Question

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:-

• A. $\frac{B{R}^2}{2\pi {\mu }_0}$
• B. $\frac{2\pi B{R}^3}{{\mu }_0}$
• C. $\frac{B{R}^2}{2\pi {\mu }_0}$
• D. $\frac{2\pi B{R}^2}{{\mu }_0}$

Answer 1

The correct option is B $\frac{2\pi B{R}^3}{{\mu }_0}$

Magnetic field due to circular loop at its centre
$B=\frac{{\mu }_{0}I}{2R}.....\left(1\right)$
Magnetic moment due to circular loop carrying current $I$ is
$M=I\left(\pi R^2\right).....\left(2\right)$
dividing eqn. (2) by (1)
$\frac{M}{B}=\frac{I\left(\pi R^2\right)2R}{{\mu }_{0}I}$
$M=\frac{2\pi B{R}^3}{{\mu }_0}$