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Two conducting, charged spheres

  1. Sep 14, 2010 #1
    1. The problem statement, all variables and given/known data
    I have found this problem in Feynman Lectures on Physics vol. 2:

    Two equal conducting spheres, one with the total charge of [tex]+Q[/tex] and the other with a total charge of [tex]-Q[/tex], are placed at some distance from each other. What is the force between them?

    2. Relevant equations

    Coulomb's Law:
    [tex]F=k\frac{q_{1}\cdot q_{2}}{r^{2}}[/tex]

    3. The attempt at a solution
    There is a tip to solve that problem by constructing an infinite number of images, so I tried to do it that way:

    [PLAIN]http://img338.imageshack.us/img338/4906/rysp.jpg [Broken]

    X-coordinate of the n-image will be:
    The charge we have to place in that coordinates is:
    [tex]q_{n}=\frac{R}{d-x_{n-1}}\cdot q_{n-1}[/tex]

    Of course: [tex]x_{0}=0[/tex] and [tex]q_{0}=Q[/tex]

    Total force, which first sphere attract on the second, will be:
    [tex]F_{12}=\sum{k\frac{q_{n}\cdot (-Q)}{(d-x_{n})^2}}[/tex]

    Is that correct solution or not? And how to do the last operation?
    Last edited by a moderator: May 4, 2017
  2. jcsd
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