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Statically Induced E.M.F.

Statically induced e.m.f. may be (a) self induced e.m.f. or (b) mutually induced e.m.f.

(a)    Self induced E.M.F.  When the current flowing through the coil is changed, the flux linking with its own winding changes and due to the change in linking flux with the coil.

Since according to Lenz’s law, any induced e.m.f. acts to oppose the change that produced it, a self induced e.m.f. is always in such a direction as to oppose the change of current in the coil or circuit in which it is induced. This property of the coil or circuit due to which it opposes any change of the current in the coil or circuit, is known as self inductance.

Consider a solenoid of N turns, length l metres, area of x-section a square metres and of relative permeability  μr. When the solenoid carries a current of i amperes, a magnetic field f flux   Ni   webers is set up around the solenoid and links with it.                                                                l / μrμo a

If the current flowing through the solenoid is changed, the flux produced by it will change and therefore an e.m.f. will be induced.

Self induced e.m.f., e = - N   = N d    [   Ni      ]  =  N     N           di
                                        dt         dt    l / μrμo a          l / μrμo a    dt

The quantity  N2μrμo a  is a constant for any given coil or circuit and is called coefficient of self
inductance. It is represetenied by symbol L and is measured in henries.

Hence self induced e.m.f. = - L di where L = - N2μrμo a  di 
                                             dt                     I           dt

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