homework and exercises - Why do electric field lines start and end at 90 degree at the surface of a conductor?

There is one property of electric lines of forces which states that:

Electric field lines start and end at 90 degree at the surface of the conductor.

But why is that so? Is there any proof for this statement or is it observed by any experiment?

Answer

The reason is the same as why the electric field inside a conductor is zero: if it isn't zero, the free electrons undergo a force and move (rearrange) until they don't feel a force any more. If the electrons don't feel a force, the electric field must be zero.

At the surface of a conductor, the free electrons feel a force perpendicular to the surface, but can't go out of the conductor. If there were a component parallel to the surface, the force on the electrons also has a parallel component and the electrons would move until that component is zero.