A conductor is in electrostatic equilibrium when the charge distribution is fixed. A conductor reaches equilibrium in a very short time after being exposed to an external field. At equilibrium, the charge and electric field follow these guidelines:

• the electric field is zero within the solid part of the conductor
• the electric field at the surface of the conductor is perpendicular to the surface
• any excess charge lies only at the surface of the conductor
• charge accumulates, and the field is strongest, on pointy parts of the conductor

As we have seen, at equilibrium the field is zero inside a conductor and perpendicular to the surface of the conductor because the electrons in the conductor move around until this happens.

Excess charge, if the conductor has a net charge, can only be found at the surface because if any was in the bulk there would be a net field inside the conductor, violating point 1. Usually the excess charge is on the outer surface.

Charge piles up at pointy ends of a conductor (making the field strongest there) to balance forces on the charges. On a sphere or circle, charges are uniformly distributed because if they weren't there would be net forces pushing the charges toward this uniform distribution.

For charges in a line, however, a uniform distribution does not correspond to equilbrium. Start out with the charges equally spaced, and you'll find that the forces the charges experience push them so that they accumulate at the ends.