What is the Electric and Magnetic Dipole Moment of a Rotating Charged Sphere?

[shaun_chou]

Homework Statement

A sphere of radius a with a total charge q uniformly distributed on the surface and the sphere spins with an angular velocity w
Find the electric dipole moment of the sphere/electric field outside the sphere/magnetic dipole moment of the sphere/magnetic induction outside the sphere

Homework Equations

$$\Phi_{in}=\sum_{l=0}^{\infty}(A_l*r^l+B_l*r^{-l-1})P_l(\cos\theta)$$

The Attempt at a Solution

I can figure out the magnetic induction but I can't figure out the rest. Your comments are highly appreciated.

 

[gabbagabbahey]

Well, for starters, what is the formula for finding the electric dipole moment of an extended charge distribution? It should involve the charge density, so you will need to represent the charge density of a uniformly charged spherical surface...

Is the magnetic field (induction) you calculated static (independent of time)? If so, $\mathbf{\nabla}\times\textbf{E}$ will be zero and the electric field will be static (the charge distribution is static too) and you can use the methods you learned in electrostatics to find the Electric field (think Gauss' Law )

As for the magnetic dipole moment, what is the formula for finding the magnetic dipole moment of a current distribution?

 

[shaun_chou]

Thanks a lot!