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Potential of a spherical shell (non-uniform charge density)

  1. Sep 8, 2015 #1
    1. The problem statement, all variables and given/known data
    Given a spherical shell of radius R and the surface charge density gif.gif ( gif.gif being the angle from the top of the sphere gif.gif and gif.gif being a constant) find the electric potential gif.gif and the electric field gif.gif inside and outside the sphere. Check that both the potential is continuous inside and outside the sphere and that gif.gif inside and out. I made this little diagram to illustrate.
    sphere_by_k4l3b-d98wxw3.png

    2. Relevant equations

    gif.gif
    gif.gif

    3. The attempt at a solution
    I can't even understand this problem. I feel like the point of interest shown in the diagram should be on the shell so that gif.gif can return a meaningful value, but I need to find the potential and electric field everywhere, so it can't be on the sphere.
     
    Last edited by a moderator: May 8, 2017
  2. jcsd
  3. Sep 9, 2015 #2

    BvU

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    Hello Guff,

    I notice that your problem statement mentions a charge distribution on the surface of the sphere, but that there is no equation where charge or charge density plays a role. Is there something you can add to your 'toolbox' ?
     
  4. Sep 9, 2015 #3
    If I looked at the charge distribution a point charge the field would look like this %5Cfrac%7B%28%5Csigma_%7B0%7Dcos%5Ctheta%29%284%5Cpi%20R%5E%7B2%7D%29%7D%7Br%5E2%7D%5Chat%7Br%7D.gif , but I know that isn't correct because I believe the total charge is zero. because half of the values of gif.gif are negative and the other half are positive.
     
  5. Sep 9, 2015 #4

    BvU

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    I still don't see how you want to find the field or the potential at a point in space.
    Where exactly on the sphere is ##\cos\theta## negative ?
     
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