Why are electric fields strongest at sharp outer corners of charged conductors?

In the study of electrostatics, the strength of an electric field is determined by how rapidly the electric potential changes over a given distance. On a charged conductor in static equilibrium, the surface acts as an equipotential, meaning the potential is the same at all points on the conductor.12

The electric field is strongest where equipotential surfaces are closest together, as this indicates the greatest rate of change in potential. At the sharp outer corners of a conductor, these equipotential surfaces are more densely packed than on flatter surfaces. Consequently, the surface charge density is highest at these sharp external points, resulting in the strongest electric fields. Because of this high field intensity, electrical breakdowns are most likely to occur at these sharp corners. Conversely, the electric field is weakest in inside corners where the surface charge density is lower.12