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(B) Let a current $i$ flow through the large square loop of side $L$. The magnetic field $B$ produced by the large loop at its center is approximately

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$\frac{l^2}{L}$

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(B) Let a current $i$ flow through the large square loop of side $L$. The magnetic field $B$ produced by the large loop at its center is approximately uniform over the area of the small loop of side $l$.The magnetic field at the center of a square loop of side $L$ is given by $B = \frac{2\sqrt{2}\mu_0 i}{\pi L}$.The magnetic flux $\phi$ linked with the small loop is $\phi = B 	imes A$,where $A = l^2$ is the area of the small loop.So,$\phi = \left(\frac{2\sqrt{2}\mu_0 i}{\pi L}ight) l^2$.The mutual inductance $M$ is defined as $M = \frac{\phi}{i}$.Therefore,$M = \frac{2\sqrt{2}\mu_0 l^2}{\pi L}$.Since $\mu_0$ and $\pi$ are constants,$M \propto \frac{l^2}{L}$.

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

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