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Magnetic field at the center of a circular coil is B. If area of the coil is A then magnetic moment of the loop is

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$\frac{{BA}^{2}}{μ_{0} π}$

$\frac{BA \sqrt{A}}{μ_{0}}$

$\frac{BA \sqrt{A}}{μ_{0} π}$

$\frac{2 BA}{μ_{0}} \sqrt{\frac{A}{π}}$

answer is D.

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Detailed Solution

magnetic moment is M= iA , $B = \frac{μ_{0} i}{2 r} \Rightarrow i = \frac{2 rB}{μ_{0}}$

$A = {πr}^{2} \Rightarrow r = \sqrt{\frac{A}{π}}$
$M = \frac{2 rB}{μ_{0}} A = \frac{2 B}{μ_{0}} \sqrt{\frac{A}{π}} A$

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