A small square loop of wire of side $$l$$ is placed inside a large square loop of wire $$L$$ ($$L \gg l$$). Both loops are coplanar and their centres coincide at point $$O$$ as shown in figure. The mutual inductance of the system is

A

$$\dfrac{2\sqrt{2}\mu_0 L^2}{\pi l}$$

B

$$\dfrac{\mu_0 l^2}{2\sqrt{2}\pi L}$$

C

$$\dfrac{\mu_0 L^2}{2\sqrt{2}\pi l}$$

D

$$\dfrac{2\sqrt{2}\mu_0 l^2}{\pi L}$$