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(A) The magnetic field $B$ at the center of the larger loop of radius $R$ carrying current $I$ is given by $B = \frac{\mu_0 I}{2R}$.The magnetic momen

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

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(A) The magnetic field $B$ at the center of the larger loop of radius $R$ carrying current $I$ is given by $B = \frac{\mu_0 I}{2R}$.The magnetic moment $m$ of the smaller loop of radius $r$ carrying current $i$ is $m = i A = i (\pi r^2)$.The torque $	au$ on a magnetic dipole in a magnetic field is given by $\vec{	au} = \vec{m} 	imes \vec{B}$.Since the planes of the two loops are at right angles,the angle between the magnetic moment vector $\vec{m}$ (perpendicular to the plane of the smaller loop) and the magnetic field vector $\vec{B}$ (perpendicular to the plane of the larger loop) is $90^\circ$.Therefore,the magnitude of the torque is $	au = m B \sin(90^\circ) = m B$.Substituting the values: $	au = (i \pi r^2) 	imes (\frac{\mu_0 I}{2R}) = \frac{\mu_0 \pi i I r^2}{2R}$.

$A$ circular loop of radius $R$ carries a current $I$. Another circular loop of radius $r (r \ll R)$ carries a current $i$ and is placed at the centre of the larger loop. The planes of the two circles are at right angles to each other. Find the torque acting on the smaller loop.

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