# Mutual induction-

In this topic students will study what is mutual induction and coefficient of mutual induction / mutual inductance? And what is the unit of mutual inductance

Mutual induction-

Let us consider two coils placed near to each other closely . One of the coil carries the battery is the primary coil and the other one is secondary coil connected with a galvanometer. When current starting flows through the primary coil  then its value increases from zero value to a fixed value during this time we observe that there is some deflection in the galvanometer . as we know when current passes through a coil (solenoid ) magnetic field setup ,due to increasing value of current magnetic field through the coil also increases and hence magnetic flux linked with the secondary  coil also increases , and according to Faraday’s law  emf  setup across the secondary coil .

So we can say , The phenomena of inducing current in a circuit by changing the current in a neighbouring circuit is called mutual induction. We can also define it the property of two circuits by virtue of which each circuit opposes any change in flux or strength of current flowing through other circuit.

It is found that the flux ‘ɸ’ linked with the secondary coil is directly proportional to the current ‘I’ flowing through the primary coil ,

i.e.      ɸ = I

or         ɸ = MI ( M is a constant called coefficient of mutual induction , the value of M depends upon the characteristics of the circuit ant their orientations . )

so,     M = ɸ/I   ; if  I =1 ampere then M=ɸ

So we can define coefficient of mutual induction is equal to the flux linked with the coil when unit current passes through the another coil.

We know that,  emf ‘e’ = -dɸ/dt =  – d(MI)/dt  =  -M dI/dt  ,

If dI/dt = 1 then , m  = – e , so we can define coefficient of mutual induction is equal to emf induced in secondary coil when rate of change of secondary coil is unity.

Unit of mutual inductance  is Henry (H) , Henry is also the unit of self inductance  , we can define that mutual induction of two circuit is said to be 1 Henry if a current changing at the rate of 1 ampere per second  in one circuit and induces 1 volt of emf in other circuit.

To derive the expression for the mutual induction of two coaxial solenoid click here

To derive the expression for  the coefficient of self induction click here