Q. Two wires of same length are shaped into a square and a circle. If they carry same current, ratio of the magnetic moment is
A) $2\ :\pi$
B) $\pi\ :2$
C) $\pi\ :4$
D) $4\ :\ \pi$
Explanation
(c) Suppose length of each wire is $l.\ A_{square} = \left( \frac{l}{4} \right)^{2} = \frac{l^{2}}{16}$
$A_{circle} = \pi r^{2} = \pi\left( \frac{l}{2\pi} \right)^{2} = \frac{l^{2}}{4\pi}$
$\because$ Magnetic moment
$M = iA$
$\Rightarrow \frac{M_{square}}{M_{circle}} = \frac{A_{square}}{A_{circle}}$
$= \frac{l^{2}/16}{l^{2}/4\pi} = \frac{\pi}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.