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)

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

Answer 2

The net magnetic moment of this system of two circular loops is :

$μ_1 = πr^2_1 \times I_1$

$μ_2 = πr^2_2 \times I_2$

Hence,$μ_{net} = (μ_2-μ_1)(-\hat k)$

= $π(r^2_2-r^2_1)I(-\hat k)$

= $3.142 \times (0.5^2-03^2)\times 7(-\hat k)$

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