A loop 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 :
IIT 2012, Advanced
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$\text { Area }=a^2+4 \times \frac{\pi\left(\frac{a}{2}\right)^2}{2} $
$=a^2+\frac{\pi a^2}{2} $
$A=\left(1+\frac{\pi}{2}\right) a^2 \hat{k}$
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