Question

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\,\hat{k}\left(Am^{2}\right) $
• B. $ -1.5\,\hat{k}\left(Am^{2}\right) $
• C. $ +1.1\,\hat{k}\left(Am^{2}\right) $
• D. $ +1.3\,\hat{j}\left(Am^{2}\right) $

Answer 1

Answer: (C)

Here, magnetic moment due to loop $1, M_{1}=iA_{1}$
$=i \pi r^{2}_{1}$
$=7 \times \pi (0.20)^{2}=0.28 \pi$
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
$=M_{1}-M_{2}=0.63\pi-0.28\,\pi$
$=1.1\,Am^{2}$