Question

A particle with charge $q$ is moving along a circle of radius $R$ with uniform speed $v$. The associated magnetic moment $\mu$ is given by:

• A. $\frac{1}{2} v^{2} R$
• B. $\frac{1}{4} qvR$
• C. $\frac{1}{2} qvR$
• D. $\frac{1}{2} q^{2} v R$

Answer 1

Answer: (C)

$N _{\text {persec }}=\frac{1}{ T }=\frac{ v }{2 \pi R }$
Current through circular orbit
$i =\frac{ q }{ T }=\frac{ vq }{2 \pi R }$
Magnetic moment $\Rightarrow \mu= IA$
$=\frac{ vq }{2 \pi R } \times \pi R ^{2}=\frac{ vqR }{2}$