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?".
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1$\begingroup$ Hint: What is $R$ for conductors? What is $R$ for superconductors? $\endgroup$– eranrechesCommented Dec 14, 2017 at 14:06
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2$\begingroup$ Possible duplicate of What happens when we connect a metal wire between the 2 poles of a battery? $\endgroup$– sammy gerbilCommented Dec 14, 2017 at 14:23
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$\begingroup$ @sammygerbil This is not a duplicate because of the extension to superconductors. $\endgroup$– garypCommented Dec 14, 2017 at 16:08
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2 Answers
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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.
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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.
