# Magnetic field at the centre of a circular loop of area $A$ is $B$. Then magnetic moment of the loop is

$\begin {array} {1 1} (a)\;\large\frac{2BA^2}{\mu_0}\sqrt{\large\frac{2}{\pi}} & \quad (b)\;\large\frac{2BA}{\mu_0}\sqrt{\large\frac{A}{\pi}} \\ (c)\;\large\frac{4BA}{\mu_0}\sqrt{\large\frac{A}{\pi}} & \quad (d)\;\large\frac{BA}{\mu_0}\sqrt{\large\frac{A}{\pi}} \end {array}$

magnetic moment $M = i\: A$......(1)
$B =\large\frac{ \mu_0 i}{2R}$ and $A=\pi R^2$
substituting for i and R in (1) we get the answer

Ans : (b)

edited Sep 17, 2014