If there is an excess of charge on a conductor, then the charges in the conductor will tend to get as far away from each other as possible.
Inside an electric conductor, the free electrons are free to move. These electrons redistribute themselves in such a way that all the excess charge gets distributed as widely spaced as possible, and the electric field inside the conductor vanishes.
This is only possible if all the excess charge gets distributed on the surface of the conductor, where the surface charge density will be minimum.
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