Walker, Halliday & Resnick — Coulomb's Law: Problem 24

24 Identical isolated conducting spheres 1 and 2 have equal charges and are separated by a distance that is large compared with their diameters (Fig. 21-17a). The electrostatic force acting on sphere 2 due to sphere 1 is \(\vec{F}\). Suppose now that a third identical sphere 3, having an insulating handle and initially neutral, is touched first to sphere 1 (Fig. 21-17b), then to sphere 2 (Fig. 21-17c), then to sphere 1 again (not shown), and then finally removed (Fig. 21-17d). The electrostatic force that now acts on sphere 2 has magnitude \(F'\). What is the ratio \(F'/F\)?