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PhysicsSimple harmonic motion and period

Linear restoring acceleration produces sinusoidal motion.

ModelPhysicsSimple pendulum and the small-angle limit

The familiar pendulum period requires a small swing.

ModelPhysicsAmplitude, phase, wavelength and polarization direction

A wave’s pattern speed differs from the motion of its medium.

ModelPhysicsEnergy carried by a sinusoidal string wave

Energy transport grows with squared amplitude and frequency in the linear model.

ModelPhysicsSound intensity and decibel level

A decibel value needs a reference and a specified measured quantity.

ModelPhysicsBeats from nearby frequencies

Slow modulation comes from superposing close frequencies.

ModelPhysicsAcoustic Doppler shift in a medium

Source and observer velocities are measured relative to the medium.

ModelPhysics · ChemistryHeat, temperature and specific heat

Heat is energy transferred because of a temperature difference.

ModelPhysicsThermal expansion coefficients

Thermal size changes depend on temperature and constraints.

ModelPhysics · ChemistryPressure–volume work and process paths

Boundary work depends on the process, while internal energy is a state function.

ModelPhysics · ChemistryReversible adiabatic ideal-gas relations

The power law needs an ideal gas and constant heat-capacity ratio.

ModelPhysics · ChemistryReversible and quasistatic processes

Restoring the system alone does not establish reversibility.

ModelPhysics · ChemistryEntropy change and reversible heat transfer

Use a reversible comparison path to calculate a state-function change.

ModelPhysicsRefrigerator and heat-pump performance

A heat pump moves heat as well as consuming work.

ModelPhysics · ChemistryMean free path in a dilute hard-sphere gas

A collision length depends on number density and cross section.

ModelPhysicsAtomic net charge and electrical neutrality

Neutral matter can contain both positive and negative charge.

ModelPhysicsConductors, insulators and electrostatic induction

Charge mobility and polarization are different from net charging.

ModelPhysicsConductors in electrostatic equilibrium

Equilibrium field vanishes in the conducting material, including a charged conductor.

ModelPhysicsElectric potential, voltage and potential energy

Voltage is energy change per unit charge.

ModelPhysicsCurrent density and carrier drift

Current measures signed charge flow across a surface.

ModelPhysicsResistance, resistivity and conductor geometry

Resistance belongs to a device geometry; resistivity is a material response.

ModelPhysicsSeries and parallel resistor networks

Series shares current; parallel shares voltage.

ModelPhysicsElectrical power and Joule heating

Voltage times signed current measures element power.

ModelPhysicsElectromotive force and terminal voltage

An emf is an energy-per-charge quantity, not a force.

ModelPhysicsSeries and parallel capacitor networks

Capacitor network rules differ from resistor rules.

ModelPhysicsEnergy stored in a linear capacitor

Charging work produces electric-field energy.

ModelPhysicsMagnetic flux and Faraday–Lenz induction

Induction responds to flux change, not simply to the presence of a magnetic field.

ModelPhysicsEnergy stored in a linear inductor

Inductive storage and resistive loss are separate.

ModelPhysicsMagnetic fields of a straight wire and circular loop

Field geometry follows the current distribution.

ModelPhysicsIdeal transformer voltage and current ratios

Turns change voltage and current while conserving ideal power.

Model
ModelSource checked

Magnetic fields of a straight wire and circular loop

Physics

Field geometry follows the current distribution.

Key knowledge

An ideal infinitely long thin straight wire carrying steady current has circulating field magnitude B=μ₀|I|/(2πr). A thin circular loop of radius R has axial field B_z=μ₀IR²/[2(R²+z²)^(3/2)], where positive I follows the right-hand orientation about +z. The loop centre has B_z=μ₀I/(2R); far along the axis the field falls as distance cubed.

Values and equations

B_wire=μ₀|I|/(2πr); B_z=μ₀IR²/[2(R²+z²)^(3/2)]

B_wire,B_z
Straight-wire field magnitude and signed loop axial field T
μ₀
Vacuum permeability H m⁻¹
I
Steady oriented current A
r,R,z
Wire distance, loop radius and axial position m

Conditions and scope

  • Vacuum magnetostatics, r>0 outside the thin wire and R>0; the straight-wire result is an infinite/long-wire idealization with distant return path.
  • Nearby return wires, finite-length effects, material response and changing currents modify the field. μ₀ is used symbolically and is not assigned the pre-2019 exact numerical value from the textbook.
Sources · 2

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. Samuel J. Ling, Jeff Sanny and William Moebs — OpenStax, Rice University, University Physics (2016)2 sources
    1. University Physics Volume 2, §12.2: magnetic field due to a thin straight wireSamuel J. Ling, Jeff Sanny and William Moebs — OpenStax, Rice University, University Physics (2016)Textbook chapteropenstax.orgRead source
    2. University Physics Volume 2, §12.4: magnetic field of a current loopSamuel J. Ling, Jeff Sanny and William Moebs — OpenStax, Rice University, University Physics (2016)Textbook chapteropenstax.orgRead source

Evidence and review

Read §12.2 long-wire Biot–Savart integral/result12.5 and §12.4 on-axis loop integral12.7. Axes are relabelled consistently. Exclude outdated exact μ₀ numerical claims and do not equate the full loop field with its far-dipole approximation.

2026-10-10 · /root/audit_life_earth_chemistry — independent Chemistry/Life/Earth editor. Independent AI editorial review of this entry's statements, equations, applicability conditions and source coverage. Source checks apply to these claims within their stated limits.

Related reference entries

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Showing 1–3 of 3 relationships

Scientific relationships · 3 / 3

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Derived from
    Relationship sources · 2

    Linked statements

    • An ideal infinitely long thin straight wire carrying steady current has circulating field magnitude B=μ₀|I|/(2πr). A thin circular loop of radius R has axial field B_z=μ₀IR²/[2(R²+z²)^(3/2)], where positive I follows the right-hand orientation about +z. The loop centre has B_z=μ₀I/(2R); far along the axis the field falls as distance cubed.

    This relation concerns the stated magnetic fields of a straight wire and circular loop claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  2. Uses definition
    Relationship sources · 2

    Linked statements

    • An ideal infinitely long thin straight wire carrying steady current has circulating field magnitude B=μ₀|I|/(2πr). A thin circular loop of radius R has axial field B_z=μ₀IR²/[2(R²+z²)^(3/2)], where positive I follows the right-hand orientation about +z. The loop centre has B_z=μ₀I/(2R); far along the axis the field falls as distance cubed.

    This relation concerns the stated magnetic fields of a straight wire and circular loop claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  3. Related to
    Relationship sources · 2

    Linked statements

    • An ideal infinitely long thin straight wire carrying steady current has circulating field magnitude B=μ₀|I|/(2πr). A thin circular loop of radius R has axial field B_z=μ₀IR²/[2(R²+z²)^(3/2)], where positive I follows the right-hand orientation about +z. The loop centre has B_z=μ₀I/(2R); far along the axis the field falls as distance cubed.

    This relation concerns the stated magnetic fields of a straight wire and circular loop claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

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