Question

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

• A. $\frac{1}{2}{V}^{2}R$
• B. $\frac{1}{4}qVR$
• C. $\frac{1}{2}qVR$
• D. $\frac{1}{2}{q}^{2}VR$

Answer 1

The correct option is C $\frac{1}{2}qVR$

Current flowing through the loop $I=q\frac{V}{2\pi R}$

Area of the circular loop $A=\pi R^2$

Magnetic moment $\mu =IA$

$\therefore$ $\mu =\frac{qV}{2\pi R}\times \pi R^2=\frac{1}{2}qVR$