Analytic sample | 9/5 | 0 | 0.539603256865 | 0 | 0.874157276122 | 0.485642931179 |
| Analytic sample | 37/20 | 0 | 0.514072469584 | 0 | 0.879706513576 | 0.475517034365 |
| Analytic sample | 19/10 | 0 | 0.490259402982 | 0 | 0.884918222382 | 0.465746432833 |
| Analytic sample | 39/20 | 0 | 0.468017074458 | 0 | 0.889817462813 | 0.456316647596 |
| Analytic sample | 2 | 0 | 0.447213595500 | 0 | 0.894427191000 | 0.447213595500 |
| Analytic sample | 41/20 | 0 | 0.427730372704 | 0 | 0.898768445644 | 0.438423632021 |
| Analytic sample | 21/10 | 0 | 0.409460552755 | 0 | 0.902860518824 | 0.429933580392 |
| Analytic sample | 43/20 | 0 | 0.392307674154 | 0 | 0.906721111889 | 0.421730749716 |
| Analytic sample | 11/5 | 0 | 0.376184494819 | 0 | 0.910366477463 | 0.413802944301 |
| Analytic sample | 9/4 | 0 | 0.361011969825 | 0 | 0.913811548620 | 0.406138466053 |
| Analytic sample | 23/10 | 0 | 0.346718357752 | 0 | 0.917070056253 | 0.398726111414 |
| Analytic sample | 47/20 | 0 | 0.333238437530 | 0 | 0.920154635629 | 0.391555164097 |
| Analytic sample | 12/5 | 0 | 0.320512820513 | 0 | 0.923076923077 | 0.384615384615 |
| Analytic sample | 49/20 | 0 | 0.308487344838 | 0 | 0.925847643695 | 0.377896997427 |
| Analytic sample | 5/2 | 0 | 0.297112541083 | 0 | 0.928476690885 | 0.371390676354 |
| Analytic sample | 51/20 | 0 | 0.286343159858 | 0 | 0.930973198487 | 0.365087528818 |
| Analytic sample | 13/5 | 0 | 0.276137753315 | 0 | 0.933345606203 | 0.358979079309 |
| Analytic sample | 53/20 | 0 | 0.266458303724 | 0 | 0.935601718951 | 0.353057252434 |
| Analytic sample | 27/10 | 0 | 0.257269893203 | 0 | 0.937748760724 | 0.347314355824 |
| Analytic sample | 11/4 | 0 | 0.248540409518 | 0 | 0.939793423488 | 0.341743063087 |
| Analytic sample | 14/5 | 0 | 0.240240283570 | 0 | 0.941741911595 | 0.336336396998 |
| Analytic sample | 57/20 | 0 | 0.232342254757 | 0 | 0.943599982133 | 0.331087713029 |
| Analytic sample | 29/10 | 0 | 0.224821160910 | 0 | 0.945372981626 | 0.325990683319 |
| Analytic sample | 59/20 | 0 | 0.217653749938 | 0 | 0.947065879416 | 0.321039281158 |
| Analytic sample | 3 | 0 | 0.210818510678 | 0 | 0.948683298051 | 0.316227766017 |
| Analytic sample | 61/20 | 0 | 0.204295520768 | 0 | 0.950229540973 | 0.311550669172 |
| Analytic sample | 31/10 | 0 | 0.198066309628 | 0 | 0.951708617761 | 0.307002779923 |
| Analytic sample | 63/20 | 0 | 0.192113734874 | 0 | 0.953124267145 | 0.302579132427 |
| Analytic sample | 16/5 | 0 | 0.186421870710 | 0 | 0.954479978035 | 0.298274993136 |
| Analytic sample | 13/4 | 0 | 0.180975906977 | 0 | 0.955779008722 | 0.294085848838 |
| Analytic sample | 33/10 | 0 | 0.175762057747 | 0 | 0.957024404433 | 0.290007395283 |
| Analytic sample | 67/20 | 0 | 0.170767478441 | 0 | 0.958219013401 | 0.286035526388 |
| Analytic sample | 17/5 | 0 | 0.165980190583 | 0 | 0.959365501571 | 0.282166323992 |
| Analytic sample | 69/20 | 0 | 0.161389013415 | 0 | 0.960466366085 | 0.278396048140 |
| Analytic sample | 7/2 | 0 | 0.156983501656 | 0 | 0.961523947641 | 0.274721127897 |
| Analytic sample | 71/20 | 0 | 0.152753888807 | 0 | 0.962540441845 | 0.271138152632 |
| Analytic sample | 18/5 | 0 | 0.148691035437 | 0 | 0.963517909630 | 0.267643863786 |
| Analytic sample | 73/20 | 0 | 0.144786381961 | 0 | 0.964458286837 | 0.264235147079 |
| Analytic sample | 37/10 | 0 | 0.141031905483 | 0 | 0.965363393028 | 0.260909025143 |
| Analytic sample | 15/4 | 0 | 0.137420080299 | 0 | 0.966234939601 | 0.257662650560 |
| Analytic sample | 19/5 | 0 | 0.133943841726 | 0 | 0.967074537263 | 0.254493299280 |
| Analytic sample | 77/20 | 0 | 0.130596552932 | 0 | 0.967883702921 | 0.251398364395 |
| Analytic sample | 39/10 | 0 | 0.127371974496 | 0 | 0.968663866044 | 0.248375350268 |
| Analytic sample | 79/20 | 0 | 0.124264236441 | 0 | 0.969416374533 | 0.245421866970 |
| Analytic sample | 4 | 0 | 0.121267812518 | 0 | 0.970142500145 | 0.242535625036 |
Every displayed and retained segment field and ratio
| Location and quantity | Dimensionless quantity | Exact expression | Displayed value (up to 12 significant digits) | Retained calculation digits (120 significant digits for nonzero values) | Exact-zero status |
|---|---|---|---|---|---|
| Control h=1/2; y field | Ey/E₀ | 2/((1/2)*sqrt(1+(1/2)^2)) | 3.57770876400 | 3.57770876399966351425467786997004197670498937537844115883343559265683348102048783906306305340605163995121308184123805361e+0 | Nonzero |
| Control h=1/2; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (1/2)/sqrt(1+(1/2)^2) | 0.447213595500 | 4.47213595499957939281834733746255247088123671922305144854179449082104185127560979882882881675756454993901635230154756701e-1 | Nonzero |
| Control h=1/2; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(1/2)^2) | 0.894427191000 | 8.94427190999915878563669467492510494176247343844610289708358898164208370255121959765765763351512909987803270460309513402e-1 | Nonzero |
| Control h=3/4; y field | Ey/E₀ | 2/((3/4)*sqrt(1+(3/4)^2)) | 2.13333333333 | 2.13333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333e+0 | Nonzero |
| Control h=3/4; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (3/4)/sqrt(1+(3/4)^2) | 0.6 | 6.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Control h=3/4; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(3/4)^2) | 0.8 | 8.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Control h=1; y field | Ey/E₀ | 2/((1)*sqrt(1+(1)^2)) | 1.41421356237 | 1.41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702e+0 | Nonzero |
| Control h=1; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (1)/sqrt(1+(1)^2) | 0.707106781187 | 7.07106781186547524400844362104849039284835937688474036588339868995366239231053519425193767163820786367506923115456148512e-1 | Nonzero |
| Control h=1; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(1)^2) | 0.707106781187 | 7.07106781186547524400844362104849039284835937688474036588339868995366239231053519425193767163820786367506923115456148512e-1 | Nonzero |
| Control h=4/3; y field | Ey/E₀ | 2/((4/3)*sqrt(1+(4/3)^2)) | 0.900000000000 | 9.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Control h=4/3; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (4/3)/sqrt(1+(4/3)^2) | 0.800000000000 | 8.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Control h=4/3; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(4/3)^2) | 0.600000000000 | 6.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Control h=2; y field | Ey/E₀ | 2/((2)*sqrt(1+(2)^2)) | 0.447213595500 | 4.47213595499957939281834733746255247088123671922305144854179449082104185127560979882882881675756454993901635230154756701e-1 | Nonzero |
| Control h=2; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (2)/sqrt(1+(2)^2) | 0.894427191000 | 8.94427190999915878563669467492510494176247343844610289708358898164208370255121959765765763351512909987803270460309513402e-1 | Nonzero |
| Control h=2; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(2)^2) | 0.447213595500 | 4.47213595499957939281834733746255247088123671922305144854179449082104185127560979882882881675756454993901635230154756701e-1 | Nonzero |
| Control h=4; y field | Ey/E₀ | 2/((4)*sqrt(1+(4)^2)) | 0.121267812518 | 1.21267812518166486759453231058061088974917624275694718658783340385145716068753576281995989729726008726016001204094533577e-1 | Nonzero |
| Control h=4; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (4)/sqrt(1+(4)^2) | 0.970142500145 | 9.70142500145331894075625848464488711799340994205557749270266723081165728550028610255967917837808069808128009632756268615e-1 | Nonzero |
| Control h=4; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(4)^2) | 0.242535625036 | 2.42535625036332973518906462116122177949835248551389437317566680770291432137507152563991979459452017452032002408189067154e-1 | Nonzero |
| Sample h=1/2; y field | Ey/E₀ | 2/((1/2)*sqrt(1+(1/2)^2)) | 3.57770876400 | 3.57770876399966351425467786997004197670498937537844115883343559265683348102048783906306305340605163995121308184123805361e+0 | Nonzero |
| Sample h=1/2; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (1/2)/sqrt(1+(1/2)^2) | 0.447213595500 | 4.47213595499957939281834733746255247088123671922305144854179449082104185127560979882882881675756454993901635230154756701e-1 | Nonzero |
| Sample h=1/2; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(1/2)^2) | 0.894427191000 | 8.94427190999915878563669467492510494176247343844610289708358898164208370255121959765765763351512909987803270460309513402e-1 | Nonzero |
| Sample h=11/20; y field | Ey/E₀ | 2/((11/20)*sqrt(1+(11/20)^2)) | 3.18623966792 | 3.18623966791508006438579292543272649483980324717258906307345505214809904609249448141338546828939280903676439517297153848e+0 | Nonzero |
