Using Gauss's theorem, show that one can not make a system of charges in a stable equilibrium, only by electrostatic forces. Hint:

Using Gauss’s theorem, show that one can not make a system of charges in a stable equilibrium, only by electrostatic forces. Hint: show that there exists no electrostatic field configuration that could create a stable equilibrium point, in free space, for a test charge. What does this result tell us about trapping charged particles? In other words, is it possible to make an electrostatic trap for ions and electrons? If not, how one can trap charged particles?