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

The magnetic flux that links the larger loop with the smaller loop of side `l(lltltL)` is `f_(12)=Bl^(2)=(2sqrt(2)mu_(0)Il^(2))/(piL)`
`therefore` Mutual inductance `M_(12)=(phi_(12))/(I)=(2sqrt(2)mu_(0))/(pi)((l^(2))/(L))`
`i.eM_(12)prop(l^(2))/(L)`
`therefore (b)`