Define the term ‘mutual inductance’ between the two coils. Obtain the expression for mutual inductance of a pair of long co-axial solenoids each of length l and radii ${ r }_{ 1 }$

and ${r_2}$. (${r_2} > > {r_1}$)

Mutual inductance, between a pair of coils, equals the magnetic flux, linked with one of them due to a change of unit current flowing in the other. Alternatively,The mutual inductance, for a pair of coils, equals the emf induced, in one of them, when the current in the other coil is changing at a unit rate.

Let a current {{I}_{2}} flow through the outer coil. The magnetic field due to this current