Answer to Question #93461 in Electricity and Magnetism for MGM

Question

Three charges q, 2q and q are to be placed on a straight wire of length 10 m.
Determine the positions where the charges should to be placed so that the
electrostatic potential energy of the system is a minimum

Answer 1

We take a charge of 2q and we will move to it from infinity two other charges along the specified line. From symmetry considerations it follows that in the position of the minimum energy, the charges q should be located on both sides of the larger charge and at an equal distance from it. Since the energy of two point charges is inversely proportional to the distance between them, the following arrangement of charges corresponds to a minimum of energy: a larger charge in the center, smaller ones at the edges of the segment.