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**Definition**

If the flux created by one coil is obtaining joined with another coil and as a result of change during this flux created by initial coil, there's induced e.m.f.in the second coil, then such an e.m.f is named mutually induced e.m.f.

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**Explanation**

Think through 2 coils that are positioned adjacent to every alternative as shown within the Fig. The coil A has N

_{1 }turns whereas coil B has N_{2}turns. The coil A has adjustable resistance R, battery of 'E' volts and switch S, in series with it. A meter is connected across coil B to sense induced e.m.f. and current due to it.
Current through coil A is I

_{1}creating flux Î¦_{1}. Part of this flux can tie with coil B i.e. can complete its path through coil B as shown within the Fig. This is often the mutual flux Î¦_{2}.
At this instant if current through coil A is modified by means that of variable resistance R, then flux Î¦

_{1}changes. As a result of this, flux related to coil B, that is mutual flux Î¦_{2}conjointly changes. As a result of Faraday’s law there'll be induced e.m.f. in .coil B which is able to found out a current through coil B, which is able to be detected by galvanometer G.####
**Magnitude of Mutually Induced E.M.F.**

Let,

N

_{1 }= Number of turns of coil A
N

_{2}= Number of turns of coil B
I

_{1}= Current flowing through coil A
Î¦

_{1}= Flux producing due to current I_{1}in webers.
Î¦

_{2}= Flux linking with coil B
According to Faraday’s law, the induced e.m.f in coil B is,

E

_{2}= -N_{2}(dÎ¦_{2}/dt)
Negative sign indicates that this e.m.f. will set up a current which will oppose the change of flux likning with it.

Now Î¦

_{2}= Î¦_{2}/I_{1}x I_{1}_{}

If permeability of the surrounds is presumed constant then Î¦

_{2}∝ I_{1}and hence Î¦_{2}/I_{1}is constant.
∴ Rate of change of Î¦

_{2}= (Î¦_{2}/I_{1}) x Rate of change of current I_{1}
∴ dÎ¦

_{2}/dt = (Î¦_{2}/I_{1}) x (dI_{1}/dt)
E

_{2}= -N_{2}x ( Î¦_{2}/I_{1}) x (dI_{1}/dt)
E

_{2}= - (N_{2}Î¦_{2}/I_{1}) (dI_{1}/dt)
Here (N

_{2}Î¦_{2}/I_{1}) is called coefficient of mutual inductance denoted by M.**E**

_{2}= -M(dI_{1}/dt) Volts

Coefficient of mutual inductance is outlined as the property by that e.m.f. gets induced within the second coil due to amendment in current through first coil.

Coefficient of mutual inductance is also called mutual inductance. It is measured in Henries.