Electromagnetic inductionEdexcel A-Level Physics: Revision notes

Electromagnetic induction is the production of an e.m.f. in a conductor when the magnetic flux linkage through it changes. If the conductor forms a complete circuit, the e.m.f. drives an induced current.

The flux linkage can change in two ways:

• Relative movement. A magnet moves into or out of a coil (or a wire cuts across field lines). The flux through the coil changes.
• A changing current in a linked coil. The current in a primary coil changes, so the field it produces changes, and the flux linkage of a nearby secondary coil changes. This happens when a switch is closed or opened, or with an alternating current.

If the flux linkage is steady, no e.m.f. is induced, even if the field is strong.

Moving magnet and coil. The induced e.m.f. is larger if:

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

Changing current in a linked coil. The e.m.f. induced in the secondary is larger if:

• the current in the primary changes faster (for example, a higher-frequency a.c. or a quicker switch)
• the current change is larger
• the secondary has more turns
• a soft iron core guides the flux through the secondary so that more of it is linked

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

$\mathcal{E} = -\frac{\mathrm{d}(N\Phi)}{\mathrm{d}t}$

For a constant rate of change this is $\mathcal{E} = -\dfrac{\Delta(N\Phi)}{\Delta t}$. The minus sign shows that the e.m.f. opposes the change producing it (Lenz's law).

Worked example. A 400-turn coil of area $2.5\times10^{-3}$ m² is perpendicular to a field that falls uniformly from 0.80 T to 0.20 T in 0.30 s.

$\Delta(N\Phi) = 400 \times 2.5\times10^{-3} \times 0.60 = 0.60$ Wb (turns)

$|\mathcal{E}| = 0.60 / 0.30 = 2.0$ V.

Lenz's law: the direction of an induced e.m.f. (and any current it drives) is always such as to oppose the change that produces it.

Example: when the north pole of a magnet approaches a coil, the induced current makes the near end of the coil a north pole, which repels the magnet. Withdrawing the magnet makes the near end a south pole, which attracts it back.

This is a consequence of conservation of energy. Work must be done against the opposing force to move the magnet, and that work becomes electrical energy. If the induced current helped the change, the magnet would accelerate while also supplying electrical energy, which would create energy from nothing.