| Sample h=11/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (11/20)/sqrt(1+(11/20)^2) | 0.481918749772 | 4.81918749772155859738351179971699882344520241134854095789860076637399980721489790313774552078770662366810614769911945194e-1 | Nonzero |
| Sample h=11/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(11/20)^2) | 0.876215908677 | 8.76215908676647017706093054493999786080945892972461992345200139340727237675435982388681003779583022485110208672567173081e-1 | Nonzero |
| Sample h=3/5; y field | Ey/E₀ | 2/((3/5)*sqrt(1+(3/5)^2)) | 2.85830975238 | 2.85830975237514728964419258703214856692225408572841762473039546317049512842976109199276486590835068556705373631144848596e+0 | Nonzero |
| Sample h=3/5; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (3/5)/sqrt(1+(3/5)^2) | 0.514495755428 | 5.14495755427526512135954665665786742046005735431115172451471183370689123117356996558697675863503123402069672536060727472e-1 | Nonzero |
| Sample h=3/5; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(3/5)^2) | 0.857492925713 | 8.57492925712544186893257776109644570076676225718525287419118638951148538528928327597829459772505205670116120893434545787e-1 | Nonzero |
| Sample h=13/20; y field | Ey/E₀ | 2/((13/20)*sqrt(1+(13/20)^2)) | 2.57982651169 | 2.57982651169426802179756260522406385647460151952780807805416545190753693208370224214533729102531519663553226728077783864e+0 | Nonzero |
| Sample h=13/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (13/20)/sqrt(1+(13/20)^2) | 0.544988350595 | 5.44988350595414119604735100353583489680259571000249456488942451715467176902682098653202502729097835289256191463064318413e-1 | Nonzero |
| Sample h=13/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(13/20)^2) | 0.838443616301 | 8.38443616300637107084207846697820753354245493846537625367603771869949502927203228697234619583227438906547986866252797559e-1 | Nonzero |
| Sample h=7/10; y field | Ey/E₀ | 2/((7/10)*sqrt(1+(7/10)^2)) | 2.34066263005 | 2.34066263005440133305807387471197586502150102020725645372514668270763004775804839768441356026709232574638244448858518082e+0 | Nonzero |
| Sample h=7/10; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (7/10)/sqrt(1+(7/10)^2) | 0.573462344363 | 5.73462344363328326599228099304434086930267749950777831162660937263369361700721857432681322265437619807863698899703369300e-1 | Nonzero |
| Sample h=7/10; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(7/10)^2) | 0.819231920519 | 8.19231920519040466570325856149191552757525357072539758803801338947670516715316939189544746093482314011233855571004813286e-1 | Nonzero |
| Sample h=3/4; y field | Ey/E₀ | 2/((3/4)*sqrt(1+(3/4)^2)) | 2.13333333333 | 2.13333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333e+0 | Nonzero |
| Sample h=3/4; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (3/4)/sqrt(1+(3/4)^2) | 0.6 | 6.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Sample h=3/4; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(3/4)^2) | 0.8 | 8.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-1 | Nonzero |
| Sample h=4/5; y field | Ey/E₀ | 2/((4/5)*sqrt(1+(4/5)^2)) | 1.95217202361 | 1.95217202360757581905128587640908940991476223555518868461258311788664108481612075435651045800300913511305238795847475099e+0 | Nonzero |
| Sample h=4/5; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (4/5)/sqrt(1+(4/5)^2) | 0.624695047554 | 6.24695047554424262096411480450908611172723915377660379076026597723725147141158641394083346560962923236176764146711920318e-1 | Nonzero |
| Sample h=4/5; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(4/5)^2) | 0.780868809443 | 7.80868809443030327620514350563635763965904894222075473845033247154656433926448301742604183201203654045220955183389900398e-1 | Nonzero |
| Sample h=17/20; y field | Ey/E₀ | 2/((17/20)*sqrt(1+(17/20)^2)) | 1.79279839473 | 1.79279839472813964151784817054489915831571653280700675595350015263528245103775647446038396577090708802564503536123629433e+0 | Nonzero |
| Sample h=17/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (17/20)/sqrt(1+(17/20)^2) | 0.647648420096 | 6.47648420095540445498322651609344820941552597476531190588201930139495785437389526398813707634740185549264269024246611328e-1 | Nonzero |
| Sample h=17/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(17/20)^2) | 0.761939317759 | 7.61939317759459347645085472481582142284179526442977871280237564869995041691046501645663185452635512410899140028525425091e-1 | Nonzero |
| Sample h=9/10; y field | Ey/E₀ | 2/((9/10)*sqrt(1+(9/10)^2)) | 1.65176476944 | 1.65176476943814736858969741708660579421374614923512833335794810108263213240348537977868036277828837580901567384799055996e+0 | Nonzero |
| Sample h=9/10; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (9/10)/sqrt(1+(9/10)^2) | 0.668964731622 | 6.68964731622449684278827453920075346656567190440226975009968980938466013623411578810365546925206792202651347908436176784e-1 | Nonzero |
| Sample h=9/10; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(9/10)^2) | 0.743294146247 | 7.43294146247166315865363837688972607396185767155807750011076645487184459581568420900406163250229769114057053231595751982e-1 | Nonzero |
| Sample h=19/20; y field | Ey/E₀ | 2/((19/20)*sqrt(1+(19/20)^2)) | 1.52631459704 | 1.52631459704087106623147912078040176094355157829564349065497274368808836692946464364492015661788391580712510127195219362e+0 | Nonzero |
| Sample h=19/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (19/20)/sqrt(1+(19/20)^2) | 0.688749461915 | 6.88749461914693068636954953252156294625777649705909125158056450589249875576920920444770220673820117007965201948968427373e-1 | Nonzero |
| Sample h=19/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(19/20)^2) | 0.724999433594 | 7.24999433594413756459952582370690836448186999690430658061112053251841974291495705731337074393494860008384423104177291971e-1 | Nonzero |
| Sample h=1; y field | Ey/E₀ | 2/((1)*sqrt(1+(1)^2)) | 1.41421356237 | 1.41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702e+0 | Nonzero |
| Sample h=1; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (1)/sqrt(1+(1)^2) | 0.707106781187 | 7.07106781186547524400844362104849039284835937688474036588339868995366239231053519425193767163820786367506923115456148512e-1 | Nonzero |
| Sample h=1; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(1)^2) | 0.707106781187 | 7.07106781186547524400844362104849039284835937688474036588339868995366239231053519425193767163820786367506923115456148512e-1 | Nonzero |
| Sample h=21/20; y field | Ey/E₀ | 2/((21/20)*sqrt(1+(21/20)^2)) | 1.31362889984 | 1.31362889983579638752052545155993431855500821018062397372742200328407224958949096880131362889983579638752052545155993432e+0 | Nonzero |
| Sample h=21/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (21/20)/sqrt(1+(21/20)^2) | 0.724137931034 | 7.24137931034482758620689655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793e-1 | Nonzero |
| Sample h=21/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(21/20)^2) | 0.689655172414 | 6.89655172413793103448275862068965517241379310344827586206896551724137931034482758620689655172413793103448275862068965517e-1 | Nonzero |
| Sample h=11/10; y field | Ey/E₀ | 2/((11/10)*sqrt(1+(11/10)^2)) | 1.22304144363 | 1.22304144362965903106639310686395694376379971318147770963085930154272622910581387565741147349024772527554030734574707651e+0 | Nonzero |
| Sample h=11/10; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (11/10)/sqrt(1+(11/10)^2) | 0.739940073396 | 7.39940073395943713795167829652693950977098826474794014326669877433349368609017394772733941461599873791701885944176981287e-1 | Nonzero |
| Sample h=11/10; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(11/10)^2) | 0.672672793996 | 6.72672793996312467086516208775176319070089842249812740296972615848499426008197631611576310419636248901547169040160892080e-1 | Nonzero |
| Sample h=23/20; y field | Ey/E₀ | 2/((23/20)*sqrt(1+(23/20)^2)) | 1.14118037378 | 1.14118037378223769207127509991905198732954785837954272674593135465189825586564657679947766839125405380013975012838899901e+0 | Nonzero |
| Sample h=23/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (23/20)/sqrt(1+(23/20)^2) | 0.754605522164 | 7.54605522163504673882130659821473126621663521353472628060747108263567721691158798908654608223716743075342409772397225593e-1 | Nonzero |
| Sample h=23/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(23/20)^2) | 0.656178714925 | 6.56178714924786672940983182453454892714490018568237067878910528924841497122746781659699659324971080935080356323823674428e-1 | Nonzero |
