Electromagnetic Induction - Mutual Inductance due to Concentric Coplanar Circular Coils

In above figure we have two concentric coplanar coils (Primary coil of radius R and Secondary coil of radius r).Due to flux change in primary coil there will be a induced emf in secondary coil.

Magnetic field due to primary coil is 


flux change in secondary coil depends on current in primary coil



Mutual Inductance is shown below


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Electromagnetic Induction - Mutual Induction