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Mar9-12, 07:27 AM
One of Gauss' Law's predictions is for a solid (conducting) charged body with a a cavity in it. According to it, no charge can exist inside the body...the only charge on it must exist on it's outer surface; that means no charge can exist on the inner surface. We get to that conclusion if we consider a Gaussian surface inside the body's material (not in the cavity).
That's only true because the electrostatic field within a conductor must be zero. That goes beyond Gauss' law and has no parallel with gravity. (Gauss' law itself works just fine for both.)