5.5 Electromagnetism

Faraday's Law of Induction

A changing magnetic flux through a loop induces an EMF: ε = −dΦ_B/dt, where Φ_B = ∫B·dA. Flux changes if B, area, or the angle between them changes. This induced EMF can drive current through a circuit, converting motion or changing fields into electrical energy.

Lenz's Law and the Minus Sign

The negative sign in Faraday's Law encodes Lenz's Law: the induced current flows in the direction that opposes the change in flux. This is a consequence of energy conservation — the induced effects always fight the change that caused them, preventing infinite energy gain.

Motional EMF and Inductors

A rod of length L moving with velocity v through field B develops motional EMF = BLv (when v, L, B are mutually perpendicular). In circuits, changing current in an inductor induces a back-EMF ε = −L(dI/dt), where L is inductance, opposing rapid changes in current.

Key terms

Faraday's Law

ε = −dΦ_B/dt; an induced EMF arises from a changing magnetic flux through a loop.

Lenz's Law

Induced current flows in the direction that opposes the change in magnetic flux, conserving energy.

Motional EMF

ε = BLv for a rod of length L moving at speed v through field B, all mutually perpendicular.

Magnetic Flux (Φ_B)

Φ_B = ∫B·dA, the measure of magnetic field passing through a surface.

Inductor Back-EMF

ε = −L(dI/dt); an inductor opposes changes in current flowing through it.

Try an AP-style question

What did Maxwell add to Ampère's law?

1. The magnetic monopole term, ∮B·dA
2. The Lorentz force term, qv × B
3. Ohm's law for conductors, J = σE
4. The displacement current term, ε₀ dΦ_E/dt