Faraday’s Law – Size of induced e.m.f.

The magnitude of the e.m.f. induced in a conductor equals the rate of change of flux linkages or the rate at which the conductor cuts a magnetic flux.

Straight Wire

Imagine a straight piece of wire of length l is moved through a magnetic field at a velocity v. If the wire is moving at right angles to the field lines an e.m.f. is induced (because field lines are being cut).

The size of the e.m.f. is given by the equation:

For one loop of wire and the flux is given by which are combine to become

B is constant so . ΔA is the area the wire cuts through in a time t and is given by so we get: The length of the wire and velocity are constant so it becomes which cancels to:

Rotating Coil of Wire

If we have a coil of wire with N turns, each of which has an area of A and placed it a magnetic field of flux density B nothing would happen. If it was rotated with an angular speed of ω it would cut through the magnetic field lines and an e.m.f. would be induced. The size of the e.m.f. is given by:

Since and we get and if we differentiate it:

This is why the Mains supply is alternating; the rotating coil cuts the field lines in one direction on the way up and the other direction on the way down.