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 ?

Options

A. `l//L`
B. `l^(2)//L`
C. `L//l`
D. `L^(2)//l`

Answer

B

Explanation

Magnetic field produced by a current`i` in a large square loop at its centre
`B prop (i)/(L)" "` say `B = K(i)/(L)`
`:.` Magnetic flux linked with smaller loop,
`phi = B.S " " phi = (K(i)/(L))(l^(2))`
Therefore, the mutual inductance `M = (phi)/(i) = K(l^(2))/(L)` or
`M prop (l^(2))/(L)`