Question

Two concentric circular loops of radii $r _1=30\, cm$ and $r _2=50 \,cm$ are placed in $X-Y$ plane as shown in the figure. A current $I=7 A$ 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. $\frac{7}{2} \hat{ k } Am ^2$
• B. $-\frac{7}{2} \hat{ k } Am ^2$
• C. $7 \hat{ k } Am ^2$
• D. $-7 \hat{ k } Am ^2$

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 } Am ^2$
$=-\frac{7}{2} \hat{ k } Am ^2$