| Sample h=6/5; y field | Ey/E₀ | 2/((6/5)*sqrt(1+(6/5)^2)) | 1.06697399944 | 1.06697399944079978061881458138785538436725480008860154374006062297688327717714850470292801260478208950558765501603925034e+0 | Nonzero |
| Sample h=6/5; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (6/5)/sqrt(1+(6/5)^2) | 0.768221279597 | 7.68221279597375842045546498599255876744423456063793111492843648543355959567546923386108169075443104444023111611548260244e-1 | Nonzero |
| Sample h=6/5; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(6/5)^2) | 0.640184399664 | 6.40184399664479868371288748832713230620352880053160926244036373786129966306289102821756807562869253703352593009623550203e-1 | Nonzero |
| Sample h=5/4; y field | Ey/E₀ | 2/((5/4)*sqrt(1+(5/4)^2)) | 0.999512076087 | 9.99512076087078819354258368721453777876358264604256606521642556357960235425853826230533354497540677177882822634739072509e-1 | Nonzero |
| Sample h=5/4; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (5/4)/sqrt(1+(5/4)^2) | 0.780868809443 | 7.80868809443030327620514350563635763965904894222075473845033247154656433926448301742604183201203654045220955183389900398e-1 | Nonzero |
| Sample h=5/4; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(5/4)^2) | 0.624695047554 | 6.24695047554424262096411480450908611172723915377660379076026597723725147141158641394083346560962923236176764146711920318e-1 | Nonzero |
| Sample h=13/10; y field | Ey/E₀ | 2/((13/10)*sqrt(1+(13/10)^2)) | 0.938016555153 | 9.38016555153372900376020201738203294844860983060479660961542211017469271656663484614628608139548793645950489710148158459e-1 | Nonzero |
| Sample h=13/10; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (13/10)/sqrt(1+(13/10)^2) | 0.792623989105 | 7.92623989104600100817737070468781784143907530686105313512503168309761534549880644499361173877918730630828163805075193898e-1 | Nonzero |
| Sample h=13/10; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(13/10)^2) | 0.609710760850 | 6.09710760849692385244413131129832141649159638989311779625002437161355026576831264999508595290706715869867818311596302998e-1 | Nonzero |
| Sample h=27/20; y field | Ey/E₀ | 2/((27/20)*sqrt(1+(27/20)^2)) | 0.881818593520 | 8.81818593519611198810303433899856079738421845374336780701616705291458638741498231663297297347886864516420405074712600992e-1 | Nonzero |
| Sample h=27/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (27/20)/sqrt(1+(27/20)^2) | 0.803557193345 | 8.03557193344745704915889004141243852661636906597364391414348222696841684553190263603179662208261905290588094124331857654e-1 | Nonzero |
| Sample h=27/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(27/20)^2) | 0.595227550626 | 5.95227550625737559196954817882402853823434745627677326973591276071734581150511306372725675709823633548583773425431005670e-1 | Nonzero |
| Sample h=7/5; y field | Ey/E₀ | 2/((7/5)*sqrt(1+(7/5)^2)) | 0.830340276742 | 8.30340276741566290707478140448814057145515015182503438176452281972724607592955310114221128445845759111600710288343865699e-1 | Nonzero |
| Sample h=7/5; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (7/5)/sqrt(1+(7/5)^2) | 0.813733471207 | 8.13733471206734964893328577639837776002604714878853369412923236333270115441096203911936705876928843929368696082576988385e-1 | Nonzero |
| Sample h=7/5; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(7/5)^2) | 0.581238193719 | 5.81238193719096403495234698314169840001860510627752406723516597380907225315068717079954789912092031378120497201840705989e-1 | Nonzero |
| Sample h=29/20; y field | Ey/E₀ | 2/((29/20)*sqrt(1+(29/20)^2)) | 0.783079939040 | 7.83079939039530394740024426536913615208871644747298154576729882975216529088550091369526076535546930192414365814083599735e-1 | Nonzero |
| Sample h=29/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (29/20)/sqrt(1+(29/20)^2) | 0.823212785915 | 8.23212785915306327470450678396930437988326316540597184998787289477696376204338283552214287957993710364775602062055384221e-1 | Nonzero |
| Sample h=29/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(29/20)^2) | 0.567732955804 | 5.67732955803659536186517709239262371026431942441791162068129165157031983589198816242906405488271524389500415215210609808e-1 | Nonzero |
| Sample h=3/2; y field | Ey/E₀ | 2/((3/2)*sqrt(1+(3/2)^2)) | 0.739600261634 | 7.39600261633638829357788977942665835128471092070819735940605755123521425290873937477870580926869890804823421953654059564e-1 | Nonzero |
| Sample h=3/2; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (3/2)/sqrt(1+(3/2)^2) | 0.832050294338 | 8.32050294337843683027512600185499064519529978579672202933181474513961603452233179662604403542728627155426349697860817010e-1 | Nonzero |
| Sample h=3/2; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(3/2)^2) | 0.554700196225 | 5.54700196225229122018341733456999376346353319053114801955454316342641068968155453108402935695152418103617566465240544673e-1 | Nonzero |
| Sample h=31/20; y field | Ey/E₀ | 2/((31/20)*sqrt(1+(31/20)^2)) | 0.699518541706 | 6.99518541705926560347123461496916943223449898786795498437795828446046960299563167409406369817998622138217084977154009838e-1 | Nonzero |
| Sample h=31/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (31/20)/sqrt(1+(31/20)^2) | 0.840296648224 | 8.40296648224244280616982058123171478047169190917638092498402238920813911059850254850549401743870844843533273328806254318e-1 | Nonzero |
| Sample h=31/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(31/20)^2) | 0.542126869822 | 5.42126869822093084269020682660110630998173671559766511289291767045686394232161454742289936608948932157118240857294357625e-1 | Nonzero |
| Sample h=8/5; y field | Ey/E₀ | 2/((8/5)*sqrt(1+(8/5)^2)) | 0.662498675004 | 6.62498675003974986750046374833050612147726308526342789372400382653091496459629077144735041214212366891503720104055468749e-1 | Nonzero |
| Sample h=8/5; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (8/5)/sqrt(1+(8/5)^2) | 0.847998304005 | 8.47998304005087983040059359786304783549089674913718770396672489795957115468325218745260852754191829621124761733190999998e-1 | Nonzero |
| Sample h=8/5; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(8/5)^2) | 0.529998940003 | 5.29998940003179989400037099866440489718181046821074231497920306122473197167703261715788032971369893513202976083244374999e-1 | Nonzero |
| Sample h=33/20; y field | Ey/E₀ | 2/((33/20)*sqrt(1+(33/20)^2)) | 0.628244504356 | 6.28244504355568727418742897194086420262867524262085520855117549501408609636605551734011352692999369706873153356766512800e-1 | Nonzero |
| Sample h=33/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (33/20)/sqrt(1+(33/20)^2) | 0.855197831554 | 8.55197831554017930198763768805450139582828417401763915264028764258792469867829307297922953853345392013481080006898415549e-1 | Nonzero |
| Sample h=33/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(33/20)^2) | 0.518301716093 | 5.18301716093344200120462890185121296716865707516220554705471978338662102950199580180559365971724480008170351519332373060e-1 | Nonzero |
| Sample h=17/10; y field | Ey/E₀ | 2/((17/10)*sqrt(1+(17/10)^2)) | 0.596494266545 | 5.96494266545169211192015698873364699825569877799762058878391765032727003853613793909756674473319788369087298097245490736e-1 | Nonzero |
| Sample h=17/10; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (17/10)/sqrt(1+(17/10)^2) | 0.861934215158 | 8.61934215157769510172462684872011991247948473420656175079276100472290520568471932199598394613947094193331145750519734113e-1 | Nonzero |
| Sample h=17/10; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(17/10)^2) | 0.507020126563 | 5.07020126563393829513213344042359994851734396129797750046633000277817953275571724823293173302321820113724203382658667125e-1 | Nonzero |
| Sample h=7/4; y field | Ey/E₀ | 2/((7/4)*sqrt(1+(7/4)^2)) | 0.567015929551 | 5.67015929550667228298311260153232255376485014899943622887848255948228567984224225263131728648244792519556393223029163057e-1 | Nonzero |
| Sample h=7/4; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (7/4)/sqrt(1+(7/4)^2) | 0.868243142124 | 8.68243142124459193331789117109636891045242679065538672547017641920724994725843344934170459492624838545570727122763405931e-1 | Nonzero |
| Sample h=7/4; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(7/4)^2) | 0.496138938357 | 4.96138938356833824761022352634078223454424388037450670026867223954699996986196197105240262567214193454611844070150517675e-1 | Nonzero |
| Sample h=9/5; y field | Ey/E₀ | 2/((9/5)*sqrt(1+(9/5)^2)) | 0.539603256865 | 5.39603256865146767075333829360458594271425651126412836595629247452728623060680753355846593991486666743445011916211432781e-1 | Nonzero |
