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By an ideal conductor, I mean one with zero resistance. Inside an ideal conductor with no current, the electric field is zero, but is the electric field still zero with the ideal conductor carrying a current?

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3 Answers 3

NOTE: This answer relates to original question, where ideal conductor was not specified to be the one with zero resistance.

No. The electric field is the requirement for the electrical current. This can be seen from the Ohm's law in th vector version

$$\vec{j} = \sigma \vec{E},$$

where $\vec{j}$ is current density and $\sigma$ is conductivity. Hence, no electric field, no current.

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I said an ideal conductor - meaning zero resistance –  Physiks lover May 20 '12 at 19:23
@Physikslover Fair enough, but "ideal conductor" usually means that the conductor conforms to Ohm's law. There are other conductors e.g. semiconductors, which are not "ideal". –  Pygmalion May 20 '12 at 19:26

If the conductor has zero resistance, then the force required in order to sustain the current is zero, (the electrons keep moving by themselves) so yes, the electric field is zero. As real example of that, an electric current flowing through a loop of superconducting wire can persist indefinitely with no power source !!!

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but "ideal conductor" usually means that the conductor conforms to Ohm's law.

I am surprised. I always heard " ideal " as " zero resistance when constant current flows ", hence zero potential drop along the wire. Hence the answer to the original question is yes, by definition.

Conductor that conforms to Ohm's law is called " ohmic ".

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