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If I have electric current going through a superconductor and instantly cut off the power supply(rendering the circuit open, and not at all closed), In what tiny fraction of a second will the flowing electrons come to a complete stop? I know it must be a very small order of magnitude but I'm curious how small. I know it probably varies so I just need a general idea, If that's too vague, well then how about how fast it would stop if I gave it for example, 1 volt, and 1 amp and If an example substance is needed, then pick one, like niobium for instance, I'm just trying to get a general idea of the ranges of on how fast the current comes to a stop, in superconductors when you break the circuit.

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    $\begingroup$ If we assume the superconducting circuit is closed (say.. a loop), since a superconductor offers no resistance to the flow of electrons, then, theoretically, the current will never stop. $\endgroup$ – Physicist137 Nov 3 '17 at 14:41
  • $\begingroup$ And the electrons don't come to a stop. Net movement (current flow) may cease, but the electrons keep moving. $\endgroup$ – Jon Custer Nov 3 '17 at 15:00
  • $\begingroup$ Every wire is an inductor and the rate of change of current in the wire is related to the voltage along the length of the wire by a property called "inductance". The inductance value is going to be different for different wires---determined mostly by geometry. It will be different for different wires. $\endgroup$ – Solomon Slow Nov 3 '17 at 16:20
  • $\begingroup$ when I said cutting off the power supply, I meant rendering the circuit open, and not at all closed... I meant instantly no longer having a complete circuit $\endgroup$ – baconcat Nov 3 '17 at 16:54
  • $\begingroup$ Do you have inductance in a superconductor? How do the electrons feel the B field if it doesn't penetrate the SC ? $\endgroup$ – Martin Beckett Nov 4 '17 at 1:54
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If you could pull away your power supply wires infinitely fast, the superconducting wire will behave as a dipole antenna. The current will (roughly speaking) bounce back and forth between the ends. There will be electromagnetic radiation, causing the current to decline at an exponential rate.
The rate could be calculated using antenna theory, but this is an un-physical problem because you can't pull away the wires so fast. In practice there will also be oscillations in the connecting wires which complicate the problem.
The dipole antenna decay time constant is only a few cycles of oscillation. See for example Figure 6 of Stored electromagnetic energy and quality factor of radiating structures.

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