| Sample h=9/5; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (9/5)/sqrt(1+(9/5)^2) | 0.874157276122 | 8.74157276121537762662040803563942922719709554824788795284919380873420369358302820436471482266208400124380919304262521105e-1 | Nonzero |
| Sample h=9/5; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(9/5)^2) | 0.485642931179 | 4.85642931178632090367800446424412734844283086013771552936066322707455760754612678020261934592338000069100510724590289503e-1 | Nonzero |
| Sample h=37/20; y field | Ey/E₀ | 2/((37/20)*sqrt(1+(37/20)^2)) | 0.514072469584 | 5.14072469584296287435115767348310888636673704984293771562033669496879719108264828457445543535439043982972896642657709784e-1 | Nonzero |
| Sample h=37/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (37/20)/sqrt(1+(37/20)^2) | 0.879706513576 | 8.79706513576127021873341856874797008179507877654372716585530116926535419324018187697803686375020064015862369379748005868e-1 | Nonzero |
| Sample h=37/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(37/20)^2) | 0.475517034365 | 4.75517034365474065877482084797187571988923177110471738694881144284613740175144966323137127770281115684249929394458381550e-1 | Nonzero |
| Sample h=19/10; y field | Ey/E₀ | 2/((19/10)*sqrt(1+(19/10)^2)) | 0.490259402982 | 4.90259402981707694239289845439868070911230471518062994505809719547056079675819043110554437403409588077420703660529720443e-1 | Nonzero |
| Sample h=19/10; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (19/10)/sqrt(1+(19/10)^2) | 0.884918222382 | 8.84918222381982388101918171018961867994771001090103705082986543782436223814853372814550759513154306479744370107256145400e-1 | Nonzero |
| Sample h=19/10; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(19/10)^2) | 0.465746432833 | 4.65746432832622309527325353167874667365668947942159844780519233569703275692028090955026715533239108673549668477503234421e-1 | Nonzero |
| Sample h=39/20; y field | Ey/E₀ | 2/((39/20)*sqrt(1+(39/20)^2)) | 0.468017074458 | 4.68017074457718349832747803341687912687876939737386220389104342395236294944453422035946171721439679866050888254961670419e-1 | Nonzero |
| Sample h=39/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (39/20)/sqrt(1+(39/20)^2) | 0.889817462813 | 8.89817462812737012619511761103384143997826031675705551514784630978943005763142068645842658985387191345329251294745875884e-1 | Nonzero |
| Sample h=39/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(39/20)^2) | 0.456316647596 | 4.56316647596275391086929108258145714870680016243951564879376733835355387570842086485047517428403687869399616048587628659e-1 | Nonzero |
| Sample h=2; y field | Ey/E₀ | 2/((2)*sqrt(1+(2)^2)) | 0.447213595500 | 4.47213595499957939281834733746255247088123671922305144854179449082104185127560979882882881675756454993901635230154756701e-1 | Nonzero |
| Sample h=2; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (2)/sqrt(1+(2)^2) | 0.894427191000 | 8.94427190999915878563669467492510494176247343844610289708358898164208370255121959765765763351512909987803270460309513402e-1 | Nonzero |
| Sample h=2; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(2)^2) | 0.447213595500 | 4.47213595499957939281834733746255247088123671922305144854179449082104185127560979882882881675756454993901635230154756701e-1 | Nonzero |
| Sample h=41/20; y field | Ey/E₀ | 2/((41/20)*sqrt(1+(41/20)^2)) | 0.427730372704 | 4.27730372703818980697939489177963271808614572593913613988845070080803624827322546473977017686846564796132799864468555855e-1 | Nonzero |
| Sample h=41/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (41/20)/sqrt(1+(41/20)^2) | 0.898768445644 | 8.98768445643899633191545351635195324887851370662960981394060703507288616668411500778444208414486344277874045715214552991e-1 | Nonzero |
| Sample h=41/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(41/20)^2) | 0.438423632021 | 4.38423632021414455215387976407412353603829936908761454338566196832823715448005610135826443129017728916036119861080269752e-1 | Nonzero |
| Sample h=21/10; y field | Ey/E₀ | 2/((21/10)*sqrt(1+(21/10)^2)) | 0.409460552755 | 4.09460552754616925209862613263007764076998706916347922533442015225432639462396044355396429454307339035803616992531128839e-1 | Nonzero |
| Sample h=21/10; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (21/10)/sqrt(1+(21/10)^2) | 0.902860518824 | 9.02860518823930320087747062244932119789782148750547169186239643572078970014583277803649126946747682573946975468531139089e-1 | Nonzero |
| Sample h=21/10; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(21/10)^2) | 0.429933580392 | 4.29933580392347771470355743926158152280848642262165318660114115986704271435515846573166250927022705987593797842157685281e-1 | Nonzero |
| Sample h=43/20; y field | Ey/E₀ | 2/((43/20)*sqrt(1+(43/20)^2)) | 0.392307674154 | 3.92307674154032325153488052942241299298206573774741205546291000476088794720309680831785889625638317972673490207771766773e-1 | Nonzero |
| Sample h=43/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (43/20)/sqrt(1+(43/20)^2) | 0.906721111889 | 9.06721111888507211510999262362755203002979943636870611318865074850360226797315749822465137397256562414341604242712495953e-1 | Nonzero |
| Sample h=43/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(43/20)^2) | 0.421730749716 | 4.21730749715584749539999656912909396745572066807846795962262825511795454324332906894169831347561191820624001973354649281e-1 | Nonzero |
| Sample h=11/5; y field | Ey/E₀ | 2/((11/5)*sqrt(1+(11/5)^2)) | 0.376184494819 | 3.76184494819258159037448295977828633197574271283325224868001775603755691700320294591312951852457436911309754155551023099e-1 | Nonzero |
| Sample h=11/5; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (11/5)/sqrt(1+(11/5)^2) | 0.910366477463 | 9.10366477462604744870624876266345292338129736505647044180564296961088773914775112910977343482946997325369605056433475899e-1 | Nonzero |
| Sample h=11/5; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(11/5)^2) | 0.413802944301 | 4.13802944301183974941193125575611496517331698411657747354801953164131260870352324050444247037703180602440729571106125409e-1 | Nonzero |
| Sample h=9/4; y field | Ey/E₀ | 2/((9/4)*sqrt(1+(9/4)^2)) | 0.361011969825 | 3.61011969825286771014752308450588755342813701257924918092944954129170788864428082660919158180634163113424098927715892773e-1 | Nonzero |
| Sample h=9/4; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (9/4)/sqrt(1+(9/4)^2) | 0.913811548620 | 9.13811548620257139131091780765552786961497181309122448922766915139463559313083584235451619144730225380854750410780853582e-1 | Nonzero |
| Sample h=9/4; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(9/4)^2) | 0.406138466053 | 4.06138466053447617391596347006912349760665413915165532854563073395317137472481592993534052953213433502602111293680379370e-1 | Nonzero |
| Sample h=23/10; y field | Ey/E₀ | 2/((23/10)*sqrt(1+(23/10)^2)) | 0.346718357752 | 3.46718357751695651843470205783969712707776866582137114707536164972446073126298889185735220033792032688688149923665215346e-1 | Nonzero |
| Sample h=23/10; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (23/10)/sqrt(1+(23/10)^2) | 0.917070056253 | 9.17070056253234999125978694298599890112069812109752668401433156352119863419060561896269656989379926461580156548094494590e-1 | Nonzero |
| Sample h=23/10; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(23/10)^2) | 0.398726111414 | 3.98726111414449999619990736651565169613943396569457681913666589718312984095243722563595503038860837591991372412214997648e-1 | Nonzero |
| Sample h=47/20; y field | Ey/E₀ | 2/((47/20)*sqrt(1+(47/20)^2)) | 0.333238437530 | 3.33238437529589299095844988212636483789876392302321133676801793318074496285282859161947953289833365683554864077704916797e-1 | Nonzero |
| Sample h=47/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (47/20)/sqrt(1+(47/20)^2) | 0.920154635629 | 9.20154635628578452128401973702142490864796188244784230365068951799533202867737294860928786021552380993715868434562701507e-1 | Nonzero |
| Sample h=47/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(47/20)^2) | 0.391555164097 | 3.91555164097267426437617861149847868453104760955227332070242107148737533135207359515288845115554204678176965291303277237e-1 | Nonzero |
| Sample h=12/5; y field | Ey/E₀ | 2/((12/5)*sqrt(1+(12/5)^2)) | 0.320512820513 | 3.20512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820512820513e-1 | Nonzero |
| Sample h=12/5; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (12/5)/sqrt(1+(12/5)^2) | 0.923076923077 | 9.23076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923076923077e-1 | Nonzero |
| Sample h=12/5; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(12/5)^2) | 0.384615384615 | 3.84615384615384615384615384615384615384615384615384615384615384615384615384615384615384615384615384615384615384615384615e-1 | Nonzero |
