A loop in form of four connected semi-circular wires carrying current $I$ lies in the $x-y$ plane as shown in the figure. The unit vector $\hat k$ is coming out of the plane of the paper. The magnetic moment of the current loop is
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Magnetic moment of the current loop
$A=\pi\left(\frac{a}{2}\right)^{2} \times 2+a^{2}$
$=\left(\frac{\pi}{2}+1\right) \mathrm{a}^{2}$
$\overrightarrow {\text{M}} = {\text{I}}\overrightarrow {\text{A}} = \left( {\frac{\pi }{2} + 1} \right){\text{I}}{{\text{a}}^2}\widehat {\text{k}}$
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