Slide 10 of 11
Notes:
The charges on a conductor flow to the surface and arrange themselves so that the electric force on each one due to all the rest is exactly perpendicular to the surface. This results in zero net field in the interior, and an external field that is perpendicular to the surface. This arrangement always has the external field greatest at places where the surface has very high convex curvature, I.e. where the conductor is “pointy.” By the same token, the external field is smaller where the surface is convex.
This is why lightning rods work -- the field gets so large near a sharp point that it ionizes molecules near it, making the air conducting, and gradually discharging the atmosphere.
