Question

A hollow conducting sphere of radius $R$ and total charge $q$ rotates about its diametrical axis with constant angular speed $\omega$. The magnitude of magnetic moment of the sphere is :

• A. $\frac{1}{3}q{R}^2\omega$
• B. $\frac{2}{3}q{R}^2\omega$
• C. $\frac{1}{5}q{R}^2\omega$
• D. $\frac{2}{5}q{R}^2\omega$

Answer 1

The correct option is A $\frac{1}{3}q{R}^2\omega$

The ratio of magnetic moment and angular momentum for a rotating charged body is given by,

$\frac{M}{L}=\frac{q}{2m}$

$\Rightarrow M=\frac{qL}{2m}$

The angular momentum of a sphere about a diametric axis is given as,

$L=I\omega$

Where $I=\frac{2}{3}m{R}^2$

$\Rightarrow M=\frac{q\left(I\omega \right)}{2m}$

$M=\frac{q}{2m}\times \left(\frac{2}{3}m{R}^2\omega \right)$

$\therefore M=\frac{1}{3}q{R}^2\omega$

Hence, option $\left(A\right)$ is the correct answer.

Why this question? Note: The ratio of magnetic moment and angular momentum for a rotating charged body is given by, $\frac{M}{L}=\frac{q}{2m}$