Question

What is the mutual inductance of a small circular coil of radius \[r_1\] at the centre of a large circular coil of radius \[r_2\] when \[r_1\ll r_2\] ?

Options

• \[M=\frac{\mu_0\pi r_1^2I_2}{2r_2}\]

• \[M=\frac{\mu_0\pi r_1^2}{2r_2}\]

• \[M=\frac{\mu_0\pi r_2^2}{2r_1}\]

• \[M=\frac{2\mu_0\pi r_1^2}{r_2}\]

Answer 1

Divide \[\Phi_1=\mu_0\pi r_1^2I_2/(2r_2)\] by \[I_2\] to obtain \[M_{12}\] . Reciprocity gives the same value for \[M_{21}\] , so \[M=\frac{\mu_0\pi r_1^2}{2r_2}\] .