A small square loop of wire of side l is placed inside a large square loop of wire of side `L(Lgtgtl)`. The loops are co-planer and their centres coincide. The mutual inductance of the system is proportional to

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
`Bpropi/L" say"B=Ki/L`
`:.`Magnetic flux linked with similar loop,
`phi=B.S" "phi=(Ki/L)(t^2)`
Therefore, the mutual inductance `M=phi/i=Kl^2/L` or
`Mprop l^2/L`