Q. Two circular concentric loops of radii $r_{1} = 20\ cm\ and\ r_{2} = 30\ cm$ are placed in the $X - Y$ plane as shown in the figure. A current $I = 7\ A$ is flowing through them. The magnetic moment of this loop system is
A) $+ \ 0.4\ \widehat{\mathbf{k}}\ \left( {Am}^{2} \right)$
B) $- 1.5\ \widehat{\mathbf{k}}\ \left( {Am}^{2} \right)$
C) $+ 1.1\ \widehat{\mathbf{k}}\ \left( {Am}^{2} \right)$
D) $+ \ 1.3\ \widehat{\mathbf{j}}\ \left( {Am}^{2} \right)$
Explanation
(c) Here, magnetic moment due to loop 1
$M_{1} = iA_{1}$
$\ \ \ \ \ \ = i\ \pi r_{1}^{2}$
$\ \ \ \ \ \ = 7 \times \pi\ (0.20)^{2} = 0.28\ \pi$
Similarly magnetic moment due to loop 2
$M_{2} = iA_{2} = i\pi r_{2}^{2}$
$\ \ \ \ \ \ = 7 \times \pi\ (0.30)^{2} = 0.63\ \pi$
Net magnetic moment
$\ \ \ \ \ \ = M_{1} - M_{2}$
$\ \ \ \ \ \ = 0.63\ \pi - 0.28\ \pi = 61.1\ {Am}^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.