A small square loop of wire of side `l` is placed inside a large square loop of wire of side `L (L gt gt l)`. The loops are coplanar and their centre coincide. What is the mutual inductance of the system ?

Explanation

Magnetic field produced by a current `i` in a large square loop at its centre is `B=(mu_(0)i2sqrt2)/(piL)`
Therefore`phi=Mi==(mu_(0)i2sqrt2)/(piL)xxl^(2) rArr M=(2sqrt2mu_(0)l^(2))/(piL)`