Question

A straight wire carrying current $I$ is made into a circular loop. If $M$ is the magnetic moment associated with the loop, then the length of the wire is

• A. $\sqrt{\frac{4\pi M}{I}}$
• B. $\sqrt{\frac{2\pi M}{I}}$
• C. $\sqrt{\frac{\pi M}{I}}$
• D. $\sqrt{\frac{\pi M}{2I}}$
• E. $\sqrt{\frac{\pi M}{4I}}$

Answer 1

The correct option is A $\sqrt{\frac{4\pi M}{I}}$

Magnetic moment $M=IA$
According to question,
$2\pi R=L$
$\pi R=\frac{L}{2}$
$M=\frac{I}{\pi }{\pi }^{2}R$
$=I{\left(\frac{L}{2}\right)}^2$
$M=\frac{I}{\pi }{\left(\frac{L}{2}\right)}^2$
$M=\frac{I}{\pi }\frac{L^2}{4}$
Length of the wire, $L=\sqrt{\frac{4M\pi }{I}}$