Q 12-04-154JEE MainJEE Main 2022 (26 Jul, Shift 2)Medium
Two concentric circular loops of radii $r_1 = 30\ \text{cm}$ and $r_2 = 50\ \text{cm}$ are placed in the $X$–$Y$ plane as shown in the figure. A current $I = 7\ \text{A}$ is flowing through them in the directions as shown in figure. The net magnetic moment of this system of two circular loops is approximately
Answer: (B) $-\dfrac72\hat k\ \text{A m}^2$
The inner loop carries current anticlockwise (moment along $+\hat k$) and the outer loop clockwise (moment along $-\hat k$).
$$\vec\mu = I\pi(r_1^2 - r_2^2)\hat k = 7\times\frac{22}{7}(0.09 - 0.25)\hat k = -3.52\hat k\approx-\frac72\hat k\ \text{A m}^2$$
Solution by Sreeraj P, M.Sc Physics