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A small square loop of wire of side l is...

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 ?

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Considering the large loop to be made up of four rod each of length L, the field at the cenre i.e at a distance (L/2) from each rod, will be
`B=4xx(mu_0)/(4pi)I/d[Sin alpha+sin beta]`
i.e `B=4xx(mu_0)/(4pi)I/((L//2))xx2 sin 45`

i.e `B_1=(mu_0)/(4pi)(8sqrt2)/(L)I`
So the flux linked with smaller loop
`phi_2 =B_1S_2=(mu_0)/(4pi)(8sqrt(21))/(L)l^2`
and hence,. `M=(phi_2)/I=2sqrt2(mu_0)/(pi)(l^2)/L rArr M prop (l^2)/L`
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