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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

Magnetic flux and Faraday–Lenz induction

Physics

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

Key knowledge

Magnetic flux through an oriented surface is Φ_B=∫B·n dA. For a fixed conducting loop, Faraday’s law gives induced electric emf ∮E·dl=−dΦ_B/dt with surface and boundary orientations related by the right-hand rule. N identical fixed turns linking the same flux give ε=−N dΦ_B/dt. The minus sign sets the circulation; any resulting current depends on the circuit response.

Values and equations

Φ_B=∫_S B·n dA; ε=∮_∂S E·dl=−dΦ_B/dt; ε_N=−N dΦ_B/dt

Φ_B
Oriented magnetic flux through S Wb
B
Magnetic flux density T
n
Oriented surface unit normal 1
A
Area m²
E
Electric field V m⁻¹
dl
Oriented path displacement m
ε,ε_N
One-loop and N-turn induced emf V
N
Number of identical turns 1
t
Time s
S,∂S
Fixed spanning surface and its right-hand-oriented boundary

Conditions and scope

  • Classical smooth fields and fixed loop geometry for the displayed electric-loop integral; use a spanning surface with compatible orientation.
  • Moving circuits additionally require the motional term in the emf model. Flux is a surface integral, not a literal count of field lines. Lenz’s opposition concerns flux change; it does not say an induced field always opposes the existing field.
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, §13.1: faradays lawSamuel J. Ling, Jeff Sanny and William Moebs — OpenStax, Rice University, University Physics (2016)Textbook chapteropenstax.orgRead source
    2. University Physics Volume 2, §13.2: lenzs lawSamuel J. Ling, Jeff Sanny and William Moebs — OpenStax, Rice University, University Physics (2016)Textbook chapteropenstax.orgRead source

Evidence and review

Read §13.1 flux/induction13.1–13.2, common N-turn flux13.3 and §13.2 Lenz flux-change direction. Fixed-loop integral is a scoped specialization of the existing Maxwell equation; no assertion that loop emf is an electrostatic endpoint voltage.

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 1–5 of 5 relationships

Scientific relationships · 5 / 5

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

  1. Related to
    Relationship sources · 2

    Linked statements

    • Magnetic flux through an oriented surface is Φ_B=∫B·n dA. For a fixed conducting loop, Faraday’s law gives induced electric emf ∮E·dl=−dΦ_B/dt with surface and boundary orientations related by the right-hand rule. N identical fixed turns linking the same flux give ε=−N dΦ_B/dt. The minus sign sets the circulation; any resulting current depends on the circuit response.

    The two records describe related physical or metrological models or distinctions; the present claim does not require every hypothesis or result in the linked record.

  2. Related to
    Relationship sources · 2

    Linked statements

    • Magnetic flux through an oriented surface is Φ_B=∫B·n dA. For a fixed conducting loop, Faraday’s law gives induced electric emf ∮E·dl=−dΦ_B/dt with surface and boundary orientations related by the right-hand rule. N identical fixed turns linking the same flux give ε=−N dΦ_B/dt. The minus sign sets the circulation; any resulting current depends on the circuit response.

    The two records describe related physical or metrological models or distinctions; the present claim does not require every hypothesis or result in the linked record.

  3. Uses definition
    Relationship sources · 2

    Linked statements

    • Magnetic flux through an oriented surface is Φ_B=∫B·n dA. For a fixed conducting loop, Faraday’s law gives induced electric emf ∮E·dl=−dΦ_B/dt with surface and boundary orientations related by the right-hand rule. N identical fixed turns linking the same flux give ε=−N dΦ_B/dt. The minus sign sets the circulation; any resulting current depends on the circuit response.

    This relation concerns the stated magnetic flux and faraday–lenz induction claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

  4. Uses definition
    Relationship sources · 1

    Linked statements

    • A fixed linear inductor with inductance L>0 stores magnetic energy U=LI²/2 relative to zero current. Under passive sign convention v=L dI/dt, so absorbed power vi=dU/dt. Current change can return this energy to the circuit; a real coil’s winding resistance and hysteresis introduce additional losses.

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

  5. Uses definition
    Relationship sources · 1

    Linked statements

    • For ideal coupled windings linking the same time-varying flux, voltage amplitudes satisfy N_pV_s=N_sV_p. With negligible magnetizing current and losses, corresponding load-current magnitudes satisfy N_sI_s=N_pI_p. Step-up voltage therefore accompanies reduced current at the same ideal transferred power; a transformer does not maintain this action from constant DC flux.

    This relation concerns the stated ideal transformer voltage and current ratios claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.

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