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(B) The magnetic field at the center of a large coil of radius $R$ carrying current $I$ is given by $B = \frac{\mu_0 I}{2 R}$.Since $R \gg r$,the magn

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

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(B) The magnetic field at the center of a large coil of radius $R$ carrying current $I$ is given by $B = \frac{\mu_0 I}{2 R}$.Since $R \gg r$,the magnetic field $B$ is approximately uniform over the area of the smaller coil of radius $r$.The magnetic flux $\phi$ passing through the smaller coil is $\phi = B 	imes A$,where $A = \pi r^2$ is the area of the smaller coil.Substituting the values,we get $\phi = \left( \frac{\mu_0 I}{2 R} ight) 	imes \pi r^2$.The mutual inductance $M$ is defined as $M = \frac{\phi}{I}$.Therefore,$M = \frac{\frac{\mu_0 I}{2 R} 	imes \pi r^2}{I} = \frac{\mu_0 \pi r^2}{2 R}$.

$A$ coil of radius '$r$' is placed on another coil (whose radius is '$R$' and current flowing through it is changing) so that their centres coincide $(R \gg r)$. If both the coils are coplanar,then the mutual inductance between them is $(\mu_0 = \text{permeability of free space})$

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