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(B) The magnetic field $B_1$ produced by the large coil of radius $R$ at its center,carrying current $I_1$,is given by $B_1 = \frac{\mu_0 I_1}{2R}$.Th

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$\frac{\mu_0 \pi r^2}{2R}$

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(B) The magnetic field $B_1$ produced by the large coil of radius $R$ at its center,carrying current $I_1$,is given by $B_1 = \frac{\mu_0 I_1}{2R}$.The magnetic flux $\phi_2$ linked with the small coil of radius $r$ is $\phi_2 = B_1 	imes A_2$,where $A_2 = \pi r^2$ is the area of the small coil.Substituting the value of $B_1$,we get $\phi_2 = \left( \frac{\mu_0 I_1}{2R} ight) (\pi r^2) = \left( \frac{\mu_0 \pi r^2}{2R} ight) I_1$.The coefficient of mutual inductance $M$ is defined by $\phi_2 = M I_1$.Comparing the two expressions,we find $M = \frac{\mu_0 \pi r^2}{2R}$.

$A$ small coil of radius $r$ is placed at the centre of a large coil of radius $R$,where $R >> r$. The coils are coplanar. The coefficient of mutual inductance between the coils is

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