Question

A long solenoid of length \(L\) and radius \(r_1\) having \(N_1\) turns is surrounded symmetrically by a coil of radius \(r_2\,(>r_1)\) having \(N_2\) turns \((N_2 \ll N_1)\) around its mid-point. Derive an expression for the mutual inductance of the solenoid and the coil. Is \(M_{12}=M_{21}\) valid in this case?

Hint:

For a long solenoid, \[ B=\mu_0 n I. \] When calculating mutual inductance, always use only the region where magnetic field actually exists. In this problem, the effective area is \(\pi r_1^2\), not \(\pi r_2^2\).

Answer 1