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Charged Conductors
Suppose that we put a negative charge on an arbitrarily shaped, solid,
conducting object. Where does the excess negative charge end up after the
charges have attained their equilibrium positions?
Let us construct a gaussian surface which lies just inside the surface
of the conductor. Application of Gauss' law yields

(75) 
where is the enclosed charge.
But, the electric fieldstrength inside a conductor must be zero, since the
charges are free to move through the conductor, and will, thus, continue to move until no field remains.
Hence, the lefthand side of the above equation is zero, and, therefore,
the righthand side must also be zero. This can only be the case if there are
no charges enclosed by the gaussian surface. In other words, there can be no excess
charge in the interior of the conductor.
Instead, all of the excess charge must be distributed
over the surface of the conductor. It follows that:
Any excess charge on a solid conductor resides entirely
on the outer surface of the conductor.
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Richard Fitzpatrick
20070714