Two loops with sides L and l (L >> l) are placed concentrically and coplanar as shown in figure. The mutual inductance of the system is proportional to

  l²/L

The value of B is given by Bigger loop at the centre is given by 

$B = \frac{2\sqrt 2 \mu_0 I}{\pi L}$

            The flux linked with the smaller loop

          $ \phi = M I = BA = Bl^2$

$\Rightarrow MI = \frac{2\sqrt 2 \mu_0 Il^2}{\pi L}$

$M \propto \frac{l^2}{L}$