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Excess charge on a conductor is unformily distributed on the surface and inside is electrically neutral. What is the charge distribution for excess charge on a non-conductor.

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In short: Whatever you apply (to some limit).
If you somehow 'place' charges on a non conductor, they will just stay where you placed them.

In practice there are some limitations, because no isolator is perfect. So depending on the charge sooner or later you will probably end up with uniformly distributed charges again, especially if you are not in a vacuum.

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