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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
A
$qvR^2$
B
$\dfrac{qvR^2}{2}$
C
$qvR$
D
$\dfrac{qvR}{2}$
Detailed Solution
A charge moving in a circle is equivalent to a current loop.
Time period of revolution: $T = \dfrac{2\pi R}{v}$
Equivalent current: $I = \dfrac{q}{T} = \dfrac{qv}{2\pi R}$
Magnetic moment: $\mu = IA$, with area $A = \pi R^2$
$\mu = \dfrac{qv}{2\pi R}(\pi R^2)$
$\mu = \dfrac{qvR}{2}$
Time period of revolution: $T = \dfrac{2\pi R}{v}$
Equivalent current: $I = \dfrac{q}{T} = \dfrac{qv}{2\pi R}$
Magnetic moment: $\mu = IA$, with area $A = \pi R^2$
$\mu = \dfrac{qv}{2\pi R}(\pi R^2)$
$\mu = \dfrac{qvR}{2}$