D.4.2 (HL)—Faraday’s law

Use the rate of change

Faraday's law states that a changing magnetic flux linkage induces an emf. For an average emf use the finite change; for an instantaneous emf use a derivative. No change in flux linkage means no induced emf.

Worked example — average induced emf

For $N=1200$ turns, flux per turn increasing from $0$ to $4.8\times10^{-5}\,\mathrm{Wb}$ in $2.7\,\mathrm{ms}=2.7\times10^{-3}\,\mathrm{s}$, $|\varepsilon|=N\Delta\Phi/\Delta t=21\,\mathrm{V}$. The minus sign determines polarity through Lenz's law; it does not make the magnitude negative.

Identify what changes

Flux linkage can change because the field strength, coil area or angle changes. The minus sign gives the direction described by Lenz’s law; the magnitude is determined by how rapidly the flux changes.

Apply it to coils

An alternating current in a primary coil creates an alternating magnetic field and changing flux in a nearby secondary coil, so an emf is induced there. A steady current after switching has no changing flux and does not sustain an induced emf in the secondary.

Common trap

Do not say that a magnetic field alone induces emf. It is the change in flux linkage, not the mere presence of B, that matters.