Q. Current $i$ is carried in a wire of length $L$. If the wire is turned into a circular coil, the maximum magnitude of torque in a given magnetic field $B$ will be
A) $\frac{LiB^{2}}{2}$
B) $\frac{Li^{2}B}{2}$
C) $\frac{L^{2}iB}{4\pi}$
D) $\frac{Li^{2}B}{4\pi}$
Explanation
(c) $\tau_{\max} = NiAB = 1 \times i \times \left( \pi r^{2} \right) \times B\ \ \ \ \left\lbrack 2\pi r = L,\ \Rightarrow r = \frac{L}{2\pi} \right\rbrack$
$\tau_{\max} = \pi\ i\left( \frac{L}{2\pi} \right)^{2}\ B = \frac{L^{2}iB}{4\pi}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.