If two coils are coupled with each, other then magnetic flux linked with a Coil( secondary coil) φ = MI where M is coefficient of mutual induction and I is current flow in through primary coil. The induced emf in the secondary coil E = – M dl / dt where dl / dt is the rate of change of current through primary coil. The unit of coefficient of mutual induction is henry( H) and its dimension is [ ML 2 T-2 A-2 ].
The coefficient of mutual induction depends on geometry of two coils, distance between them and orientation of the two coils.
Coefficient of Coupling Two coils are said to be coupled if full a part of the fuse produced by one links with the other.
K = √M / L 1 L2, where L 1 and L 2 are coefficients of self-induction of the two coils and M is coefficient of mutual induction of the two coils.
Coefficient of coupling is maximum( K = 1) in case( a), when coils are coaxial and minimum in case( b), when coils are placed a right angles.
Mutual inductance of two long coaxial solenoids is given by M = μ N 1 N 2 A / l = μ n 1 n 2 Al
where N 1 and N 2 are total number of turns in both coils, n 1 n 2 are number of turns per unit length in coils, A is area of cross-section of coils and 1 is length of the coils.
Grouping of Coils
( a) When three coils of inductances L 1, L 2 and L 3 are connected in series and the coefficient of coupling K = 0, as in series, then