First slide
Inductance
Question

A small square loop of wire of side l is placed inside a large square loop of wire of side L (L >> l) The loops are coplanar and their centre coincide. The mutual inductance of the system is proportional to

Moderate
Solution

Magnetic field produced due to large loop,

B=μ04π82iL

Flux linked with smaller loop,

ϕ=B(l)2=μ04π82il2L

ϕ=MiM=ϕi=μ04π82l2LMl2L

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