Question

Two particles, each of mass $m$ and charge $q$, are attached to the two ends of a light rigid rod of length $2R$. The rod is rotated at constant angular speed about a perpendicular axis passing through its center. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the center of the rod is

• A. $\frac{q}{2m}$
• B. $\frac{q}{m}$
• C. $\frac{2q}{m}$
• D. $\frac{q}{\pi m}$

Answer 1

The correct option is A $\frac{q}{2m}$

Current, $i=$ (frequency) (charge)

$=\left(\frac{\omega }{2\pi }\right)\left(2q\right)=\frac{q\omega }{\pi }$

Magnetic moment,

$M=\left(I\right)\left(A\right)=\left(\frac{q\omega }{\pi }\right)\left(\pi R^2\right)=\left(q\omega R^2\right)$

Angular momentum, $L=2I\omega =21\left(m{R}^2\right)\omega$

$\frac{M}{L}=\frac{q\omega R^2}{2\left(m{R}^2\right)\omega }=\frac{q}{2m}$