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A small square loop of wire of side `l` is placed inside a large squre loop of wire of side `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 larger loop to be made up of four rods, each of length `L`, the field at the center, i.e., at a distance `L//2` from each rod, will be
`B = (mu _(0) I)/(4 pi d) [ sin alpha + sin beta]`
`= (mu _(0) I)/(4 pi (L//2)) 2 sin 45^(@) = (mu _(0)I)/(sqrt2 pi L)`

Net field: `B_(1) = 4 B_(0) = 2sqrt(2) (mu_(0) I)/(pi L)`
So the flux linked with the smaller loop is
`phi = B_(1)S_(2) = (2 sqrt(2) mu _(0) I)/(pi L) l^(2)`
Hence, `M = (phi)/(I) = 2 sqrt(2) (mu_(0)l^(2))/(pi L)`
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