Question

A straight wire carrying current I is turned into a circular loop. If the magnitude of magnetic moment associated with it in M.K.S unit is $M$, then length of the wire will be:

• A. $4 \pi IM$
• B. $\sqrt{4 \pi IM }$
• C. $\sqrt{\frac{4 \pi M }{ I }}$
• D. $\frac{ M \pi}{4 I }$

Answer 1

Answer: (C)

Magnetic moment of circular loop carrying current
$M=I A=I\left(\pi R^{2}\right)$
$M=I \pi\left(\frac{L}{2 \pi}\right)^{2}$
$ \Rightarrow \frac{I L^{2} \pi}{4 \pi^{2}} $
$\Rightarrow \frac{\Pi^{2}}{4 \pi}=M$
$L =\sqrt{\frac{4 \pi M }{ I }}$