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Method of images& half a sphere

  1. Apr 6, 2010 #1
    1. The problem statement, all variables and given/known data
    [PLAIN]http://img532.imageshack.us/img532/3751/39842434.png [Broken]
    Find the potential in all space for this configuration.

    2. Relevant equations
    ..basic electrostatics stuff, I guess.

    3. The attempt at a solution
    I can easily cancel the whole z=0 plane by placing a charge of -q under it, of course, but I have no idea what I should do about the half-sphere. I naturally went for placing a charge in the center of the sphere to cancel the other two, and I attempted this by calculating the potential on the top of the sphere ([PLAIN]http://img15.imageshack.us/img15/6324/kqr.gif, [Broken] if pythagoras was right) and negating that with another charge, but this naturally messes the z=0 plane. Is it some other configuration of charges that's symmetrical for the z=0 plane? I guess it has to be, but I have no idea what such configuration would also negate the potential of the sphere.
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 6, 2010 #2
    ..no, wait, I think I actually got this. Once I place the -q charge under the plane, the problem becomes equivalent to this:
    [PLAIN]http://img189.imageshack.us/img189/6430/spherel.png [Broken]
    , and then I just need to place charges q' and -q' symmetrically to the z=0 plane so that the potential on the sphere equals zero. Right?
    Last edited by a moderator: May 4, 2017
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