Two uniformly charged hollow hemispheres have charges Q and q, and radii R and r, respectively. The hemispheres are concentric and share their equatorial plane as shown in the figure. Calculate the electrostatic force F between the hemispheres.

(Contributed by José Ignacio Íñiguez-de-la-Torre Bayo, Universidad de Salamanca, Salamanca, Spain)

Column Editor’s note: Our December Challenge, Ride goes before the fall — 2, turned into an emotional roller coaster for the Column Editor, pun definitely intended. I am incredibly grateful to Carl Mungan who has graciously agreed to help me analyze the approaches presented by the readers. As a result, most of the solutions that we received (including Carl’s own) turned out to be incorrect, to the best of our judgment. Needless to say, the discussions produced some tension (this statement is intended not only as another pun but also as a hint).

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