There is no electric field in a metal if the current through the conductor remains constant.

Question

In a chapter of superconductor, I found, "There is no electric field in a metal if the current through the conductor remains constant". My question is, "Why the electric field is zero in such case?". And, "Is it only true for superconductors or for all conductors?".

Answer 1

In a superconductor, there are no collisions to slow moving electrons down. Therefore, if there were a nonzero electric field, the electrons making up the current would be ballistically accelerated by the constant force $\vec{F}=-e\vec{E}$. If the current flowing is constant, then the charge carriers are not accelerating through the superconductor; hence $\vec{E}$ must be zero inside.

Answer 2

It is not true for ordinary conductors where ρ = E / J; ρ = resistivity, E = electric field and J = current density. J != 0 means E != 0 within the conductors.

For superconductors, ρ = 0 and a uniform J may flow with E = 0.