Two conducting circular loops of radii R_1 and R_2 are placed in...

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} \quad \therefore \quad M \propto \frac{R_2^2}{R_1}.