Question

A conducting loop of radius $r$ is placed concentric with another loop of a much larger radius $R$ so that both the loops are coplanar. Find the mutual inductance of the system of the two loops. Take $R>>r$.

Answer 1

Magnetic field at the centre of coil

$B_2=\frac{{\mu }_0{I}_2}{2R}$

Hence

$\varphi =B.A$

${\varphi }_1=\pi r^2{B}_2$

${\varphi }_1=\frac{{\mu }_0\pi r^2{I}_2}{2R}$

${\varphi }_1=M{I}_2$

$\therefore M=\frac{{\varphi }_1}{I_2}=\frac{{\mu }_0\pi r^2}{2R}$