Induced e.m.f

When the magnetic flux through a coil changes, the e.m.f. E generated in the coil can be expressed as:

where N is the number of turns in the coil and Φ the magnetic flux through one coil. Magnetic flux is a measurement of the 'amount' of magnetism. (See magnetic flux density (B) = Φ/A). In a way it is the 'flow' of magnetic field through the coil.

The quantity NΦ is known as the magnetic flux linkage and is measured in webers.

This law is known as Faraday's Law and in words it states that the induced emf is equal to the negative of the rate of change of the magnetic flux linking the circuit.

The quantity d(NΦ)/dt is the rate of change of flux linkage in webers per second.


This change of flux can be produced by either:
(a) moving the wire or coil through the field or
(b) changing the intensity of the magnetic field

If we think of a conductor moving through a constant magnetic field (Figure 1) then the e.m.f (E) generated between the two ends of the conductor at any moment is given by the equation:

E = -NdΦ/dt

where N is the number of conductors cutting the flux (There is only one wire cutting through the field in Figure 1 and so in this example N = 1).

Example problem
Calculate the e.m.f. induced in a coil of 200 turns placed in a field where the rate of change of flux is 0.01 Wbs^-1

Induced e.m.f. (E) = - NdΦ/dt = -200x0.01 = -2 V.

(See also: Induced emf in a straight conductor)