Question

A circular loop with $N$ turns has radius $r$ . It lies in the x-y plane carrying current $I$ in the anti-clockwise direction. If the magnetic field in the region is $\overset{ \rightarrow }{B}=B_{0}\hat{i},$ then find the torque $\left(\right.\overset{ \rightarrow }{\tau}\left.\right)$ acting on the loop.

• A. $B_{0} \, NI \, \pi r^{2}\hat{j}$
• B. $B_{0}I \, \pi r^{2}\hat{j}$
• C. $B_{0} \, NI \, \pi r^{2}\hat{k}$
• D. $B_{0} \, \pi r^{2 \, }\hat{k}$

Answer 1

Answer: (A)

Magnetic moment $\overset{ \rightarrow }{M}=NI\left(\pi r^{2}\right)\hat{k}$
Torque $\overset{ \rightarrow }{\tau}=\overset{ \rightarrow }{M}\times \overset{ \rightarrow }{B}$
$=\left(N I \left(\pi r^{2}\right) \hat{k}\right)\times \left(\right.B_{0}\hat{i}\left.\right)$
$=B_{0}NI \, \pi r^{2} \, \, \, \hat{j} \, Nm$