What will happen to the charges if we dig a hole in a hollow charged conductor(example a hollow conducting sphere)? I am confused about how will the charges on outer surface of a hollow charged conductor would distribute themselves to make electric field zero inside after we dig a hole in the hollow conductor going from outer surface till the inner surface(imagine a thick hollow sphere having a hole piercing completely the thick layer of the sphere).my question is that are the charges now going to distribute themselves on the outer as well as the inner surface, as the inner surface is no longer inner because its connected to outer surface now because of the hole we dug?
 A: As an experimental fact a faraday cage keeps the charge on the outside even when it's made of mesh... as a first approximation that could be considered a sphere with huge numbers of holes dug through it... and yet the excess charge is only on the outside.
From that it follows if you made a hollow sphere as you described and cut a hole through it, the charge would all migrate to the outside to get the excess electrons as far away as possible from each other. The only non-uniformity would be around the lip of the hole... depending what the form of the lip was and how large the hole was.
If you increase the size of the hole at some point there won't be enough of a sphere to force the uniform charge onto the outside face... but the hole can be quite big.
A: If we can assume the hole to be very small, then we can assume this situation to be similar to a thick hollow sphere. In that case, the electron will allign themselves as per Gauss law with the additional facts that there are no electric fields within the conductor and the potential of the conductor through out its surface is constant. Hence,they will obviously distribute within the "inner surface" too.
