Question

A wire of length $L$ metre carrying a current $I$ ampere is bent in the form of a circle. It's magnitude of magnetic moment will be

• A. $\frac{IL}{4\pi }$
• B. $\frac{I^2{L}^2}{4\pi }$
• C. $\frac{I{L}^2}{4\pi }$
• D. $\frac{I{L}^2}{8\pi }$

Answer 1

The correct option is C $\frac{I{L}^2}{4\pi }$

If $r$ is the radius of the circle,

then $L=2\pi r$ or, $r=\frac{L}{2\pi }$
$Area=A=\pi r^2=\frac{\pi L^2}{4{\pi }^2}=\frac{L^2}{4\pi }$
$\text{Magnetic Moment}=IA=\frac{I{L}^2}{4\pi }$