When an electric current passing through a coil changes with time, an emf is induced in the neighbouring coil. This phenomenon is known as mutual induction and the emf is called mutually induced emf.

**Mutual induction**

When an electric current
passing through a coil changes with time, an emf is induced in the neighbouring
coil. This phenomenon is known as mutual induction and the emf is called
mutually induced emf.

Consider two coils which
are placed close to each other. If an electric current *i*_{1} is
sent through coil 1, the magnetic field produced by it is also linked with coil
2 as shown in Figure 4.22(a).

Let Φ_{21} be the magnetic flux
linked with each turn of the coil 2 of *N*_{2} turns due to coil
1, then the total flux linked with coil 2 ( *N*_{2} Φ_{ 21} ) is proportional to
the current *i*_{1} in the coil 1.

The constant of
proportionality *M*_{21} is the mutual inductance of the coil 2
with respect to coil 1. It is also called as coefficient of mutual induction.
If *i*_{1} =1*A*
, then *M* _{21} = *N*_{2} Φ _{21} .
Therefore, **the mutual inductance M_{21}
is defined as the flux linkage of the coil 2 when 1A current flows through coil
1**.

When the current *i*_{1}
changes with time, an emf ε_{2} is induced in coil 2. From Faraday’s law of electromagnetic
induction, this mutually induced emf ε_{2} is given by

The negative sign in the
above equation shows that the mutually induced emf always opposes the change in
current *i*_{1} with respect to time. If di_{1}/dt = 1 A s^{-1},
then M_{21} = − ε .

**Mutual inductance M_{21}
is also defined as the opposing emf induced in the coil 2 when the rate of
change of current through the coil 1 is 1 As^{-1}.**

Similarly, if an
electric current *i*_{2} through coil 2 changes with time, then
emf ε_{1} is induced in coil 1.
Therefore,

where *M*_{12}
is the mutual inductance of the coil 1 with respect to coil 2. It can be shown
that for a given pair of coils, the mutual inductance is same.

In general, the mutual
induction between two coils depends on size, shape, the number of turns of the
coils, their relative orientation and permeability of the medium.

The unit of mutual
inductance is also henry (H).

If *i*_{1} =1*A* and *N* _{2}
Φ_{21} =1 *Wb turns*, then *M
*_{21}* *=1*H
*.

Therefore, **the mutual
inductance** **between two coils is said to be one henry if a current of 1 A
in coil 1 produces unit flux linkage in coil 2.**

If di_{1}/dt = 1 A*s*^{−1}
and ε_{2} = −1 V , then M_{21}
= 1H.

Therefore, **the mutual
inductance** **between two coils is one henry if a current changing at the
rate of 1 As^{-1} in coil 1 induces an opposing emf of 1V
in coil 2.**

Tags : Definition, Explanation, Formula, Unit | Electromagnetic Induction , 12th Physics : Electromagnetic Induction and Alternating Current

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12th Physics : Electromagnetic Induction and Alternating Current : Mutual induction | Definition, Explanation, Formula, Unit | Electromagnetic Induction

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