Thank you for reporting, we will resolve it shortly
Q.
A small circular loop of radius $a$ is placed inside a circular loop of radius $b(b>>a) .$ The loops are coplanar and concentric. The mutual inductance of the system is proportional to
Solution:
Flux through smaller coil
$=B \times \pi a^{2}$
and $B$ at centre of large coil
$B=\frac{\mu_{0} I}{2 b}$
$\therefore \phi=\left(\frac{\mu_{0} I}{2 b}\right) \times \pi a^{2}$
$=\left(\frac{\mu_{0} \pi}{2}\right)\left[\frac{a^{2}}{b}\right] I$
$\phi=M I .$
$\therefore \phi \propto \frac{a^{2}}{b}$
