Question

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

Answer 1

Correct Answer - B
Magnetic field produced due to large loop `B=(mu0)/(4pi)(8sqrt(2i))/(L)`
flux linked with smaller loop
`varphi=B(l)^(2)=(mu_(0))/(4pi)(8il^(2))/(L)`
`:.varphi=Mi=M=(varphi)/(i)=(mu_(0))/(4pi).(8sqrt(2l^(2))/(L))impliesMprop(l^(2))/(L)`