Question

A straight wire carrying current i is turned into a circular loop. If the magnitude of magnetic moment associated with it in MKS unit is M, the length of wire will be

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

Answer 1

Answer: (B)

$l=2 \pi r$ or $r=\frac{l}{2 \pi}$
Area of circular loop $A=\pi r^{2}$
Magnetic moment $M=i A=i \pi r^{2}$
$M=i \pi \times l^{2} / 4 \pi^{2}$
or $l=\sqrt{\frac{4 \pi M}{i}}$