Electric potential inside a conductor due to a point charge outside the conductor

Question

I am a highschool student. I recently learned about conductors with cavity in school. How does a point charge outside the cavity, kept at a certain distance from the conductor, affect the potential of any point inside the cavity. I understand that the potential at any point inside the cavity. But how can an external point affect this.

Answer 1

Let the conducting cavity be neutral in empty space. A point charge far away has the Coulomb potential around its postion, that is very weak at the cavtity surface.

The conductor is defined to have a constant potential at its surface, a value, somehow equal to a mean over the value of the point charge at the cavity position.

Then by continuity of the potential as an integral over the electric field from infinity to the inner, the potential inside is constant.

The conductor rearranges its positive and negative charges at the surface exactly in such a way, that the electric field inside is zero and the potential is constant.

This is a thermodynamical phenomenon, only possible in the conduction band with its quasi-free electron gas at the Fermi energy edge of the thermal distribution.

The ultra short relaxation time of equlibrium reorganization rests on the fact, that the Fermi energy is greater than the thermal excitation energies by powers of 10; the reason, why immediate charge transport following the external fields in electronic devices functions up to GHz frequencies over distances of nm.