Charge induced on conductor

  1. Imagine that there is a point charge in vicinity of an infinite grounded sheet of conductor of arbitrary shape and size such that the problem of finding the potential can be solved by using the method of images. Is their a way to prove that the total charge induced on this sheet is always equal to the sum of the imaginary charges? (there exists a way for proving this for finite conductors using the Gauss law) I am confused because in all the texts I referred to this conclusion was stated to be 'expected' or 'obvious', and I couldnt see why it would be so.
     
  2. jcsd
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