Charge distribution on a conductor surface I understand that if a conductor was charged with a charge of say 1 coulomb, the charge would spread uniformly over it's entire surface to neutralize any difference in potential. However, and though this would obviously not be something done practically, what would happen if you added just one electron to the metal sphere.  Obviously the electron is incapable of splitting to distribute charge uniformly.
So would the electron just keep moving around the surface of the conductor? This would imply that the electric field just outside the conducting sphere wouldn't need to be perpendicular to it at all points.
 A: If electrons obeyed classical mechanics, they would rearrange in a new configuration in order to maximize the distance between them. They would not stay still because of thermal motion, as pointed out by CuriousOne, but on average they will still maximize this distance.
However, electrons don't obey classical mechanics, but quantum mechanics. The behavior of electrons in a conductor is more like that of waves (a plane wave in the free electron model, which is the crudest approximation). So the electron are delocalized on the whole surface of the conductor and it is probably more meaningful to talk about a single charge density function $\rho(\mathbf{r})$ rather than talking about individual electrons.
A: Electrons in metals have states which people call Bloch states. If we want to describe these states we should bear in mind that electrons have wave like behavior. Bloch states are a subset of the many infinite wave states which electrons can have in general. They're such that when an electron is in a Bloch state, it somehow fills everywhere in the metal. If you are familiar with the problem of a quantum mechanical particle in a box, you understand what I mean. So when we add a new electron to a metal, it spreads all over the metal, and hence it produces a uniform charge density(if we put away the effect of boundaries).
