# Superconducting wire in a Magnetic Field?

A superconducting wire($SC$) is moved rapidly in a magnetic field( $1$ $Tesla$), what would happen to the wire? Are there any forces induced of attraction or repulsion?

In a typical conductor, we know that if it is moved around a magnetic field $-V$ is induced within the wire based on Faraday's law, however, with the condition of the $SC$ what could happen if $R = 0$ $ohms$?

Will Faraday's law still be applied to that wire with no resistance? moving a $SC$ in a magnetic field will not induced $EMF$?

• I think a plot of the experiment you have in head is warm welcome. The superconducting electromagnetism is well understood using the London theory. You could resolve the problem yourself. The problem in your case is that you want the superconductor to move. In some circumstance, non-trivial effects appear, related to the so-called London momentum. As long as the wire does not form a loop, I don't see any reason why the Faraday's law should be invoked, though (there is trivially no magnetic flux then). Only the Ampère's law should be useful. So again, a plot please :-) – FraSchelle Mar 12 '14 at 11:01
• I assume by "plot" you mean a better explanation of the set up? If we had a SC that's length is 5 m, and moved it up and down in a magnetic field of 1 Tesla would faraday's law still hold? Faradays law states that V will be induced due to the change in flux over time, however ,this is a SC where R = 0, shouldn't V = 0 as well based on ohms law? – Pupil Mar 12 '14 at 11:57
• No by plot, I mean a plot, a drawing, a scheme, whatever like a picture, an image, something like that, anything which help understanding how the field is oriented with respect to the superconductor, what the superconductor is doing, etc... – FraSchelle Mar 13 '14 at 9:07
• @FraSchelle well the question is quite general, and simple in a sense I doubt a plot is necessary. If you still require a plot I will produce one immediately. However, my initial question is relating Faraday's law of induction to ohms law with any conductor. Even in the case of superconductors, if R = 0 how can you induce any EMF in a superconductor by changing it's surrounding magnetic field? – Pupil Mar 13 '14 at 11:37

The induced current will flow in such a way that the flux produced will tend to cancel the change in flux. According to traditional classical electrodynamics, the magnetic field does not do any work and it is the electric field and the charge carriers which do the work and ultimately limit Faraday's law in extreme cases.

I suppose that the moving wire is a closed circuit and that the magnetic flux enclosed is time-dependent. The Faraday’s law is of course always applicable. The current will not be infinite. Yes R=0 but, what about the self inductance L? It is never zero, in such a manner that the total E field will be null. If you make the calculations the electric field in the superconducting wire has two contributions. The first one related to the variation of the external magnetic flux and the second associated to the time-dependent current by means of the self inductance L.

Kind of complicated thing to answer, best way is to do an experiment and not rely on math completely! and the fact that this is still unknown territory.

I will try my best, watch this ted talk very helpful: