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From Gauss's law you can easily conclude that in an electrostatic situation the only place where a net charge on a conductor can be is it's surface.

How can I demonstrate this experimentally?

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I think you'd have to be satisfied with a hollow conductor such as a thin-walled metal sphere with a large hole in the metal. You could charge the sphere, then sample the charge on the inside wall by sticking a proof-plane (metal disc on insulating handle) through the hole, withdrawing the proof plane and touching it on to the top disc of a gold leaf electroscope or its electronic equivalent.

You'd expect to find no charge on this inside wall. By contrast, if the proof plane is touched on to the outer surface, you should collect some charge.

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