question_answer

[a] A circular coil having N turns and radius r carries a current I. It is held in the XZ plane in a magnetic \[B\hat{i}.\]The torque on the coil due to the magnetic field is :

A) \[\frac{B\pi {{r}^{2}}I}{N}\]

B) Zero

C) \[B\pi {{r}^{2}}IN\]

D) \[\frac{B{{r}^{2}}I}{\pi N}\]

Correct Answer: C

Solution :

\[\tau =NI\pi {{r}^{2}}B\sin 90{}^\circ =B\pi {{r}^{2}}IN.\]