Q. Magnetic induction at the centre of a circular loop of area $\pi\ m^{2}$ is 0.1 T. The magnetic moment of the loop is $\left( \mu_{0} = permeability\ of\ air \right)$
A) $\frac{0.1\pi}{\mu_{0}}$
B) $\frac{0.2\pi}{\mu_{0}}$
C) $\frac{0.3\pi}{\mu_{0}}$
D) $\frac{0.4\pi}{\mu_{0}}$
Explanation
(b) Magnetic induction at the center of circulre loop
$\ B = \frac{\mu_{0}}{2}\ .\frac{ni}{r}$
Magnetic moment of the loop
$M = niA = \frac{2BrA}{\mu_{0}}$
$\ \ \ \ \ = \frac{2 \times 0.1 \times 1 \times \pi \times (1)^{2}}{\mu_{0}}$
$\ \ \ \ \ = \frac{0.2\pi}{\mu_{0}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (\because r = 1)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.