**Co-efficient of Mutual Induction or Mutual Inductance**

Mutual Inductance is the interaction of one coil magnetic field on another coil as it induces a voltage in the adjacent coil. It is the property of a circuit which permits mutual induction. It is to be remembered that when the value of current is either constant or zero, then the galvanometer does not give any deflection: this is because that no change of magnetic flux takes place then.

Suppose, due to the flow of current ‘i’ in the primary coil P, the value of magnetic flux in the secondary coil S is φ.

We know, φ ∞ i … … … … (1)

or, φ = Mi … … … … (2)

Here M is a constant, It is called co-efficient of mutual induction.

Now, let us give its definition in language.

If i = 1 unit, then from equation (2) we get, φ = M.

*So, due to the flow of one unit of current in a coil, the number of magnetic flux enclosed in the coil is called the co-efficient of mutual induction or mutual inductance.*

Again, according to Faradays’s law we get,

E = dφ/dt [ignoring negative sign]

or, E = d/dt (Mi) = M (di/dt) … … (3)

Now, if (di/dt) = 1, then E = M.

So, the electromotive force produced in a secondary coil due to the change of one unit current in one second in the primary coil is called the co-efficient of mutual induction or mutual inductance.

Mutual Inductance is the basic operating principle of the transformer, motors, generators and any other electrical component that interacts with another magnetic field. Then we can define mutual induction as the current flowing in one coil that induces a voltage in an adjacent coil.

Unit of co-efficient of mutual induction or mutual inductance: Similar to self-inductance, the S.I. unit of mutual inductance is Henry. Besides, milli-henry (mh) (10^{-3} Henry) and micro-henry (μh) (10^{-6} Henry) are also used as the unit of mutual inductance.

‘Mutual inductance of 1 Henry means’ that is due to the change of 1 As^{-1} current through one of the two coils, an electromotive force of 1V is induced in the secondary coil, then the mutual inductance of the two coils is 1 Henry.