Equal Charges May Attract

Let us consider the interaction between an isolated conducting sphere of radius with net charge +q+q (on its surface) and a point charge +q+q, located at a distance d>Rd>R from the center of the sphere. For large distances dd, the sphere and the point charge repel. It turns out, however, that they attract if the point charge is sufficiently close to the sphere. Show that for dR<η\frac{d}{R}< \eta, the sphere attracts the point charge. Determine η\eta.

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