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  4. 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

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Q. 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

JIPMERJIPMER 2015Moving Charges and Magnetism

Solution:

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 $n = 1$
$\therefore \:\:\:\:\: \tau_{max} = \frac{B I\, L^2}{4 \pi}$