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Showing 1561–1590 of 1709 reference entries

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

Electric potential, voltage and potential energy

Physics

Voltage is energy change per unit charge.

Key knowledge

In electrostatics, potential difference V_B−V_A is the potential-energy change of a small fixed test charge divided by that signed charge: ΔU=qΔV. Equivalently ΔV=−∫_A^B E·dr and E=−∇V. Potential has an arbitrary additive reference, while differences determine work. A volt is a joule per coulomb; voltage is not itself stored energy.

Values and equations

ΔU=q(V_B−V_A); V_B−V_A=−∫_A^B E·dr; E=−∇V

U,ΔU
Electrostatic potential energy and its change J
q
Signed fixed test charge C
V,V_A,V_B
Potential and endpoint values V
E
Electric field V m⁻¹
r
Position m

Conditions and scope

  • Static electric field with a single-valued potential in the stated domain; a test charge small enough not to change the source configuration.
  • For time-varying magnetic fields the electric field can have a nonconservative part; the general potential representation includes −∂A/∂t and a measured loop emf need not be a scalar endpoint difference.
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, §7.2: electric potential and potential differenceSamuel J. Ling, Jeff Sanny and William Moebs — OpenStax, Rice University, University Physics (2016)Textbook chapteropenstax.orgRead source
    2. University Physics Volume 2, §7.4: determining field from potentialSamuel J. Ling, Jeff Sanny and William Moebs — OpenStax, Rice University, University Physics (2016)Textbook chapteropenstax.orgRead source

Evidence and review

Read §7.2 voltage/potential-energy definitions7.1–7.3 and §7.4 field-gradient7.15. Time-dependent limitation directly reuses the already reviewed general potential record; do not equate scalar voltage with arbitrary induction-loop work.

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

Explore relationships within this area of study and its connections to other areas.

Showing 1–7 of 7 relationships

Scientific relationships · 7 / 7

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

  1. Uses definition
    Relationship sources · 2

    Linked statements

    • In the ideal macroscopic electrostatic conductor model, electric field is zero in the conducting material and each connected conductor is at a constant potential. Excess charge occupies its surfaces; a smooth surface in vacuum has E_out=σ_s n/ε₀ immediately outside. A cavity can contain a field if it contains charge, so field-free material does not guarantee an empty-field cavity under every condition.

    This relation concerns the stated conductors in electrostatic equilibrium claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  2. Uses definition
    Relationship sources · 2

    Linked statements

    • In electrostatics, potential difference V_B−V_A is the potential-energy change of a small fixed test charge divided by that signed charge: ΔU=qΔV. Equivalently ΔV=−∫_A^B E·dr and E=−∇V. Potential has an arbitrary additive reference, while differences determine work. A volt is a joule per coulomb; voltage is not itself stored energy.

    This relation concerns the stated electric potential, voltage and potential energy claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  3. Uses definition
    Relationship sources · 2

    Linked statements

    • In electrostatics, potential difference V_B−V_A is the potential-energy change of a small fixed test charge divided by that signed charge: ΔU=qΔV. Equivalently ΔV=−∫_A^B E·dr and E=−∇V. Potential has an arbitrary additive reference, while differences determine work. A volt is a joule per coulomb; voltage is not itself stored energy.

    This relation concerns the stated electric potential, voltage and potential energy claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  4. Related to
    Relationship sources · 2

    Linked statements

    • In electrostatics, potential difference V_B−V_A is the potential-energy change of a small fixed test charge divided by that signed charge: ΔU=qΔV. Equivalently ΔV=−∫_A^B E·dr and E=−∇V. Potential has an arbitrary additive reference, while differences determine work. A volt is a joule per coulomb; voltage is not itself stored energy.

    This relation concerns the stated electric potential, voltage and potential energy claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  5. Uses definition
    Relationship sources · 1

    Linked statements

    • A source emf measures supplied work per unit charge and has units of volts. An ideal emf source with a series internal resistance r models a discharging battery’s terminal voltage as V_terminal=ε−Ir, where I leaves its positive terminal. At zero current this model gives V_terminal=ε; under load internal dissipation lowers terminal voltage.

    This relation concerns the stated electromotive force and terminal voltage claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  6. Uses definition
    Relationship sources · 1

    Linked statements

    • For a fixed linear capacitance C>0 charged from zero, stored energy is U=Q²/(2C)=CV²/2=QV/2. The factor one-half comes from integrating the rising voltage during charging, not multiplying the final voltage by every charge increment. An ideal vacuum parallel-plate capacitor of area A and gap d has C≈ε₀A/d when edge fields are negligible.

    This relation concerns the stated energy stored in a linear capacitor claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  7. Uses definition
    Relationship sources · 1

    Linked statements

    • For one-photon emission from a specified surface with work function Φ, maximum initial electron kinetic energy is K_max=hf−Φ when hf≥Φ. An ideal stopping-potential magnitude V_stop satisfies eV_stop=K_max, and threshold frequency is Φ/h. At fixed frequency and surface state in this regime, increasing intensity increases the number/rate of photoelectrons rather than this maximum energy.

    This relation concerns the stated photoelectric threshold and stopping potential claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

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