Question

Two circular concentric loops of radii $r_1=20cm$ , $r_2=30cm$ are placed in the $X-Y$ plane as shown in the figure. A current $I=7A$ is flowing through them. The magnetic moment of this loop system is

• A. $+0.4\hat{k}\left(A{m}^2\right)$
• B. $-1.5\hat{k}\left(A{m}^2\right)$
• C. $+1.1\hat{k}\left(A{m}^2\right)$
• D. $+1.3\hat{j}\left(A{m}^2\right)$

Answer 1

Answer: (C)

Here, magnetic moment due to loop $1$
$M_1=i{A}_1$
$=i\pi r_1^2$
$=7\pi {\left(0.20\right)}^2=0.28\pi$
Similarly magnetic moment due to loop- $2$
$M_2=i{A}_2=i\pi r_2^2$
$=7\pi {\left(0.30\right)}^2=0.63\pi$
Net magnetic moment
$=M_1-M_2$
$=0.63\pi -0.28\pi =1.1A{m}^2$
Since the net moment is along positive z-direction the answer is $+1.1\hat{k}\left(A{m}^2\right)$