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Which basic physics principle could I use to formulate a simple explanation of the homogeneous distribution of electric charge on the surface of a hollow metallic sphere?

P.S.: targeted audience with no background in physics.

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    $\begingroup$ I'd argue that this question isn't quite a duplicate, since it requests an answer that is comprehensible to a lay audience, which the other question does not. $\endgroup$
    – Brionius
    Commented Dec 10, 2015 at 22:27

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My explanation is that same kind of charge repel each other. So they place themselves on the surface of any sphere to maintain maximum distance among themselves.

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Like charges repel each other, and the closer they are, the more strongly they repel$^{†}$.

Therefore, if there is a place on a conducting sphere where the charges are closer than in other areas, the charges there will repel each other more strongly, and will push each other away from that place.

In this way, any inhomogeneities are quickly dispersed, and the distribution becomes homogenous.

$^{†}$See Coulomb's law for more detail

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