A loop carrying current i lies in \( x-y \) plane as shown in the f...

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A loop carrying current i lies in \( x-y \) plane as shown in the figure. The loop is made of 4 semicircular portions. The magnetic moment of the current loop is
(1) \( a^{2} \hat{i k} \)
(2) \( (2 \pi+1) a^{2} i \hat{k} \)
(3) \( \left(1+\frac{\pi}{2}\right) \mathrm{ia}^{2} \hat{\mathrm{k}} \)
(4) \( -\left(1+\frac{\pi}{2}\right) i a^{2} \hat{k} \)
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