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Mutually Induced E.M.F.

Consider two coils A and B placed closed to gather so that flux created by one coil completely links with the other coil. Let coil A have a battery and switch S and coil B be connected to the galvanometer G.

When switch S is opered, no current flows through coil A,  so no flux is created in coil A, i.e. no flux links with coil B, therefore, no e.m.f is induced across coil B, the fact is indicated by galvanometer zero deflection. Now when the switch S is closed current in coil A starts rising from zero value to a finite value, the flux is produced during this period and increases with the increase in current of coil A, therefore, flux linking with current of coil A , therefore, flux linking with the coil B increases and an e.m.f. known as mutually induced e.m.f. is produced in coil B, the fact is induced by galvanometer deflection. As soon as the current in coil A reaches its finite value, the flux produced or flux linking with coil B becomes constant, so no e.m.f. is induced in coil B, and galvanometer pointer returns back to zero position. Now if the switch S is opened, current will start decreasing, resulting in decrease in flux linking with coil B, an e.m.f. will be again induced but in direction opposite to previous one, this fact will be shown by the galvanometer deflection in opposite direction.

Hence whenever the current in coil A changes, the flux linking with coil B changes and an e.m.f. known as mutually induced e.m.f. is induced  coil B.

Consider coil A of turns N1 wound on a core of length l metres, area of cross-section a square metres and relative permeability μr. When the current of  i1 amperes flows through it, a flux of   N1i1   is set up
                                                                                                                           l /μoμra
around the coil. Let whole of the flux produced due to flow of current in coil A be linked with the coil B having N2 turns and placed near by coil A.

Mutually induced e.m.f. = - Rare of change of flux linkage of coil B
                                   = - Na x  rate of change of flux in coil A
                                   = - N2 d    [  N1i1  ]  = - N1N2μoμra  di1
                                             dt   l /μoμra             l            dt

The quantity  N1N2μoμra is called the coefficient of mutual induction of coil B with respect to coil A. It is
 represented by symbol M and is measured in henrys.

Hence mutually induced e.m.f., em = - M di1 where

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