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

The correct option is A $B\pi r^{2}IN$


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