Question

Magnetic field at the centre of a circular loop of area $A$ is $B$. The magnetic moment of the loop will be

• A. $\frac{B A^{2}}{\mu_{0} \pi}$
• B. $\frac{B A^{3 / 2}}{\mu_{0} \pi}$
• C. $\frac{B A^{3 / 2}}{\mu_{0} \pi^{1 / 2}}$
• D. $\frac{2 B A^{3 / 2}}{\mu_{0} \pi^{1 / 2}}$

Answer 1

Answer: (D)

$B=\frac{\mu_{0}}{4 \pi} \frac{2 \pi i}{r}=\frac{\mu_{0} i}{2 r}$
or $i=\frac{2 B r}{\mu_{0}}$
Also, $A=\pi r^{2}$ or $r=\left(\frac{A}{\pi}\right)^{1 / 2}$
Magnetic moment, $M=i A=\frac{2 B r}{\mu_{0}} A$
$=\frac{2 B A}{\mu_{0}} \times\left(\frac{A}{\pi}\right)^{1 / 2}$
$=\frac{2 B A^{3 / 2}}{\mu_{0} \pi^{1 / 2}}$