- #1
drumercalzone
- 13
- 1
Homework Statement
Show for a solid spherical ball of mass m rotating about an axis through its center with a charge q uniformly distributed on the surface of the ball that the magnetic moment [itex]\mu[/itex] is related to the angular momentum
[itex] \vec{\mu}={\frac{5q}{6mc}}\vec{L} [/itex]
Homework Equations
[itex]\mu = \frac{IA}{c}[/itex]
[itex]I_{sphere} = \frac{2mr^2}{5}
[/itex]
The Attempt at a Solution
My initial thought was to think of the sphere as rings of charge, each of which is comprised of point particles of charge [itex] dq=\frac{q}{4{\pi}r^2} [/itex] which trace out current rings of area [itex] A={\pi}r^2 [/itex]. Then I could integrate dI w.r.t dr, but I got a factor of 1/4 instead of 5/6, making me think that I'm going about the integration the wrong way.
Any ideas?