A small square loop wire of side $l$ is placed inside a large squre loop of side $L(L \ l).$ If the loops are coplanar and their centres coincide, the mutual induction of the system is directly proportional to

Question

A small square loop wire of side $l$ is placed inside a large squre loop of side $L(L > \ > l).$ If the loops are coplanar and their centres coincide, the mutual induction of the system is directly proportional to

Dr. Abubacker · Accepted Answer

(d) Considering the larger loop to be made up of four rods each of length $L$, the field at the centre,
$i.e.,$ at a distance $\left( \frac{L}{2} ight)$from each rod, will be
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$B = 4 	imes \frac{\mu_{0}}{4\pi}\frac{l}{d}\left\lbrack \sin\alpha + \sin\beta ightbrack$
$ie,\ \ \ \ B = 4 	imes \frac{\mu_{0}}{4\pi}\frac{I}{\left( \frac{L}{2} ight)} 	imes 2\sin{45{^\circ}}$
$ie,\ \ \ \ B_{1} = \frac{\mu_{0}}{4\pi}\frac{8\sqrt{2}}{L}I$
So, the flux with smaller loop
$\ \ \ \ \ \ \ \ \ \ \phi = B_{1}S_{2} = \frac{\mu_{0}}{4\pi}\frac{8\sqrt{2}}{L}l^{2}I$
and hence, $M = \frac{\phi_{2}}{I} = 2\sqrt{2}\frac{\mu_{0}}{\pi}\frac{l^{2}}{L}$
or $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ M \propto \frac{l^{2}}{L}$

Q. A small square loop wire of side $l$ is placed inside a large squre loop of side $L(L > \ > l).$ If the loops are coplanar and their centres coincide, the mutual induction of the system is directly proportional to

Explanation

Reviewed by Dr. Abubacker

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