Question

Explain why a conductor in electrostatic equilibrium should have no electric field parallel to its surface, nor within its bulk. (Hint: think about forces on a few charged particle).

Answer 1

the field inside a conductor must be zero in order for the system to be equilibrium and therefore there must be no excess charge inside.

Their proof:

1) Place a gaussian surface inside the conductor. Since the system is at equilibrium, all points on the surface must have an electric field of zero.

2) Therefore the net flux is zero, implying the charge inside is zero.

3) If there is no charge inside, all excess charge must lie on the surface.

In my opinion, equilibrium should be understood as no electron moving. It is easily to show that the electric field in conductor is zero. If the electric field is non-zero, then electrons in the conductor will feel it and move, until go to the boundary of the conductor, and then stop there. Hence, the surface will accumulate charge, and finally, the distribution of charge on the surface will make the field zero in the conductor.

Now, let us talk about the surface. If it is possible, I would like to say that the charge(electrons) are on the outside surface, mathematically. The field is zero in the conductor, as well as on the inside surface. But the field on the outside surface is not zero.

However, actually, in physics, this statement is not appropriate in microcosm, "surface" is many atoms layers. The electric field changes continuously in space, and external field is not zero but internal is zero.

In fact, when we talk about macroscopic description, we can treat the surface as a surface in mathematics. Therefore, we should distinguish two sides of surface.