A wire of length L metre carrying a current of I ampere is bent in the form of a circle. Its magnetic moment…

When a wire of length, $L$ bent in the form of a circle of radius, $r$ then the relation between radius and length, by the formula of circumference, $2\pi r=L$, 

$\Rightarrow r=\frac{L}{2\pi }$, for one number of turns, the formula for the magnetic moment is, 

$M=I\left(A\right)$$\Rightarrow M=I\left(\pi r^2\right)$$=I\left(\pi \right){\left(\frac{L}{2\pi }\right)}^2$$=\frac{I{L}^2}{4\pi }$ $\mathrm{Am}^{2}$