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Old May 10th 2011, 02:49 PM   #11
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Okay, time to eat a little crow.

I had a reason for my mistake, but mind you it was still a rather large mistake. Looking back practically all of my experience with Gauss' Law has been with conductors and conductors have the rather special property that (in the static case) no electric fields can exist inside them. Apparently I got to the point of thinking that no electric field could exist inside any closed surface that did not contain a charge distribution. My apologies for that!

To answer your original question: There is no reason for the electric field to be 0 in a region if the exterior charge distribution is non-uniform. (Unless that region is in a conductor.)

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Old May 22nd 2011, 10:26 PM   #12
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I feel your frustration. It's happened to me many times, topsquark.

I believe the missing ingredient is that the charge on a simply connected closed conducting surface will rearrange such that the electric field on every surface element is normal to the surface. This means that the surface must be smooth, so that the norm is well defined for each element.

Interestingly, this will not work for a superconductor in the same way as a normal conductor. Rearrangement of charge is to a minimum energy state. In a normal conductor this is via resistive dissipation. A superconductor must radiate to obtain a minimum energy state.
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