Question

A small coil of radius $r$ is placed at the center of a large coil of radius $R$, where $R>>r$. The two coils are coplanar. The mutual inductance between the coils is proportional to

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

Answer 1

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

Magnetic field at the centre of a large coil , $B=\frac{{\mu }_{0}I}{2R}$
as, $r<<R$,
Magnetic flux linkage $\varphi =\frac{{\mu }_{0}I}{2R}\times \pi r^2$
$M=\frac{\varphi }{I}=\frac{{\mu }_0\pi r^2}{2R}$
$\therefore M\propto \frac{r^2}{R}$