Q.
A loop carrying current I lies in the $x$-$y$ plane as shown in the figure. The unit vector $\widehat{k}$ is coming out of the plane of the paper. The magnetic moment of the current loop is
A) $a^{2}I\widehat{k}$
B) $\left( \frac{\pi}{2} + 1 \right)a^{2}I\widehat{k}$
C) $- \left( \frac{\pi}{2} + 1 \right)a^{2}I\widehat{k}$
D) $(2\pi + 1)a^{2}U\widehat{k}$
Explanation
(b) $M = I \times$ Area of loop $\widehat{k}$
$= I \times \left\lbrack a^{2} + \frac{\pi a^{2}}{4 \times 2} \times 4 \right\rbrack\widehat{k}$
$= I \times a^{2}\left\lbrack \frac{\pi}{2} + 1 \right\rbrack\widehat{k}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.