Why does the electric field of a conducting charged sphere have lower energy than that of an insulating uniformly charged sphere? I know how to do the calculations, but I want to rationalize or understand intuitively why this is true.
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$\begingroup$ What is your definition for "charged sphere," and where are you getting this claim? $\endgroup$– probably_someoneCommented Sep 19, 2018 at 16:53
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$\begingroup$ @Aaron Stevens, yes, I do mean that. $\endgroup$– HBHSUCommented Sep 19, 2018 at 17:14
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1 Answer
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As I am sure you know, "like charges" repel. The farther away these charges can get away from each other, the less energy there is in the system. Charges will move to reduce the energy of the system.
In the insulating sphere, the excess charge cannot move around. However, if we somehow started with a conducting sphere with charges distributed throughout, the charges would almost instantaneously move to the outside of the sphere, since charges can freely move throughout a perfect conductor. Since we are not providing any additional energy to the system (the charges are moving around due to their own interactions), it must be that the charges are moving to a lower energy configuration.
answered Sep 19, 2018 at 17:38