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About Coefficients of Potentials

  1. Dec 20, 2011 #1
    1. The problem statement, all variables and given/known data

    I want to prove that coefficients of potential are non-negative. i.e. Pij ≥ 0

    2. Relevant equations

    By coefficients of potential method we know that in a system of conductors the potential on ith conductor is related to charges on conductors by:

    [itex]\Phi[/itex]i = [itex]\sum[/itex] Pij Qj

    3. The attempt at a solution

    It is written in Reitz and Milford that it is hard to prove in a rigorous way. I think that we should use Pii ≥ Pij.
  2. jcsd
  3. Dec 20, 2011 #2
    how is the system arranged?
  4. Dec 21, 2011 #3
    This is a general statement. Of course we should set a specific arrangement to obtain a result. for example put Qi on ith conductor and assume jth conductor to be grounded and Q on other conductors to be zero.
    But I haven't found the correct conditions.
  5. Dec 21, 2011 #4
    in your scenario, should the conductors be sufficiently a long way away, their potentials will not effect each other (to a certain approximation) hence defeating the equation connecting the potential of one to the charge of another.
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