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. `mu_(0)L^(2)l`
B. `2sqrt(2)(mu_(0)l^(2))/(piL)`
C. `2sqrt(2)(mu_(0)L^(2))/(pil)`
D. `mu_(0)l^(2)L`

Answer

B

Explanation

`phi = BA = Mi`
`M = (BA)/(i)`
`B = (mu_(0)i)/(4pi((L)/(2))) (sin 45^(@) + sin 45^(@)) xx 4 = (mu_(0)i)/(piL) (4)/(sqrt(2))`
`M = (mu_(0)i4 xx l^(2))/(piL sqrt(2))`
`= (2sqrt(2mu_(0)l^(2)))/(piL)`