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I am assuming that the charge distribution will be nonuniform due to the edges present at the holes and possibly at the seam between the two halves since charge is always more dense at edges and corners, so V will not be exactly kq/r.

I am mainly interested in whether the voltage would be greater or less than kq/r and how significant the difference would be. Although I wouldn't mind it if someone actually came up with a new function for the voltage.