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(A) The magnetic field $B$ produced by a large square loop of side $L$ at its center is given by $B = \frac{2\sqrt{2}\mu_0 I}{\pi L}$.Since the small

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$l^2 / L$

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(A) The magnetic field $B$ produced by a large square loop of side $L$ at its center is given by $B = \frac{2\sqrt{2}\mu_0 I}{\pi L}$.Since the small loop of side $l$ is placed at the center,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.Thus,$\phi = \left( \frac{2\sqrt{2}\mu_0 I}{\pi L} ight) l^2$.The mutual inductance $M$ is defined as $M = \frac{\phi}{I}$.Substituting the expression for $\phi$,we get $M = \frac{2\sqrt{2}\mu_0 l^2}{\pi L}$.Therefore,$M \propto \frac{l^2}{L}$.

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

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