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TSny
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Here's another example that I think supports the conjecture that the congruent conductors do not need to end up with equal charges.
Consider a thin-walled conical conductor
If you put charge on this, then I believe that most of the charge will be located on the outer surface. Very little charge will be on the inner surface, especially if the apex angle is small. But I don't know how to prove this.
Now slip an identically shaped, uncharged conductor inside of the charged one until they touch.
This is almost like a single conical conductor. So, most of the charge should remain on the outer surface of the outer conductor.
This example is not meant as a proof, but I think it is suggestive.
Consider a thin-walled conical conductor
If you put charge on this, then I believe that most of the charge will be located on the outer surface. Very little charge will be on the inner surface, especially if the apex angle is small. But I don't know how to prove this.
Now slip an identically shaped, uncharged conductor inside of the charged one until they touch.
This is almost like a single conical conductor. So, most of the charge should remain on the outer surface of the outer conductor.
This example is not meant as a proof, but I think it is suggestive.
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