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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
E = -d(N)/dt
= -Nddt
where N is the number of turns in the coil and the
magnetic flux through one coil. Magnetic flux is a
measurement of the ‘amount’ of magnetism. (See
magnetic flux density). In a way it is the ‘flow’ of
magnetic field through the coil.
The quantity N is known as the flux linkage and is
measured in webers.
The quantity d(N)/dt is the rate of change of flux
linkage in webers per second.
Figure 1
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 = - Nd
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
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 Wb s-1
e.m.f. = - Nd/dt = -200 x 0.01 = -2 V.
(See also:
Induced emf in a straight wire)
1