| Sample h=49/20; y field | Ey/E₀ | 2/((49/20)*sqrt(1+(49/20)^2)) | 0.308487344838 | 3.08487344838050350363257202038327980067983905292351442986744501914427839878463892598392096092995801069343680301652471048e-1 | Nonzero |
| Sample h=49/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (49/20)/sqrt(1+(49/20)^2) | 0.925847643695 | 9.25847643695198614027725677617531850179036695758669768263966936370676554435239757660924278399103647959367720505334478734e-1 | Nonzero |
| Sample h=49/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(49/20)^2) | 0.377896997427 | 3.77896997426611679194990072496951775583280283983130517658762014845174103851118268433030317713919856309946008369524277034e-1 | Nonzero |
| Sample h=5/2; y field | Ey/E₀ | 2/((5/2)*sqrt(1+(5/2)^2)) | 0.297112541083 | 2.97112541083282981034521958153949216899041112366609039320297305931952880707732893400090139678887475002411300512769421275e-1 | Nonzero |
| Sample h=5/2; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (5/2)/sqrt(1+(5/2)^2) | 0.928476690885 | 9.28476690885259315732881119231091302809503476145653247875929081037352752211665291875281686496523359382535314102404441484e-1 | Nonzero |
| Sample h=5/2; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(5/2)^2) | 0.371390676354 | 3.71390676354103726293152447692436521123801390458261299150371632414941100884666116750112674598609343753014125640961776594e-1 | Nonzero |
| Sample h=51/20; y field | Ey/E₀ | 2/((51/20)*sqrt(1+(51/20)^2)) | 0.286343159858 | 2.86343159857612696539837645439438003476205185271325811389281309334711789780961070247568825249075084957419530629728775010e-1 | Nonzero |
| Sample h=51/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (51/20)/sqrt(1+(51/20)^2) | 0.930973198487 | 9.30973198487063279625147144734972808802012108613398044279400856974481706525349679642408143091055369967810248959905679752e-1 | Nonzero |
| Sample h=51/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(51/20)^2) | 0.365087528818 | 3.65087528818456188088292997935283454432161611220940409521333669401757531970725364565650252192570733320709901552904188138e-1 | Nonzero |
| Sample h=13/5; y field | Ey/E₀ | 2/((13/5)*sqrt(1+(13/5)^2)) | 0.276137753315 | 2.76137753314514657780883008098994720582759643261554442292630331882354286190845193564228740598981393300463355032889065962e-1 | Nonzero |
| Sample h=13/5; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (13/5)/sqrt(1+(13/5)^2) | 0.933345606203 | 9.33345606203059543299384567374602155569727594224054014949090521762357487325056754247093143224557109355566140011165042952e-1 | Nonzero |
| Sample h=13/5; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(13/5)^2) | 0.358979079309 | 3.58979079308869055115147910528693136757587536240020774980419431447060572048098751633497362778675811290602361542755785751e-1 | Nonzero |
| Sample h=53/20; y field | Ey/E₀ | 2/((53/20)*sqrt(1+(53/20)^2)) | 0.266458303724 | 2.66458303723956494093037681623331517989474283734604609210677761086530593274661623528656454133862385557361494876126838770e-1 | Nonzero |
| Sample h=53/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (53/20)/sqrt(1+(53/20)^2) | 0.935601718951 | 9.35601718950742239884178559599922792540541578763130434090992288615080545635655625614994974577524301288285548883800362630e-1 | Nonzero |
| Sample h=53/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(53/20)^2) | 0.353057252434 | 3.53057252434242354673274928150914261336053425948351107204148033439653036088926651175469801727367660863503980710868061370e-1 | Nonzero |
| Sample h=27/10; y field | Ey/E₀ | 2/((27/10)*sqrt(1+(27/10)^2)) | 0.257269893203 | 2.57269893202662177701619574229565437069479970725361493866050967710657489421470366547652737659639938777572439777035271048e-1 | Nonzero |
| Sample h=27/10; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (27/10)/sqrt(1+(27/10)^2) | 0.937748760724 | 9.37748760723703637722403348066766018118254493293942645141755777305346548941259486066194228769387576844251542987293562971e-1 | Nonzero |
| Sample h=27/10; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(27/10)^2) | 0.347314355824 | 3.47314355823593939897186425209913340043797960479238016719168806409387610718984994839331195840513917349722793698997615915e-1 | Nonzero |
| Sample h=11/4; y field | Ey/E₀ | 2/((11/4)*sqrt(1+(11/4)^2)) | 0.248540409518 | 2.48540409517603187452732013785876492927900422418725364080373354844130000842744941447889694173269865542414816531871339620e-1 | Nonzero |
| Sample h=11/4; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (11/4)/sqrt(1+(11/4)^2) | 0.939793423488 | 9.39793423488437052555642927127845488883623472270805282928911748004366565686629309849832906092676679082256025011138502936e-1 | Nonzero |
| Sample h=11/4; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(11/4)^2) | 0.341743063087 | 3.41743063086704382747506518955580177775863080825747375610513362910678751158774294490848329488246065120820372731323091977e-1 | Nonzero |
| Sample h=14/5; y field | Ey/E₀ | 2/((14/5)*sqrt(1+(14/5)^2)) | 0.240240283570 | 2.40240283570111595388041503133991542525032086517790264391775934231606937860070582718420110864155803179123988942914604314e-1 | Nonzero |
| Sample h=14/5; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (14/5)/sqrt(1+(14/5)^2) | 0.941741911595 | 9.41741911594837453921122692285246846698125779149737836415761662187899196411476684256206834587490748462166036656225248911e-1 | Nonzero |
| Sample h=14/5; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(14/5)^2) | 0.336336396998 | 3.36336396998156233543258104387588159535044921124906370148486307924249713004098815805788155209818124450773584520080446040e-1 | Nonzero |
| Sample h=57/20; y field | Ey/E₀ | 2/((57/20)*sqrt(1+(57/20)^2)) | 0.232342254757 | 2.32342254757249806912883511313832982987765121682159316005241725254506903785390374455732261551162139588433949272824777329e-1 | Nonzero |
| Sample h=57/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (57/20)/sqrt(1+(57/20)^2) | 0.943599982133 | 9.43599982132880778324948160323304202159061100431669522126287956689866162998416658258342647224657239403527376484259626927e-1 | Nonzero |
| Sample h=57/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(57/20)^2) | 0.331087713029 | 3.31087713029080974850859003622212000757565298397077025307469458487672337894181283599418472710406048913518377713775307694e-1 | Nonzero |
| Sample h=29/10; y field | Ey/E₀ | 2/((29/10)*sqrt(1+(29/10)^2)) | 0.224821160910 | 2.24821160909933927373909741705035022552315526075466065045169838321649551828729878380798948921379228364847039298080130839e-1 | Nonzero |
| Sample h=29/10; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (29/10)/sqrt(1+(29/10)^2) | 0.945372981626 | 9.45372981626272164607290463869672269832486787147334803514939170142536365439809138591259580214399655274181800248426950176e-1 | Nonzero |
| Sample h=29/10; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(29/10)^2) | 0.325990683319 | 3.25990683319404194692169125472300782700857512809425794315496265566391850151658323652158475935999881129028206982216189716e-1 | Nonzero |
| Sample h=59/20; y field | Ey/E₀ | 2/((59/20)*sqrt(1+(59/20)^2)) | 0.217653749938 | 2.17653749937557878687779296298655346797016625466735528963612827503645094403886114294946027576014578030367929759668590326e-1 | Nonzero |
| Sample h=59/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (59/20)/sqrt(1+(59/20)^2) | 0.947065879416 | 9.47065879415798719640199663019524077750518591562132970402920315675235717024909454825883902490133432654638454366757953654e-1 | Nonzero |
| Sample h=59/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(59/20)^2) | 0.321039281158 | 3.21039281157897871064474462040516636525599522563434905221328920567876514245732018585045390674621502594792696395511170730e-1 | Nonzero |
| Sample h=3; y field | Ey/E₀ | 2/((3)*sqrt(1+(3)^2)) | 0.210818510678 | 2.10818510677891955466592902962181235581303675955014455123833656852839629242615881422949873891953353012489818943522670343e-1 | Nonzero |
| Sample h=3; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (3)/sqrt(1+(3)^2) | 0.948683298051 | 9.48683298050513799599668063329815560115866541797565048057251455837778331591771466403274432513790088556204185245852016545e-1 | Nonzero |
| Sample h=3; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(3)^2) | 0.316227766017 | 3.16227766016837933199889354443271853371955513932521682685750485279259443863923822134424810837930029518734728415284005515e-1 | Nonzero |
