Question

A small coil of radius $r$ is placed at the centre of a large coil of radius $R$, where $R>>r$. The coils are coplanar. The coefficient of mutual inductance between the coils is:

• A. $\frac{{\mu }_o\pi r}{2R}$
• B. $\frac{{\mu }_o\pi r^2}{2R}$
• C. $\frac{{\mu }_o\pi r^2}{2R^2}$
• D. $\frac{{\mu }_o\pi r}{2R^2}$

Answer 1

The correct option is B $\frac{{\mu }_o\pi r^2}{2R}$

current coil having the radius R $B_1=\frac{{\mu }_0{I}_1}{2R}$

magnetic flux of the secondary coil

$I_2=B_1{A}_2=\frac{{\mu }_0{I}_1{\pi r}^2}{2R}$

mutual inductance

$\frac{{\mu }_0{\pi r}^2}{2R}$