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Homework Help: Method of image charges

  1. Feb 17, 2009 #1
    1. The problem statement, all variables and given/known data

    We have a conducting and grounded wall for [tex]z<0[/tex], so [tex]\Phi=0[/tex] for [tex]z<0[/tex]. In front of this wall, we place a homogeneous charged sphere with radius [tex]R[/tex] and total charge [tex]Q[/tex]. The center of the sphere has a distance of [tex]a[/tex] to the front of the wall.

    http://david.muelheims.googlepages.com/image_charges.png [Broken]

    I need to find the electrostatic potential [tex]\Phi(\vec{x})[/tex] for [tex]z>0[/tex] with the method of image charges.
    I just need the potential outside the sphere. I do not need to determine the potential inside the sphere.

    So... Where do I place the image charges?

    2. Relevant equations

    All electrostatic equations.

    3. The attempt at a solution

    I placed a first image charge in the center of the sphere, because a charged sphere acts like a point-charge in it's center. So I can replace the sphere with a single point-charge.
    Then I added a second image charge inside the wall with opposite charge [tex]-Q[/tex]. This second charged is placed exactly symmetrical to the first image charge.
    So... if the first charge is placed by [tex]z=a[/tex], I have placed the second at [tex]z=-a[/tex].

    Is this a correct/possible solution for this problem? Or do I need some different approaches here, because the wall has an effect on the charge on the sphere?
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Feb 17, 2009 #2


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    Homework Helper
    Gold Member

    You are going about this the correct way.
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