| Sample h=61/20; y field | Ey/E₀ | 2/((61/20)*sqrt(1+(61/20)^2)) | 0.204295520768 | 2.04295520768287606186836779833748779713896696532419313651131379572106226073415907690123104479023636893276413826823605888e-1 | Nonzero |
| Sample h=61/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (61/20)/sqrt(1+(61/20)^2) | 0.950229540973 | 9.50229540973497728276524572201724011644262009746415332619824829234759084023975740643685089708058691099851919812013296886e-1 | Nonzero |
| Sample h=61/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(61/20)^2) | 0.311550669172 | 3.11550669171638599434926089246466889063692462211939453317975353847461994761959259227437734330511046262246531085905998979e-1 | Nonzero |
| Sample h=31/10; y field | Ey/E₀ | 2/((31/10)*sqrt(1+(31/10)^2)) | 0.198066309628 | 1.98066309627586037322245508808799658858457682766777724304923875287013345261013395192268807070174147590059367836449928730e-1 | Nonzero |
| Sample h=31/10; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (31/10)/sqrt(1+(31/10)^2) | 0.951708617761 | 9.51708617760550909333389669826282360814889165694366965285159220754099123979169363898851617972186779170235262454141907546e-1 | Nonzero |
| Sample h=31/10; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(31/10)^2) | 0.307002779923 | 3.07002779922758357849480538653639471230609408288505472672632006694870685154570762548016650958769928764592020146497389531e-1 | Nonzero |
| Sample h=63/20; y field | Ey/E₀ | 2/((63/20)*sqrt(1+(63/20)^2)) | 0.192113734874 | 1.92113734874183448130609828487300773375015328833588411240977259692201197447367076695258070035414582665967557243119167002e-1 | Nonzero |
| Sample h=63/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (63/20)/sqrt(1+(63/20)^2) | 0.953124267145 | 9.53124267144542632037988011582620961906794800175640505269298429647933190835749909254349099963200598251531543372424967291e-1 | Nonzero |
| Sample h=63/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(63/20)^2) | 0.302579132427 | 3.02579132426838930805710479867498718065649142912901747704539184015216885979603145795031460305777967698898902657912688029e-1 | Nonzero |
| Sample h=16/5; y field | Ey/E₀ | 2/((16/5)*sqrt(1+(16/5)^2)) | 0.186421870710 | 1.86421870709966749649084692576913620536039646213816671177218789883494128764849500223327617637719313402203141843688051978e-1 | Nonzero |
| Sample h=16/5; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (16/5)/sqrt(1+(16/5)^2) | 0.954479978035 | 9.54479978035029758203313625993797737144522988614741356427360204203489939276029441143437402305122884619280086239682826129e-1 | Nonzero |
| Sample h=16/5; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(16/5)^2) | 0.298274993136 | 2.98274993135946799438535508123061792857663433942106673883550063813590606023759200357324188220350901443525026949900883165e-1 | Nonzero |
| Sample h=13/4; y field | Ey/E₀ | 2/((13/4)*sqrt(1+(13/4)^2)) | 0.180975906977 | 1.80975906976937291908922243619890403698877411530215588622920089600590419696168420486596193691966830564742170781811028514e-1 | Nonzero |
| Sample h=13/4; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (13/4)/sqrt(1+(13/4)^2) | 0.955779008722 | 9.55779008721950072893995599117546194534696329643951077414796723203118154020389470694836147935699823920044589441439494340e-1 | Nonzero |
| Sample h=13/4; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(13/4)^2) | 0.294085848838 | 2.94085848837523099351998645882321906010675793736600331512245145600959432006273683290718814749446099667706027520442921336e-1 | Nonzero |
| Sample h=33/10; y field | Ey/E₀ | 2/((33/10)*sqrt(1+(33/10)^2)) | 0.175762057747 | 1.75762057747194407292944801624156146951581494024210677800678743388817335939456777294787519486938397381658068422481809694e-1 | Nonzero |
| Sample h=33/10; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (33/10)/sqrt(1+(33/10)^2) | 0.957024404433 | 9.57024404433473547710084444843530220151361234961827140624695757752110394190342152370118043606379573743128182560413453786e-1 | Nonzero |
| Sample h=33/10; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(33/10)^2) | 0.290007395283 | 2.90007395282870772033358922679857642470109465139947618371119926591548604300103682536399407153448355679735812897094985996e-1 | Nonzero |
| Sample h=67/20; y field | Ey/E₀ | 2/((67/20)*sqrt(1+(67/20)^2)) | 0.170767478441 | 1.70767478440857748152007600349276609702299685042869475185477871940956881611084104655233480747501889841922656672548696515e-1 | Nonzero |
| Sample h=67/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (67/20)/sqrt(1+(67/20)^2) | 0.958219013401 | 9.58219013401263039317952647459878376192029107696801342634512708928694301940195682246678868844419979375488507253838873321e-1 | Nonzero |
| Sample h=67/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(67/20)^2) | 0.286035526388 | 2.86035526388436728154612730585038321251351972446806370935675435501102776698565875297516080252065665485220449926519066663e-1 | Nonzero |
| Sample h=17/5; y field | Ey/E₀ | 2/((17/5)*sqrt(1+(17/5)^2)) | 0.165980190583 | 1.65980190583264803315765502974300442588385960674685553280046081893124107563591471662847616256454588586583819659800332257e-1 | Nonzero |
| Sample h=17/5; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (17/5)/sqrt(1+(17/5)^2) | 0.959365501571 | 9.59365501571270563165124607191456558160870852699682497958666353342257341717558706211259221962307522030454477633645920443e-1 | Nonzero |
| Sample h=17/5; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(17/5)^2) | 0.282166323992 | 2.82166323991550165636801355056310752400256133146965440576078339218310982858105501826840947635972800597192493421660564836e-1 | Nonzero |
| Sample h=69/20; y field | Ey/E₀ | 2/((69/20)*sqrt(1+(69/20)^2)) | 0.161389013415 | 1.61389013414762872817822481587220041662829292548274150805487093935733715321692279247309913226110075470778722818669190402e-1 | Nonzero |
| Sample h=69/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (69/20)/sqrt(1+(69/20)^2) | 0.960466366085 | 9.60466366084607546857066043545943272945912827277916539981155067785035273308221176870553121086887586645471874174605019379e-1 | Nonzero |
| Sample h=69/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(69/20)^2) | 0.278396048140 | 2.78396048140465955610743780737954571868380529645772910139465237039140658929919181701609600315039880187093296862204353443e-1 | Nonzero |
| Sample h=7/2; y field | Ey/E₀ | 2/((7/2)*sqrt(1+(7/2)^2)) | 0.156983501656 | 1.56983501655644598837677681757995316307874278869573637485243812210978236951480435220044839009831304629490772409122540424e-1 | Nonzero |
| Sample h=7/2; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (7/2)/sqrt(1+(7/2)^2) | 0.961523947641 | 9.61523947640823167880775800767721312385729958076138529597118349792241701327817665722774638935216740855630981005875560096e-1 | Nonzero |
| Sample h=7/2; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(7/2)^2) | 0.274721127897 | 2.74721127897378047965935943076491803538779988021753865599176671369211914665090761635078468267204783101608851715964445742e-1 | Nonzero |
| Sample h=71/20; y field | Ey/E₀ | 2/((71/20)*sqrt(1+(71/20)^2)) | 0.152753888807 | 1.52753888806976981859635317462086806283330561282413820223774429157227626158420967783070962974950912930324039291046102936e-1 | Nonzero |
| Sample h=71/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (71/20)/sqrt(1+(71/20)^2) | 0.962540441845 | 9.62540441844963706943027044157974488092836699280810084685058621726980579330750123243075905445909440102204352582704256125e-1 | Nonzero |
| Sample h=71/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(71/20)^2) | 0.271138152632 | 2.71138152632384142800852688495204081152911746276284530897199611754079036431197217814950959280537870451325169741606832711e-1 | Nonzero |
| Sample h=18/5; y field | Ey/E₀ | 2/((18/5)*sqrt(1+(18/5)^2)) | 0.148691035437 | 1.48691035436719232318296875872994732340129174277377536996365562692831881997830210296686181557163405964231969925114063100e-1 | Nonzero |
| Sample h=18/5; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (18/5)/sqrt(1+(18/5)^2) | 0.963517909630 | 9.63517909629940625422563755657005865564037049317406439736448846249550595345939762722526456490418870648223165114739128887e-1 | Nonzero |
| Sample h=18/5; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(18/5)^2) | 0.267643863786 | 2.67643863786094618172934376571390518212232513699279566593458012847097387596094378534035126802894130735617545865205313580e-1 | Nonzero |
| Sample h=73/20; y field | Ey/E₀ | 2/((73/20)*sqrt(1+(73/20)^2)) | 0.144786381961 | 1.44786381960876845477506174160823454608754595382481250551938315055034028682135881218097435670318091324283647302186732574e-1 | Nonzero |
