Question

Hello,
If I have a conductor that has a whole inside and there's an electric field outside of it, that has nothing to do with it. How can I tell that the electric field inside the whole is 0?

Answer 1

In the same manner, if we put a conductor in a static electric field in the beginning the electric field will penetrate inside the material. As time passes the free electrons in the conductor will move in the opposite direction of the electric field and the holes will move in the same direction with the electric field which causes the positive charges and negative charges being collected on opposite sides of the material creating a field opposing the static electric field and a current density in the same direction with the electrostatic field. We can investigate the current density formula and the below graph for a better understanding of these situations.

Ј (current density) = σ (conductivity).E (electric field)
In part (1) all the electric field is penetrating through the material causing a current density in the same direction.

In part (2) as a result of the current in the material there happens to be an electric field opposing the external electric field so now only part of the external electric field is penetrating and the magnitude of the current density got smaller (can be seen by looking at the formula). The electric field inside the material is still in the + x direction with a magnitude equal to E - Ei.

In part (3) the same action continues as in part (2) and J gets smaller and Ei gets bigger. As a result the electric field penetrating through the material got even more smaller than part (2).

In part (4) E = Ei which means there is no more electric field in the material and the current density is zero. We can see that the negative charges are collected on the left side and positive charges on the right that creates a potential difference and the electric field Ei. We have to remember that and electric field is from positive to negative, the external electric field attracted the electrons to its source and repelled the protons away from its source.

The charge distribution on the material depends on the shape of the material and there will newer be tangential component of electric field on the surface because the it would cause the charges on the surface to move. That means under static conditions the E field on a conductor surface is everywhere normal to the surface which makes its surface an equipotential surface.