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Q.

Two concentric circular loops of radii r₁ = 30 cm and r₂ = 50 cm 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 :

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a

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

b

$7 \hat{k} {Am}^{2}$

c

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

d

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

answer is B.

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Detailed Solution

Question Image

Magnetic moment

$\begin{array}{l} \vec{M} = - iπ (0 .5)^{2} \hat{k} + iπ (0 .3)^{2} \hat{k} \\ \vec{M} = - 7 \times \frac{22}{7} (\frac{25}{100} - \frac{9}{100}) \hat{k} \\ = - 22 (\frac{16}{100}) \hat{k} \\ \vec{M} = - 3 .52 \hat{k} {Am}^{2} \\ = - \frac{7}{2} \hat{k} {Am}^{2} \end{array}$

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