Question

Two concentric circular loops of radii $r_1=30cm$ and $r_2=50cm$ are placed in $X-Y$ plane as shown in the figure. A current $I=7A$ is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately:

• A. $\frac{7}{2}\hat{k}A{m}^2$
• B. $-\frac{7}{2}\hat{k}A{m}^2$
• C. $7\hat{k}A{m}^2$
• D. $-7\hat{k}A{m}^2$

Answer 1

Answer: (B)

Magnetic moment
$\overrightarrow{M}=-i\pi (0.5{)}^2\hat{k}+i\pi (0.3{)}^2\hat{k}$
$\overrightarrow{M}=-7\times \frac{22}{7}\left(\frac{25}{100}-\frac{9}{100}\right)\hat{k}$
$=-22\left(\frac{16}{100}\right)\hat{k}$
$\overrightarrow{M}=-3.52\hat{k}A{m}^2$
$=-\frac{7}{2}\hat{k}A{m}^2$