Identical isolated conducting spheres 1 and 2 have equal charges q and are separ

Question

Identical isolated conducting spheres 1 and 2 have equal charges q and are
separated by a distance r large compared to the diameters of the spheres. The electrostatic
force acting on sphere 2 due to sphere 1 is 3x10^(-6) N. Suppose now, that the third identical
sphere 3, having an isolating handle, and initially electrically neutral, is touched first to
the sphere 1, then to the sphere 2, and finally removed. Find the electrostatic force which
will be acting on the sphere 2 after all these manipulations.
Problem

Explanation / Answer

You have three identical spheres. The spheres 1 and 2 are placed at such a distance that the can be looked upon as point-like particles. When sphere 3 touches sphere 1 the charge of sphere 1 is equally spread over sphere 1 and 2. So each has That is a conclusion simple made out of symmetry considerations. When after-wards the sphere 3 touches sphere 2 the same effect happens and spher 2 and 3 both have 3/4 of the original charge of 1 and 2. In the end you have 2 charges of 1/2 and 3/4 times the original charges. The electric force is linear dependent on both charges. So the new force = (1/2)*(3/4)* 8.2 (8.2 is the old force). So the new one force = 3.1 N.

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