Physicist John Lekner, has proven mathematically that they will attract when they get close enough together (paper's not live yet, but the link where it will eventually live is here). A region of positive charge on one sphere can cause the positive charge on the other to retreat, piling up further away and leaving a patch of negative charge behind.
English scientist William Snow Harris, who invented lightning conductors for ships, saw something like this in 1836 with charged disks. So now all that remains is for someone to prove Lekner's math experimentally today.
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