Faraday's law

Faraday found that a changing magnetic field can produce a current. Move a magnet into a coil and the galvanometer kicks; hold it still and the needle returns to zero. The current appears only while something changes.

What must change is the magnetic flux through the coil: Φ = BA cos θ, where θ is the angle between B and the normal to the coil. Unit: weber (Wb) = T m².

Faraday's law: the induced emf equals the rate of change of flux linkage:

ε = –N dΦ/dt, for a coil of N turns.

Since Φ = BA cos θ, there are three ways to change it:

• change B (move a magnet, switch a nearby current on or off);
• change the area A in the field (slide a rod, stretch a loop);
• change the angle θ (turn the coil, as in a generator).

Example: a 50-turn coil of area 0.01 m² sits at right angles to B = 0.2 T. The field drops to zero in 0.1 s. ε = 50 × (0.2 × 0.01) / 0.1 = 1 V. If the coil's resistance is 5 Ω, the induced current is I = ε/R = 0.2 A.

Changing faster gives a bigger emf: push the magnet in quickly and the needle swings further. An iron core in the coil increases the flux and the effect.

A steady current in a nearby coil makes a steady field, and induces nothing. Only switching it on, off, or changing it does.

Turning a flat coil through 180° reverses the flux, from +BA to –BA, so the change is 2BA, not zero.