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I think there are two separate discussions going on here. When you use
values for C (or for coefficients of capacitance), you don't have to
think about how the charges arrange themselves on the individual
conductors--isn't that the whole point of using C or Cij?
But in order to calculate C in the first place, you do need to know
details of how the charges distribute themselves, using the fact that
E=0 inside each conductor, V is constant over each, etc.