Why does charge on a pointy conductor not uniformly spread?

[friendbobbiny]

Homework Statement

If charged is place on a spherical conductor, it distributes uniformly. If charged is placed on a conical conductor, it does not spread uniformly.

Homework Equations

Remember that, in a conductor, the motion of electrons is fluid.

The Attempt at a Solution

Taking the given example, a cone, if we placed charge on it, charge would spread. It would spread in the sense that every square centimeter would have a constant charge. Because surface area clumps near the cone's tip, however, charge would be more concentrated there.

I get the impression that this attempt is bogus. I don't see why a surface's surface area is greater at a vertex than on a flat plane.

 

[Windadct]

Why do they distribute at all?