I am not sure if I understood your answer. I rephrase my question in more detail. Imagine you have one charged point in the plane. The electrostatic potential due to this point charge is up to a multiplicative factor: phi=1/r. Consider an equipotential line by setting phi=c. This equipotential...
Imagine that you have N points scattered in the plane. Each point is charged and contributes to the total potential the same Coulomb potential proportional to 1/r. Now consider some equipotential line of the total electrostatic potential. Is there an analytical expression for the surface...