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 manetic moment of the loop is:-

• A. $\frac{B{R}^3}{2{\pi }_3{\mu }_0}$
• B. $\frac{2\pi B{R}^3}{{\mu }_0}$
• C. $\frac{B{R}^2}{2{\pi }_2{\mu }_0}$
• D. $\frac{2\pi B{R}^2}{{\mu }_0}$

Answer 1

Answer: (B)

$\frac{2\pi B{R}^3}{{\mu }_0}$

The magnetic field due to the loop is:

$B=\frac{{\mu }_{0}i}{2R}$

$\Rightarrow i=\frac{B\times 2R}{{\mu }_0}$

Now, the magnetic moment is

$M=i\times A=i\pi R^2$

$=\frac{B\times 2R}{{\mu }_0}\times \pi R^2$

$=\frac{2\pi B{R}^2}{{\mu }_0}$