New solutions for charge distribution on conductor surface

• Exact expressions for surface charge density for three cases are obtained.
• The method derives a set of complicated surfaces of revolution.
• The expressions can be used to verify different numerical solutions for the problem.

In the paper, a problem of electrostatics for charge distribution on a conductor surface is analytically solved for three new particular cases of conducting surfaces with complicated shape and specified value of electrostatic potential. The exact analytical expressions for surface charge density for the bodies are obtained. All the solutions are represented in a clear view of 3D graphs. It is shown that the proposed method of electrostatic problem for conductors allows to obtain infinitely many numerical solutions for the problem but only several special cases can be solved analytically.