Question

A solid conducting sphere of radius R and total charge q rotates about its diametric axis with constant angular speed $\omega$.The 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

Answer: (C)

$\frac{1}{5}q{R}^2\omega$

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

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

$=(\frac{q}{2m}\left)\right(\frac{2}{5}m{R}^2\omega )$
$=\frac{1}{5}q{R}^2\omega$