Question

A wire of length L is formed into a circular coil of n turns. If the coil carries a current i and placed in a given magnetic field B, the maximum possible torque developed is

• A. $\frac{nBi{L}^2}{4\pi }$
• B. $\frac{Bi{L}^2}{4\pi n}$
• C. $\frac{Bi{L}^2}{4\pi }$
• D. $Zero$

Answer 1

The correct option is B $\frac{Bi{L}^2}{4\pi n}$

$\left(2\pi r\right)\left(n\right)=L$
$r=\frac{L}{2\pi n}$
Area$=\pi r^2$
$=\frac{L^2}{4\pi n^2}$
$M=niA$
$=n\times i\times \frac{L^2}{4\pi n^2}$
$=\frac{i{L}^2}{4\pi n}$
Torque is
$Z_{max}=MBsin{90}^{\circ }$