Q. A wire of length 2 m carrying a current of 1 A is bent to form a circle, the magnetic moment of the coil is
A) $2\pi\ {Am}^{2}$
B) $\frac{1}{\pi}\ {Am}^{2}$
C) $\pi\ {Am}^{2}$
D) $\frac{2}{\pi}\ {Am}^{2}$
Explanation
(b) Circumference = length of the wire
$2\pi r = L$
$\ \ \ \ \ r = \frac{L}{2\pi}$
$\ \ \ \ \ r = \frac{1}{\pi}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (\because L = 2\ m)$
Magnetic moment $M = nIA$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 1 \times 1 \times \pi\left\lbrack \frac{1}{\pi} \right\rbrack^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{1}{\pi}\ {Am}^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.