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In the aproximation that distance between the plates are very small in
comparition to their size, that is, infinite area of the capacitor, or
no end effects, we have total electrostatic influence between the plates:
No E field line will reach infinity. That establishes a one-to-one aplication
between charges of both plates. Charges are the source of E, and it also die
at them.
Won't this be enough? I guess what your answer will be: no, but it will be
interesting to know why)