| Sample h=73/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (73/20)/sqrt(1+(73/20)^2) | 0.964458286837 | 9.64458286836890886937038002628785237012566548491553230239099101160345423558877638764051543358906385833884445591691372356e-1 | Nonzero |
| Sample h=73/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(73/20)^2) | 0.264235147079 | 2.64235147078600242996448767843502804660977136573028282257287424975437102344897983223027820098330516666817656326490786947e-1 | Nonzero |
| Sample h=37/10; y field | Ey/E₀ | 2/((37/10)*sqrt(1+(37/10)^2)) | 0.141031905483 | 1.41031905482580907221659260949219442165079622094882269532537852044232641767841495184400769951959429876378114188800484705e-1 | Nonzero |
| Sample h=37/10; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (37/10)/sqrt(1+(37/10)^2) | 0.965363393028 | 9.65363393028266309932257641197407081619970013239469134950221597242772432900875034537223270321162297503808191622339317806e-1 | Nonzero |
| Sample h=37/10; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(37/10)^2) | 0.260909025143 | 2.60909025142774678360069632756055968005397300875532198635195026281830387270506766091141424411124945271299511249280896704e-1 | Nonzero |
| Sample h=15/4; y field | Ey/E₀ | 2/((15/4)*sqrt(1+(15/4)^2)) | 0.137420080299 | 1.37420080298843916825338527399594849929316051799906415939689609511148614859966730286507632976591266789267580549198205558e-1 | Nonzero |
| Sample h=15/4; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (15/4)/sqrt(1+(15/4)^2) | 0.966234939601 | 9.66234939601246290178161520778401288565503489218091987075942566875263698234141072327006794366657344612037675736549882832e-1 | Nonzero |
| Sample h=15/4; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(15/4)^2) | 0.257662650560 | 2.57662650560332344047509738874240343617467597124824529886918017833403652862437619287201811831108625229876713529746635422e-1 | Nonzero |
| Sample h=19/5; y field | Ey/E₀ | 2/((19/5)*sqrt(1+(19/5)^2)) | 0.133943841726 | 1.33943841726128310078351195748203652139826706851613858175310215143028853606386585134231346797211732000431185899146028727e-1 | Nonzero |
| Sample h=19/5; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (19/5)/sqrt(1+(19/5)^2) | 0.967074537263 | 9.67074537262646398765695633302030368449548823468652056025739753332668323038111144669150323875868705043113162191834327411e-1 | Nonzero |
| Sample h=19/5; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(19/5)^2) | 0.254493299280 | 2.54493299279643789148867271921586939065670743018066330533089408771754821852134511755039558914702290800819253208377454582e-1 | Nonzero |
| Sample h=77/20; y field | Ey/E₀ | 2/((77/20)*sqrt(1+(77/20)^2)) | 0.130596552932 | 1.30596552932463363447041451127335255662691842832946186099086237390674666132762544725639071122114957021848665842658119133e-1 | Nonzero |
| Sample h=77/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (77/20)/sqrt(1+(77/20)^2) | 0.967883702921 | 9.67883702920719102346885954667463413530124920195672421726852876861637619376436409597892565853774475228175924726399985426e-1 | Nonzero |
| Sample h=77/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(77/20)^2) | 0.251398364395 | 2.51398364394991974635554793420120367150681797453421408240741006977048732305567898596855211910071292267058681747116879331e-1 | Nonzero |
| Sample h=39/10; y field | Ey/E₀ | 2/((39/10)*sqrt(1+(39/10)^2)) | 0.127371974496 | 1.27371974496258374427559124515852241092544547352828418379250686835122323455175960752931243026266536345886515849938996967e-1 | Nonzero |
| Sample h=39/10; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (39/10)/sqrt(1+(39/10)^2) | 0.968663866044 | 9.68663866044044937521587141943056293508801282618260121774201473381105269876613181526042103214757008910466953038786071932e-1 | Nonzero |
| Sample h=39/10; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(39/10)^2) | 0.248375350268 | 2.48375350267703830133740292805911870130461867338015415839538839328488530737593123468215923901219745874478705907381044085e-1 | Nonzero |
| Sample h=79/20; y field | Ey/E₀ | 2/((79/20)*sqrt(1+(79/20)^2)) | 0.124264236441 | 1.24264236440702799643214375510771817912909082444101694228347539122871252134550376487567117272139596571646400482333506507e-1 | Nonzero |
| Sample h=79/20; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (79/20)/sqrt(1+(79/20)^2) | 0.969416374533 | 9.69416374533032715716626146953408644493081979417048342098896239582299355714661124573632973619279027754556481762804267635e-1 | Nonzero |
| Sample h=79/20; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(79/20)^2) | 0.245421866970 | 2.45421866970388029295348391633774340377995437827100846100986389767670722965736993562945056612475703229001640952608675351e-1 | Nonzero |
| Sample h=4; y field | Ey/E₀ | 2/((4)*sqrt(1+(4)^2)) | 0.121267812518 | 1.21267812518166486759453231058061088974917624275694718658783340385145716068753576281995989729726008726016001204094533577e-1 | Nonzero |
| Sample h=4; ratio to the total-charge far form | (Ey/E₀)/(2/h²) | (4)/sqrt(1+(4)^2) | 0.970142500145 | 9.70142500145331894075625848464488711799340994205557749270266723081165728550028610255967917837808069808128009632756268615e-1 | Nonzero |
| Sample h=4; ratio to the local infinite-line form | (Ey/E₀)/(2/h) | 1/sqrt(1+(4)^2) | 0.242535625036 | 2.42535625036332973518906462116122177949835248551389437317566680770291432137507152563991979459452017452032002408189067154e-1 | Nonzero |
The diagrams and tables scroll within their own keyboard-focusable regions.
| h | Eᵧ/E₀ |
|---|---|
| 1/2 | 8/√5 |
| 3/4 | 32/15 |
| 1 | √2 |
| 4/3 | 9/10 |
| 2 | 1/√5 |
| 4 | 1/(2√17) |
Check units, sign and near and far limits
The segment field is upward for h > 0, as expected for a positive line below the observation point. E₀ supplies units N/C; h and the remaining factor are dimensionless. Reflection to negative y would reverse the y field, but the displayed formula was derived with the explicitly positive parameter h.
Far from the segment, h ≫ 1, √(1 + h²) is approximately h. Thus Eᵧ/E₀ is approximately 2/h². This agrees with the leading field of total charge 2q₀ at a distance hL₀, provided the observation distance is large compared with the segment's length scale.
For 0 < h ≪ 1, the same expression is approximately 2/h. In dimensional form this is 2kₑλ/y for positive y = hL₀, the local infinite-line form away from the endpoints. It is an approximation in a specified distance regime, not permission to replace the entire finite segment by an infinite line at all distances.
The divergence as h approaches zero belongs to the zero-thickness continuous line idealization. A real wire has cross-sectional structure and a microscopic charge distribution. Those can matter before the mathematical singular limit is reached. Our displayed samples use 1/2 ≤ h ≤ 4; statements about smaller or larger h are analytic limits rather than additional plotted data.
A calculation you can audit
Start by listing the actual sources, their signed charges or densities and their positions or support. State the observation point and the regime. Then form each source-to-observation displacement, reject source coincidences, calculate components and add them. Convert to a force only after choosing the recipient charge.
Check dimensions, reflection symmetries, directions and a few exact control values before trusting a dense diagram. Keep cancellation checks separate from rounded output. Our literal model retains exact rational or radical expressions alongside high-precision values; twelve significant digits are a display convention, not a measurement-accuracy claim.
Near a cancellation point, two large contributions can leave a small difference. Small input changes may then produce a large relative change in the resultant, even when each source contribution changes little. If the true result is zero, relative error measured against that zero is not a useful finite accuracy measure; state an absolute scale instead.
Near an ideal source, very small separations can dominate the sum. A tiny plotting cell or a clipped arrow does not make that regime physically resolved. Before adding more digits or more samples, ask whether the source geometry, charge uncertainty and idealizations support the claimed interpretation.
Return path: far fields and the meaning of linearity
For a localized source distribution, a distant observation point can admit an expansion in source size divided by observation distance. If total charge Q is nonzero, the leading electrostatic field is the monopole field kₑQ r̂/r², measured from a fixed origin within the localized-source region. Corrections depend on the source moments and require the distance to be large compared with that region.
