If a superconducting wire has infinite conductivity, then there should be zero electric field inside it. However if there's no electric field inside it, there should be no current (as there's no voltage difference), right? In the AC case, one could imagine the current being strictly carried on the outter surface, but what about the DC case? In ordinary conductors the current flows in the whole bulk (but there's an electric field inside it as the conductivity is finite). How can we explain DC current in a superconductor?
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$\begingroup$ $J = \sigma E$. If $\sigma=\infty$ and $E=0$ then $J$ could have any value? $\endgroup$– ProfRobCommented Mar 17, 2021 at 15:32
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1$\begingroup$ Zero times infinity can be anything you want --- zero here being the electric field, and infinity being the conductance. $\endgroup$– mike stoneCommented Mar 17, 2021 at 15:32
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$\begingroup$ physics.stackexchange.com/questions/374393/… $\endgroup$– BowlOfRedCommented Mar 17, 2021 at 17:06
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1 Answer
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The electrons in a conductor, even without a net current, move to many different directions. There is a distribution of momentum, as in the case of molecules of gases. The distribution is isotropic without any applied voltage, and the net current is zero.
In a superconductor, after an emf (from an external changing magnetic field for example) starts a current, the distribution of momentum keeps unbalanced, even after the initial event is over.
The reason is conservation of momentum and energy. If there is no scattering with the crystalline nuclei to release energy as heat, there is no reason to stop the current. It is similar to conservation of momentum and energy for a mechanical object.
answered Mar 17, 2021 at 16:25
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$\begingroup$ So it's possible to sustain current without a sustained electric field? $\endgroup$ Commented Mar 17, 2021 at 16:52
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$\begingroup$ In a superconductor yes. $\endgroup$ Commented Mar 17, 2021 at 22:24