A coil of radius 'r' is placed on another coil (whose radius is 'R' and current flowing through it is…
A coil of radius 'r' is placed on another coil (whose radius is 'R' and current flowing through it is changing) so that their centres coincide. $(\mathrm{R} \gg \mathrm{r})$ If both the coils are coplanar then the mutual inductance between them is proportional to
$\frac{r}{R}$
$\frac{R}{r}$
$\frac{R}{r^{2}}$
$\frac{r^{2}}{R}$
Solution
Magnetic field at the centre $\mathrm{B}=\frac{\mu_{\mathrm{o}} \mathrm{I}}{\mathrm{R}}$
$\phi=$ Magnetic flux passing through the smaller coil $=\pi r^{2} B$
$\therefore \phi=\pi r^{2} \times \frac{\mu_{0} I}{R}$
$\therefore M=\frac{\phi}{I}=\frac{\mu \pi r^{2}}{R} \quad \therefore M \propto \frac{r^{2}}{R}$