Question

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

• A. $B \pi r^2 IN$
• B. $ \frac{B r^2 I}{\pi N}$
• C. Zero
• D. $ \frac{B \pi r^2 I}{N}$

Answer 1

Answer: (A)

Magnetic moment of coil = $NIA \hat{j}$
$ = NI(\pi r^2) \hat{j}$
Torque on loop (coil) = $\vec{M} \times \vec{B}$
$ = NI (\pi r^2) B \sin 90^{\circ} ( - \hat{k})$
$ = NI \pi r^2 B ( - \hat{k} ) $