Electromagnetic induction

Induced e.m.f. from relative motion of magnets and coils or changing currents, and Faraday's and Lenz's laws.

Understand and use the terms magnetic flux density $B$ , flux $\Phi$ and flux linkage $N\Phi$

Understand the factors affecting the e.m.f. induced in a coil when there is relative motion between the coil and a permanent magnet

Understand the factors affecting the e.m.f. induced in a coil when there is a change of current in another coil linked with this coil

Understand how to use Faraday's law to determine the magnitude of an induced e.m.f. and be able to use the equation that combines Faraday's and Lenz's laws, $\varepsilon = -\frac{d(N\Phi)}{dt}$

A coil of 200 turns and cross-sectional area $4.0 \times 10^{-4}\,\text{m}^2$ is placed with its plane perpendicular to a magnetic field of flux density $0.30\,\text{T}$ . The field is reduced uniformly to zero in $0.050\,\text{s}$ .

Calculate the magnitude of the e.m.f. induced in the coil.

Change in flux linkage $= N\Delta(BA) = 200 \times 0.30 \times 4.0 \times 10^{-4} = 0.024\,\text{Wb}$ (1)

A bar magnet is dropped, north pole first, through a vertical coil connected to a data logger, which records the induced e.m.f. against time.

Describe the shape of the e.m.f.–time graph and explain its features using the laws of electromagnetic induction.

Indicative content:

As the magnet enters the coil, the flux linkage increases, so an e.m.f. is induced (Faraday's law) (1)
When the magnet is fully inside/at the centre, the flux linkage is (momentarily) not changing, so the e.m.f. falls to zero (1)
As the magnet leaves, the flux linkage decreases, so the e.m.f. is in the opposite direction (Lenz's law) (1)
The second peak is larger because the magnet is moving faster as it leaves (it is accelerating under gravity) (1)
The second pulse is shorter in duration because the magnet passes through more quickly (1)
The areas under the two peaks are equal because the total change in flux linkage is the same on entry and exit (1)

Award 1 mark per relevant point, max 6.

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