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Lesson Directive // ElectromagnetismREF_CORE

Magnetic Fields

E\mathcal{E}==−-NNdΦBd\Phi_Bdtdt

Hover over a variable in the formula above, or see glossary below:

E\mathcal{E}
Electromotive Force (EMF)
Volts (V)
NN
Number of Turns
Count
ΦB\Phi_B
Magnetic Flux
Webers (Wb)

Moving electric charges create magnetic fields. A current-carrying wire produces a circular magnetic field around it. Bar magnets create dipole fields running from south to north pole internally, and north to south externally.

INSIGHT: Electricity and magnetism are two faces of the same underlying force.

Faraday's Law of Induction

A changing magnetic flux through a coil induces an electromotive force (voltage). The faster the flux changes, the greater the induced EMF. This is the operating principle of every electric generator on Earth — from bicycle dynamos to nuclear power stations.

INSIGHT: Change is key: a static field induces nothing; a changing field induces voltage.

Lenz's Law and the Negative Sign

The negative sign in Faraday's law reflects Lenz's Law: the induced current flows in a direction that opposes the change in flux that created it. This is an expression of energy conservation — you must do work against the opposing force to move the magnet.

INSIGHT: Induced currents always resist the change that caused them.
Detailed Theory & ReferencesEXT_DOC

Faraday's Law of Electromagnetic Induction

Electromagnetic induction is the production of an electromotive force across an electrical conductor in a changing magnetic field. Independently discovered by Michael Faraday (1831) and Joseph Henry (1832).

Magnetic Flux

ΦB=∬SB⃗⋅dA⃗\Phi_B = \iint_S \vec{B} \cdot d\vec{A}

For a uniform field BB through flat area AA at angle θ\theta to the surface normal: ΦB=BAcos⁡θ\Phi_B = BA\cos\theta

The SI unit is the Weber (Wb): 1 Wb=1 V⋅s=1 T⋅m21 \text{ Wb} = 1 \text{ V}\cdot\text{s} = 1 \text{ T}\cdot\text{m}^2.

Faraday's Law

For a single loop: E=−dΦBdt\mathcal{E} = -\frac{d\Phi_B}{dt}

For a coil of NN turns: E=−NdΦBdt\mathcal{E} = -N \frac{d\Phi_B}{dt}

Lenz's Law

The negative sign encodes Lenz's Law: the induced emf drives a current whose magnetic field opposes the change in flux. This is a direct consequence of energy conservation.

Maxwell's Equations

Faraday's Law in differential form (one of Maxwell's four equations): ∇×E⃗=−∂B⃗∂t\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}

Applications

  • Generators: Rotating a coil in a magnetic field continuously changes flux, generating AC power.
  • Transformers: Two coils share a core; changing flux in one induces emf in the other.
  • Induction Charging: Wireless charging pads use alternating magnetic fields to induce current.

References

AI NOTICE

AI Assistance Disclaimer: This module uses AI-assisted educational models and interactive visual representations to help explain scientific and mathematical concepts. For formal research or academic evaluation, please verify formulas and data against standard primary reference materials.