Two coaxial coils A and B of radii 'R ' and '$R_2$' are placed in the same plane. (R $_{2}>$…
Two coaxial coils A and B of radii 'R ' and '$R_2$' are placed in the same plane. (R $_{2}>$ $\mathrm{R}_{1}$). If a current is passed through coil $\mathrm{B}$, the coefficient of mutual inductance between the coils is proportional to
$\frac{1}{\mathrm{R}_{1} \mathrm{R}_{2}}$
$\frac{\mathrm{R}_{2}^{2}}{\mathrm{R}_{1}}$
$R_{1} R_{2}$
$\frac{\mathrm{R}_{1}^{2}}{\mathrm{R}_{2}}$
Solution
Magnetic field at the centre of primary coil
$B=\mu_{0} i_{1} / 2 R_{1} .$
Considering it to be uniform, magnetic flux passing through secondary coil is
$\phi_{2}=B A=\frac{\mu_{0} i_{1}}{2 R_{1}}\left(\pi R_{2}^{2}\right)$
Now, $M=\frac{\phi_{2}}{i_{1}}=\frac{\mu_{0} \pi R_{2}^{2}}{2 R_{1}}$
$\therefore \quad M \propto \frac{R_{2}^{2}}{R_{1}} .$