Consider an uncharged sphere, made of electrically conducting material. We then charge the sphere with excess charges.
I understand that these excess charges repel each other till the electric field lines parallel to the surface of the sphere cancel out. Each charge experiences the superposition of electric fields provided by all other charges, and no net force is exerted on any charge. This results in an evenly distributed charge distribution on the surface of the sphere.
The system is in stable electrostatic equilibrium.
Consider that we take the same sphere with all the excess charges on the surface, and insert an additional charge into the center of the sphere, such that the system is in unstable electrostatic equilibrium.
Is this particular distrubution of charges (including the center charge) the only configuration of unstable electrostatic equilibrium?
Put another way, other than the distributions above, is there no other configuration of charges such that the closed system is in unstable electrostatic equilibrium?