Answer to Question #45154 in Electricity and Magnetism for Anurodh

Question

Three charges 4q, 2q and 4q are to be placed on a 10 m long straight wire.
Determine the positions where the charges should to be placed so that the potential energy of the
system is a minimum.

Answer 1

First thing is obvious that charges that are bigger in amplitude must be at maximum distance, as they are repelling (and closer they are, bigger potential energy is) hence 4q charges must be at the ends of the wire. Then, the only place where 2q charge will be in equilibrium is center of the wire. Equilibrium is always minimum of potential energy. Therefore, positions are 4q at 0, 2q at 5 and another 4q at 10 m.