Identical isolated conducting spheres 1 and 2 have equal charges and are separat

Question

Identical isolated conducting spheres 1 and 2 have equal charges and are separated by a distance that is large compared with their diameters (see Figure (a)). The magnitude of the electrostatic force acting on sphere 2 due to sphere 1 is F = 0.99 N. Suppose now that a third identical sphere 3, having an insulating handle and initially neutral, is touched first to sphere 1 (see Figure (b)), then to sphere 2 (see Figure (c)), and finally removed (see Figure (d)). What is the magnitude of the electrostatic force F' that now acts on sphere 2?

Explanation / Answer

when sphere 3 touches sphere 1, the charge q on sphere 1 moves freely around both conducting surfaces, so both spheres 1 and 3 share the charge equally, and thus both have charges of q/2

when sphere 3 touches sphere 2, the total charge of 3q/2 is shared by both spheres, so they both have a charge of 3q/4

then, the charge between 1 and 2 is (1/2)(3/4) of the original charge F, so F'/F=3/8

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