Why are electrical breakdowns more likely near sharp corners of conductors?

Electrical breakdowns are more likely to occur near the sharp corners of conductors because those areas experience the strongest electric fields.12

In a static situation, a conductor is an equipotential, meaning all parts of it are at the same potential. The electric field is defined by the negative gradient of the electric potential, and its magnitude is determined by how rapidly the potential changes over a given distance.12

When observing equipotential surfaces around a charged conductor, these surfaces are found to be closest to one another at sharp external corners. This proximity indicates a high rate of change in potential, which corresponds to a significantly higher electric field strength at those points. Furthermore, these locations of high field intensity coincide with the largest surface charge density, making them the most probable sites for electrical discharge or breakdown.12