# Equal Charges May Attract

Let us consider the interaction between an isolated conducting sphere of radius with net charge $$+q$$ (on its surface) and a point charge $$+q$$, located at a distance $$d>R$$ from the center of the sphere. For large distances $$d$$, 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 $$\frac{d}{R}< \eta$$, the sphere attracts the point charge. Determine $$\eta$$.

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