Electric field inside a conductor?
In the case of a finite conductor rod moving at a constant velocity perpendicularly to a uniform magnetic field, E. Purcell says that the free charges in the rod suffer a force such that they move to an extremity of the rod. When in the final state, he says (at least this is what I understand) that the force exerted on the charges, f is worth -qE where E is the electric field resulting of the polarization of the rod. I think I can understand this thanks to Lorentz force.
But... it means that there's an electric field not null inside a conductor (also outside it). I have had previously difficulties in grasping the fact that inside a charged conductor sphere, the electric field is null.
I realize that there are 2 different cases, but I think I could compare. As an example, in one case there is an excess of negative charges (over the conductor sphere), but the electric field inside the sphere is null.
In the other case, the rod (one could also take a sphere. Let's take a sphere!) is globally neutral, but on one side there's an excess of electrons and on the other side there's an excess of positive ions. However here the electric field inside the sphere is not null? Or is it? In the case of the rod it is NOT NULL. It is also not null outside it.
I have some doubts. I still don't understand well why is the electric field inside a conductor sphere null it seems.