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Can a charge, brought into a chargeless world filled with some geometry of conductors and dielectrics, induce a

I feel the answer is no. But I cannot think of a good way to prove it, or even attack the problem.

More explicitly, imagine a world with conductors and dielectrics in some fixed configuration.

There's no net charge anywhere, so all conductors at at 0 V, and every point in space is also at 0V. You bring some charge Q and stick it onto a conductor. The potential of that conductor will obviously go up. (The exact potential increase will depend on the world's configuration, with that conductor's capacitance relating the potential to the charge Q).

Is it possible for any other conductor in the world to reach a negative potential because of this charge?

My gut feeling is "no way", but I don't know how to prove it at all. I keep thinking of a conservation of energy explaination.. something on the lines of "if there was another conductor that had negative potential, I could bring even

I asked myself this question when I was learning about http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=131-12-32" I was asking myself how you might have negative entries in this matrix.. a matrix like [2, -1, 0][-1, 2, -1][0, -1, 2] is symmetric and positive definite, but is it a feasible capacitance matrix? What would such a conductor configuration be like?

**negative**potential anywhere in that world?I feel the answer is no. But I cannot think of a good way to prove it, or even attack the problem.

More explicitly, imagine a world with conductors and dielectrics in some fixed configuration.

There's no net charge anywhere, so all conductors at at 0 V, and every point in space is also at 0V. You bring some charge Q and stick it onto a conductor. The potential of that conductor will obviously go up. (The exact potential increase will depend on the world's configuration, with that conductor's capacitance relating the potential to the charge Q).

Is it possible for any other conductor in the world to reach a negative potential because of this charge?

My gut feeling is "no way", but I don't know how to prove it at all. I keep thinking of a conservation of energy explaination.. something on the lines of "if there was another conductor that had negative potential, I could bring even

**more**charge from infinity and put it on that conductor and get free work out of it." but that's not a full argument, much less a proof.I asked myself this question when I was learning about http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=131-12-32" I was asking myself how you might have negative entries in this matrix.. a matrix like [2, -1, 0][-1, 2, -1][0, -1, 2] is symmetric and positive definite, but is it a feasible capacitance matrix? What would such a conductor configuration be like?

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