Question

A circular coil having N turns is made from a wire L meter long. If a current of I ampere is passed through this coil suspended in a uniform magnetic field of B tesla, find the maximum torque that can act on this coil.

Answer 1

We know that torque is given by

$\tau =\overrightarrow{M}\times \overrightarrow{B}$

${\tau }_{max}=MB$

$M=NIA=NI\pi R^2$

Length=$N\times circumference⟹L=N2\pi R$

$⟹R=\frac{L}{2\pi N}$

$M=NI\pi \frac{L^2}{4{\pi }^2{N}^2}=\frac{I{L}^2}{4\pi N}$

${\tau }_{max}=\frac{I{L}^{2}B}{4\pi N}$