Due to the flow of current in a circular loop of radius $R$, the magnetic field produced at the centre of the loop is $B$. The magnetic moment of the loop is :-
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$\mathrm{M}=\mathrm{IA}$
$\mathrm{M}=\mathrm{I} \times \pi \mathrm{R}^{2}$
$\mathrm{B}=\frac{\mu_{0} \mathrm{I}}{2 \mathrm{R}} \Rightarrow \mathrm{I}=\frac{2 \mathrm{BR}}{\mu_{0}}$
So, $M=\frac{2 B R}{\mu_{0}} \times \pi R^{2}$
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