Q. 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) $\sqrt{\frac{r\ \pi\ i}{M}}$
D) $\frac{M\ \pi}{4\ i}$
Explanation
(b) $l = 2\pi\ r\ \ \ \ \ \ \ \ \ \ \ or\ \ r = l/2\pi$
Area of circular loop, $A = \ \pi\ r^{2}$
Magnetic moment $M = lA = i\ \pi\ r^{2}$
$= i\ \pi \times l^{2}/4\pi^{2}$ or $l = \ \sqrt{4\ \pi\ M/i}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.