Problem 4. Identical isolated conducting spheres 1 and 2 have equal charges and are separated by a distance that is large compared with their diameters (a).
The electrostatic force acting on sphere 2 due to sphere 1 is F.
Suppose now that a third identical sphere 3, having an insulated handle and initially neutral, is touched first to sphere 1 and then to sphere 2 and finally removed.
The electrostatic force that now acts on 2 is f.
What is the ratio f/F
See attached file for full problem description.
For convenience of our deliberations, let us denote the original charge on each of the spheres as Q and the distance between the spheres as R, so that
F = kQ^2/R^2. ...
The solution calculates the f/F ration of identical isolated conducting spheres.