Homework Help: Current density of rotating spherical shell

1. Nov 11, 2008

icelevistus

Express the current density of a spherical shell of radius a, rotating with angular velocity omega, with surface charge density sigma

Delta function will be denoted d(x). Spherical coordinates will be used

I have concluded that for a given chunk (if we restrict to the 0<theta<pi/2 domain), the velocity will be given by v=a*Sin(theta)*(omega). It is clear that the current density will only have a phi component. I have concluded:

J_phi = (sigma)*a*Sin(theta)*(omega)*d(r'-a)

Where the delta function is used to restrict the current density to the sphere's surface.

Can anyone confirm that this reasoning is correct?

2. Nov 11, 2008

gabbagabbahey

It looks good, except I see no reason for you to restrict theta to $0<\theta<\frac{\pi}{2}$....what is wrong with your expression for the lower half of the sphere?

3. Nov 11, 2008

icelevistus

you're right, as I was writing it I thought I was using cosine and it would introduce a sign error. Whole shell it is!