Question

A wire of length $L$ is bent in the form 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. $\frac{2IBL^{2}}{\pi}$

Answer 1

Answer: (B)

$\frac{IBL^{2}}{4\pi}$

Answer 2

Let $r$ be the radius of the coil and $n$ be the number of turns formed. Then
$L = 2 \pi r n$ or $r = \frac{L}{2 \pi n}$ ....(i)
Maximum torque, $\tau_{max} = B \, n\, IA = B \, n \, I \, \pi r^2$
$= B\, n \, I \, \pi \times \frac{L^2}{4 \pi^2 n^2} = \frac{B IL^2}{4 \pi n}$
Torque will be maximum if $n = 1$
$\therefore \:\:\:\:\: \tau_{max} = \frac{B I\, L^2}{4 \pi}$