The electric field on the metal surface is perpendicular to the surface, and it's strength is proportional to the surface charge density.
This applets try to demonstrate why the charge density is higher at the sharp edge.
Charge repel each other, however, there are free to move along the metal surface.
(Charge density is higher at the sharp edge, do not imply there are more charges. )
You can use mouse to drag the right slider up and down to change the shape of the ellipse.