Q. A wire of length $l$ is bent in the from of a circular coil of some turns. A current $i$ flows through the coil. The coil is placed in a uniform magnetic field $B$. The maximum torque on the coil can be
A) $\frac{iBl^{2}}{2\pi}$
B) $\frac{iBl^{2}}{4\pi}$
C) $\frac{iBl^{2}}{\pi}$
D) $\frac{2iBl^{2}}{\pi}$
Explanation
(b) Let $r$ be the radius of the coil and $n$ be the number of turns formed. Then
$l = 2\pi rn\ \ \ \ \ \ \ \ \ or\ r = \frac{1}{2\pi n}$ (i)
Maximum torque, $\tau_{\max} = B\ n\ iA = Bni\pi r^{2}$
= $B\ ni\ \pi \times \frac{l^{2}}{4\pi^{2}n^{2}} = \frac{iBl^{2}}{4\pi n}$
Torque will be maximum if $n = 1$
$\therefore\ \ \tau_{\max} = \frac{Bil^{2}}{4\pi}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.