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Electromagnetic induction

Electricity and magnetism · level 7, lesson 4 of 6

A question to start

Push a magnet into a coil joined to a meter. The needle flicks one way. Pull it out, and the needle flicks the other way. Hold it still, and nothing. Where does the current come from?

The idea

A changing magnetic field through a coil makes a voltage in it. This is electromagnetic induction, found by Michael Faraday in 1831.

The magnetic flux through a loop of area \(A\), with the field \(B\) straight through it, is \(\Phi = BA\), in webers (Wb). Faraday's law says the induced voltage (the emf) in a coil of \(N\) turns is

\[\varepsilon = -N\frac{\Delta\Phi}{\Delta t}.\]

The faster the flux changes, the bigger the voltage. The minus sign is Lenz's law: the induced current flows so as to oppose the change that made it.

A straight wire of length \(L\) moving at speed \(v\) across a field also has an emf: \(\varepsilon = BLv\).

SN push the magnet inthe meter flicks

Worked examples

1. A coil. 200 turns, area 0.01 m². The field falls from 0.5 T to 0 in 0.1 s: \(\Delta\Phi = 0.005\) Wb, so \(\varepsilon = 200 \times 0.005/0.1 = 10\) V.

2. Faster. The same change in 0.01 s gives 100 V.

3. A moving rod. A 0.5 m rod moves at 4 m/s across a 0.3 T field: \(\varepsilon = 0.3 \times 0.5 \times 4 = 0.6\) V.

Try it

  1. Why does nothing happen when the magnet is held still inside the coil?
  2. A 50-turn coil of area 0.02 m² sees the field rise from 0 to 0.4 T in 0.2 s. Find the emf.
  3. Find the emf across a 1.2 m wing of a model plane flying at 20 m/s through a field of \(5\times10^{-5}\) T at right angles.
  4. What does Lenz's law say about the current induced as the magnet is pushed in?
Answers
  1. The flux is not changing, so there is no induced voltage.
  2. \(\Delta\Phi = 0.008\) Wb: \(\varepsilon = 50 \times 0.008/0.2 = 2\) V.
  3. \(5\times10^{-5} \times 1.2 \times 20 = 1.2\times10^{-3}\) V, 1.2 mV.
  4. It flows so that the coil's own field pushes back against the incoming magnet.

Common mistake

"A strong magnet in a coil makes a current." Only a changing flux does. A magnet sitting still, however strong, induces nothing.

Where it leads