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