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A charged particle (charge $q$) is moving in a circle of radius $R$ with uniform speed $v$. The associated magnetic moment $\mu$ is given by:
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Verified Answer
The correct answer is:
$q v R / 2$.
Magnetic moment $\mu=I A$
Since $T=\frac{2 \pi R}{v}$
also $I=\frac{q}{T}=\frac{q v}{2 \pi R}$
$\begin{aligned}
\therefore \quad \mu & =\left(\frac{q v}{2 \pi R}\right)\left(\pi R^2\right) \\
& =\frac{q v R}{2}
\end{aligned}$
Since $T=\frac{2 \pi R}{v}$
also $I=\frac{q}{T}=\frac{q v}{2 \pi R}$
$\begin{aligned}
\therefore \quad \mu & =\left(\frac{q v}{2 \pi R}\right)\left(\pi R^2\right) \\
& =\frac{q v R}{2}
\end{aligned}$
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