# Mutual Induction

Whenever the current passing through a coil or circuit changes, the magnetic flux linked with a neighbouring coil or circuit will also change. Hence, an emf will be induced in the neighboring coil or circuit. This phenomenon is called mutual induction.

**Fig. 14**

# Coefficient of mutual induction

Total flux linked with the secondary due to current in the primary is

*N*_{2}*φ*_{2}and*N*_{2}*φ*_{2}∝*i*_{1}⇒*N*_{2}*φ*_{2}=*Mi*_{1}where*N*_{1}is the number of turns in primary;*N*_{2}is the number of turns in secondary;*φ*_{2}is the flux linked with each turn of secondary;*i*_{1}is the current flowing through primary; and*M*is the coefficient of mutual induction or mutual inductance.- According to Faraday’s second law, emf induces in secondary, ;
- If then |
*e*_{2}| =*M*. Hence, coefficient of mutual induction is equal to the emf induced in the secondary coil when rate of change of current in primary coil is unity.

**Units and dimensional formula**Similar to self-inductance (

*L*).

# Dependence of mutual inductance

- Number of turns (
*N*_{1},*N*_{2}) of both coils - Coefficient of self inductances (
*L*_{1},*L*_{2}) of both the coils - Area of cross section of coils
- Magnetic permeability of medium between the coils (
*μ*) or nature of material on which two coils are wound_{r} - Distance between two coils (as
*d*increases so*M*decreases) - Orientation between primary and secondary coil (for 90
^{o}orientation no flux relation*M*= 0) - Coupling factor
*K*between primary and secondary coil