Faraday's law of induction

Faraday's law: an emf is induced in a circuit whenever the magnetic flux through it changes, and the size of the emf equals the rate of change of flux: ε = −dΦB/dt.

The minus sign fixes the direction of the emf (Lenz's law, next section).

For a closely wound coil of N turns, each turn links the same flux, so ε = −N dΦB/dt. More turns give more emf.

Experiment 6.3 explained: pressing the key makes the current, and so the flux through the other coil, rise quickly; a steady current means steady flux and no emf; releasing the key makes the flux fall, giving an emf the other way.

Example 6.2: a 10 cm square loop of resistance 0.5 Ω has a 0.10 T field at 45° to its normal. The field falls steadily to zero in 0.70 s. Initial flux = 0.1 × 10⁻² × cos 45° = 10⁻³/√2 Wb, so ε = 1.0 mV and I = 2 mA.

The earth's field also threads such a loop, but it is steady over the experiment, so it induces nothing.

Example 6.3: a 500-turn coil of radius 10 cm and resistance 2 Ω faces the earth's horizontal field of 3.0 × 10⁻⁵ T and is turned through 180° in 0.25 s. The flux per turn goes from +3π × 10⁻⁷ to −3π × 10⁻⁷ Wb, so the average emf is about 3.8 × 10⁻³ V and the current 1.9 × 10⁻³ A.

Switching a large electromagnet on or off can induce emfs large enough to damage sensitive instruments close by.