Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Two circular concentric loops of radii $r_{1}=20 \, cm$ , $r_{2}=30 \, cm$ 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
Question

NTA AbhyasNTA Abhyas 2022

Solution:

Here, magnetic moment due to loop $1$
$M_{1}=iA_{1}$
$ \, =i\pi r_{1}^{2}$
$ \, =7\pi \left(0 .20\right)^{2}=0.28\pi $
Similarly magnetic moment due to loop- $2$
$M_{2}=iA_{2}=i\pi r_{2}^{2}$
$ \, =7\pi \, \left(0 .30\right)^{2}=0.63\pi $
Net magnetic moment
$ \, =M_{1}-M_{2}$
$ \, =0.63\pi -0.28\pi =1.1Am^{2}$
Since the net moment is along positive z-direction the answer is $+1.1 \hat{ k }\left( Am ^{2}\right)$