A charged particle (charge $q$) is moving in a circle of radius $R$ with uniform speed $v$. The associated…

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:
  1. $q v R^2$
  2. $q v R^2 / 2$
  3. $q v R$
  4. $q v R / 2$.

Solution

Magnetic moment $\mu=I A$ Since $T=\frac{2 \pi R}{v}$ also $I=\frac{q}{T}=\frac{q v}{2 \pi R}$ $\begin{aligned} \therefore \quad \mu & =\left(\frac{q v}{2 \pi R}\right)\left(\pi R^2\right) \\ & =\frac{q v R}{2} \end{aligned}$

Asked in: NEET 2007

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