Question

Two circular concentric loops of radii $r_1=20cm$ and $r_2=30cm$ 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. $+1.1\hat{k}\left(A{m}^2\right)$
• B. $-1.5\hat{k}\left(A{m}^2\right)$
• C. $6$
• D. none of these

Answer 1

The correct option is A $+1.1\hat{k}\left(A{m}^2\right)$

$\begin{array}{c}Here,magneticmomentduetoloop1\\ M_1=i{A}_1\\ =i\pi {r_1}^2\\ =7\times \pi {\left(0.20\right)}^2=0.28\pi \\ similarlymagneticmomentduetoloop2\\ M_2=i{A}_2=i\pi {r_2}^2\\ =7\times \pi {\left(0.30\right)}^2=0.63\pi \\ Netmagneticmoment\\ =M_1-M_2\\ =0.63\pi -0.28\pi =61.1A{m}^2=+1.1\hat{k}\left(A{m}^2\right)\end{array}$

Hence,

option $\left(A\right)$ is correct answer.