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(D) The magnetic field at the center of a circular loop of radius $r_1$ carrying current $I$ is given by $B = \frac{\mu_0 I}{2 r_1}$.Since the rings a

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$\frac{\mu_0 \pi r_2^2}{2 r_1}$

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(D) The magnetic field at the center of a circular loop of radius $r_1$ carrying current $I$ is given by $B = \frac{\mu_0 I}{2 r_1}$.Since the rings are concentric and coplanar,the magnetic field $B$ is uniform over the area of the smaller ring (radius $r_2$).The magnetic flux $\phi$ linked with the smaller ring is $\phi = B 	imes A_2$,where $A_2 = \pi r_2^2$ is the area of the smaller ring.$\phi = \left( \frac{\mu_0 I}{2 r_1} ight) 	imes \pi r_2^2 = \frac{\mu_0 \pi r_2^2}{2 r_1} I$.The mutual inductance $M$ is defined as $M = \frac{\phi}{I}$.Therefore,$M = \frac{\mu_0 \pi r_2^2}{2 r_1}$.

The planar concentric rings of metal wire having radii $r_1$ and $r_2$ (with $r_1 > r_2$) are placed in air. The current $I$ is flowing through the coil of larger radius. The mutual inductance between the coils is given by $(\mu_0 = \text{permeability of free space})$

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