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Let's say that you have a superconducting loop (resistivity=0 exactly) whose area is increasing in a uniform non-changing magnetic field. Obviously there will be a CHANGING flux associated with the superconducting circuit and hence cyclic integral of $$E.dl$$ is non zero. But $$E=0$$ in a superconductor which implies integral of $$E.dl$$ is zero. How to resolve this paradox?

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  • $\begingroup$ I've removed some comments discussing the edit history of this question. $\endgroup$ – rob Jul 17 '18 at 15:46
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Obviously there will be a CHANGING flux associated with the superconducting circuit

It's true that the magnetic flux threading the loop, due to the external magnetic field, is increasing.

How to resolve this paradox?

The circulating current changes at just the rate required to keep the total magnetic flux threading the loop constant.

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  • $\begingroup$ Who is changing the current?(as there can be no electric field inside the superconductor. $\endgroup$ – Aman Jul 3 '18 at 1:20
  • $\begingroup$ @Aman, rather than asking who (what) is changing the current, ask what happens if the current doesn't change in just the right way. In other words, imagine an infinitesimal perturbation to the rate of change of current and see that the resulting infinitesimal rate of change of flux acts to null the perturbation. $\endgroup$ – Hal Hollis Jul 3 '18 at 14:42
  • $\begingroup$ But you are just skipping over the question. What is changing the current? $\endgroup$ – Aman Jul 3 '18 at 16:37
  • $\begingroup$ Any explanation? @Hal $\endgroup$ – Aman Jul 16 '18 at 10:54
  • $\begingroup$ @Aman I don't understand your follow-up question. The supercurrent changes to cancel the induced electric field associated with the non-constant magnetic field. $\endgroup$ – rob Sep 23 '18 at 20:35

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