Our A/B arrangement has Q = +3q₀. It is not a neutral dipole. A separately defined pair +q and −q has zero total charge, so its monopole term cancels; its leading far electric field is usually a dipole term of order 1/r³ when its dipole moment is nonzero. Neither statement justifies replacing the exact nearby field by its far-field form.
For a charge distribution built by combining measures dq₁ and dq₂, the vacuum integral is linear: E[dq₁ + dq₂] = E[dq₁] + E[dq₂] on a common domain where the expressions are defined. This is the continuous version of vector superposition. It does not say that every material response, source-generation process or measurement is linear.
A continuum approximation also separates scales. A smooth density may describe fields at distances large compared with microscopic charge spacing, while microscopic fluctuations remain important near individual particles. Refining a smooth-density numerical mesh cannot restore microscopic information that the source model never contained.
Keep the static model inside its domain
For time-dependent sources, the electromagnetic field must respect finite propagation and the coupled electric and magnetic field equations. In general, a changed source cannot update an arbitrary distant observation point instantaneously. Summing static Coulomb kernels evaluated at simultaneous source positions is therefore not a general solution for moving or varying sources.
A quasistatic approximation can be useful when its spatial and time scales justify neglecting appropriate propagation effects, but those scales and neglected terms must be stated. No such moving-source approximation is used in the present prescribed stationary examples.
For a moving probe, the magnetic contribution to the Lorentz force may also matter. The force rule F = qE used here concerns a stationary ideal probe, or a setting where the magnetic contribution is separately shown negligible. It is not a replacement for the full electromagnetic force law in every situation.
The next flux and Gauss-law lesson will organize fields by surfaces and symmetry. The later potential lesson will connect fields with work and spatial derivatives, followed by conductor and material response. Those tools complement superposition; they do not remove the need to specify the sources and choose the correct physical regime.
Worked examples
A negative probe at P
A stationary nonperturbing probe has charge −q₀/2. What force do A and B exert on it at P?
- The source field remains E/E₀ = (15, 12, 0)/125.
- Use η = −1/2 in F/F₀ = ηE/E₀.
- Multiply every vector component by the same signed scalar.
F/F₀ = (−3/50, −6/125, 0). The force points opposite to the fixed source field.
Reflect the observation point
Find the field at (0, −4, 0)L₀ without repeating every distance calculation.
- Reflecting y leaves source distances and x displacements unchanged.
- Each y displacement reverses, so the total y component reverses.
- The sources remain A and B; do not reflect their charge signs.
E/E₀ = (3/25, −12/125, 0).
Find and check the null
Where on the right-hand x axis does the A/B field vanish?
- For x > 3, A points right and B points left.
- Require 4/(x + 3)² = 1/(x − 3)² and retain the positive distances in this region.
- Solving 2(x − 3) = x + 3 gives x = 9.
- At x = 9 the contributions are +1/36 and −1/36 in units E₀; both y components vanish.
At (9, 0, 0)L₀ the field is exactly zero. This is a null, not a source point or a stable positive-probe trap.
Evaluate the exact segment expression
What is the field of the separate uniform segment at (0, 4/3, 0)L₀?
- Use the segment source only, with total charge 2q₀.
- For h = 4/3, √(1 + h²) = 5/3.
- Then Eᵧ/E₀ = 2/[(4/3)(5/3)] = 9/10; symmetry sets the other components to zero.
E/E₀ = (0, 9/10, 0).
Which far-field model belongs to which source?
A learner calls the +4q₀/−q₀ arrangement a neutral dipole and predicts its leading field scales as 1/r³. What fails?
- Add the source charges: Q = +3q₀.
- A nonzero total charge supplies a leading monopole field at sufficiently large distance.
- A neutral-pair dipole approximation belongs to a separately specified zero-total-charge distribution.
The arrangement is not neutral. Its leading distant field scales as 1/r²; exact nearby calculations still require the original two contributions.
Try it yourself
Must a test charge occupy P for the prescribed source field at P to be defined?
Show the answer and reasoning
No.
The field is determined by A and B at any non-source observation point in this model. A probe measures or experiences the field under a nonperturbing assumption.
For B = −q₀, which direction should the displacement r − r_B take before multiplication by the charge?
Show the answer and reasoning
From B to the observation point.
The negative source factor then reverses that vector. Reversing the displacement as well would apply the sign twice.
Why is the midpoint field 5E₀/9 to the right rather than a difference of magnitudes?
Show the answer and reasoning
Both source contributions point right there.
A pushes a positive probe away from the left; B attracts it toward the right. Their dimensionless magnitudes are 4/9 and 1/9 and therefore add.
A zero-charge ideal probe has zero force at P. Does that establish E(P) = 0?
Show the answer and reasoning
No.
F = qE vanishes for q = 0 even when E is nonzero. Dividing by zero cannot define the field; the source calculation gives E(P)/E₀ = (15, 12, 0)/125.
Two direction-only arrows have equal drawn length. What can you conclude about their field magnitudes?
Show the answer and reasoning
Nothing from their lengths alone.
The convention deliberately normalizes nonzero arrow lengths. Use the magnitude table; an exact null has no direction arrow.
Does cancellation of the segment's x contributions also cancel its y field for h > 0?
Show the answer and reasoning
No.
Symmetric source pairs have opposite x components and equal positive y components. Only x cancels; y adds.
Which total charge must the segment's far-field coefficient reproduce?
Show the answer and reasoning
2q₀.
Its length is 2L₀ and λ = q₀/L₀. The exact field approaches 2E₀/h² for h ≫ 1, consistent with that total charge.
May a source's drawing mask be used as a finite physical radius that regularizes Coulomb's law?
Show the answer and reasoning
No.
The mask is a display convention only. A finite-size source model requires separately specified charge geometry and a new field calculation.
Why can adding fields from two separately isolated conductors fail after the conductors are brought near each other?
Show the answer and reasoning
Their charge distributions may rearrange.
Superposition uses contributions from the actual prescribed sources. The nearby configuration may not retain the source distributions used in the separate calculations.
Does this static kernel alone describe arbitrary rapidly moving sources at their simultaneous positions?
Show the answer and reasoning
No.
General time-dependent electromagnetism requires finite propagation and the coupled fields. A static or quasistatic approximation needs its own justified regime.
What to carry forward
- A prescribed electric field is a vector defined independently of a probe's presence or sign; an ideal stationary probe experiences F = qE.
- Form observation-minus-source displacements, retain signed charges and add components in one coordinate system. A point-source position is excluded before division.
- The A/B field at P is (15, 12, 0)E₀/125, and its exact axial null is at (9, 0, 0)L₀. A null is distinct from source singularity, zero probe charge and stable equilibrium.
- A direction-only sampled slice carries no magnitude information in arrow lengths and is neither a set of field lines nor a particle trajectory.
- For the separate uniform segment and h > 0, symmetry and an exact integral give Eᵧ/E₀ = 2/[h√(1 + h²)]. Its analytic limits must keep their distance regimes.
- Superposition retains its meaning only when the sources, support, response assumptions and time regime are specified. More digits or denser plotting cannot repair a mismatched physical model.
References
Sources for the concepts and teaching approaches in this article.
California Institute of Technology5 sources
- The Feynman Lectures on Physics, Vol. II: ElectromagnetismRichard P. Feynman, Robert B. Leighton and Matthew SandsTextbook chapterThe Feynman Lectures on Physics, Vol. II: ElectromagnetismElectrical forces, §1–1The electric and magnetic fields, §1–2
- The Feynman Lectures on Physics, Vol. II: ElectrostaticsRichard P. Feynman, Robert B. Leighton and Matthew SandsTextbook chapterThe Feynman Lectures on Physics, Vol. II: ElectrostaticsStatics, §4–1Coulomb’s law and superposition, §4–2Field lines, §4–8
- The Feynman Lectures on Physics, Vol. II: The Electric Field in Various CircumstancesRichard P. Feynman, Robert B. Leighton and Matthew SandsTextbook chapterThe Feynman Lectures on Physics, Vol. II: The Electric Field in Various CircumstancesThe electric dipole, §6–2
- The Feynman Lectures on Physics, Vol. II: DielectricsRichard P. Feynman, Robert B. Leighton and Matthew SandsTextbook chapterThe Feynman Lectures on Physics, Vol. II: DielectricsThe dielectric constant, §10–1The electrostatic equations with dielectrics, §10–4Fields and forces with dielectrics, §10–5
- The Feynman Lectures on Physics, Vol. II: Solutions of Maxwell’s Equations with Currents and ChargesRichard P. Feynman, Robert B. Leighton and Matthew SandsTextbook chapterThe Feynman Lectures on Physics, Vol. II: Solutions of Maxwell’s Equations with Currents and ChargesLight and electromagnetic waves, §21–1