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Homework Help: Current density of rotating spherical shell

  1. Nov 11, 2008 #1
    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. jcsd
  3. Nov 11, 2008 #2


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    It looks good, except I see no reason for you to restrict theta to [itex]0<\theta<\frac{\pi}{2}[/itex]....what is wrong with your expression for the lower half of the sphere?
  4. Nov 11, 2008 #3
    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!
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