Electromagnetic inductionEdexcel International A Level Physics: Revision notes

An e.m.f. is induced in a conductor or coil whenever the magnetic flux linkage through it changes. This happens when a conductor cuts field lines, a coil moves relative to a magnet, or the field itself changes.

The key idea is the flux linkage $N\Phi$ (number of turns × flux through each turn). Only a change in flux linkage induces an e.m.f. A constant flux linkage, however large, induces nothing.

When a magnet moves relative to a coil, the induced e.m.f. is larger when:

• the magnet moves faster (flux linkage changes more quickly)
• the magnet is stronger (larger flux)
• the coil has more turns
• the coil has a larger area (more flux through each turn)

Pushing the magnet in and pulling it out gives e.m.f.s of opposite polarity. Reversing the magnet also reverses the polarity. A stationary magnet gives no e.m.f.

A current in a primary coil produces a magnetic field. If a secondary coil shares this flux (for example on a common soft iron core), a change of current in the primary changes the flux linkage in the secondary and induces an e.m.f. there.

• switching the current on or off, or changing it, induces an e.m.f. only while the current is changing
• a steady current induces no e.m.f.
• an alternating current gives a continuously changing flux, so a continuous alternating e.m.f.
• a soft iron core, more turns on the secondary and a faster change of current all increase the e.m.f.

This is the principle behind the transformer.

Faraday's law: the magnitude of the induced e.m.f. is directly proportional to the rate of change of flux linkage.

Lenz's law: the direction of the induced e.m.f. (and any current) is such that it opposes the change that produced it.

Combined: $\varepsilon = -\frac{d(N\Phi)}{dt}$ and for a uniform rate of change $\varepsilon = -\frac{\Delta(N\Phi)}{\Delta t}$.

The minus sign shows the opposition of Lenz's law. It is a statement of conservation of energy: the work done against the opposing effect is the source of the electrical energy.

Question. A coil of 200 turns has area $5.0 \times 10^{-3}$ m². A field perpendicular to it falls from 0.80 T to 0.20 T in 0.30 s. Find the induced e.m.f.

Change in flux linkage = $N A \Delta B = 200 \times 5.0 \times 10^{-3} \times 0.60 = 0.60$ Wb turns.

$\varepsilon = \frac{0.60}{0.30} = 2.0$ V

By Lenz's law the induced current makes a field in the same direction as the original field, to oppose the fall.