# Strength of Magnetic Field Around a Superconductor

I recently learned that the strength of a Magnetic field around a conductor is proportional to the current flowing in it. So if we have a Mercury wire at absolute zero and pass a current through it (Resistance = 0) and then toss some iron filings at it, will the filings cylindrically float around the conductor (along the Magnetic field lines) due to the extreme strength of the field or just behave the way they do for an ordinary conductor (like Copper), in which case we must rest the filings on cardboard and then give it a jerk to align it along the lines.

• There is no qualitative difference between an ordinary conductor and a superconductor here. A superconductor can, at the same cross-section, carry much more current than a copper wire, but you still get to a limit at some point (the currect has to be supplied from some source). – leftaroundabout May 23 '12 at 17:49

First thing: even with huge fields, iron will not "float" like that in circular motion. Iron will always be attracted to the region where the magnetic field is the most intense: which is in contact with the conductor/superconductor.

In addition, there is a limit to the magnetic field you can achieve with any superconductor: it is called the critical field. There are 2 types of critical fields, Hc_1 and Hc_2, which correspond to 2 things:

• Hc_1 corresponds to the maximum field that can be "ejected" (screened) automatically by the superconductor (Meissner effect: http://en.wikipedia.org/wiki/Meissner_effect). It corresponds to a magnetic energy (B^2/(2*µ0) locally) that equals the volumic energy difference at zero field, between normal (resistive) and superconducting macroscopic states.
• Hc_2 corresponds to another limit, only existing in so-called type II superconductors: when Hc_1 is reached, either the whole bulk superconductor goes to resistive state (type I superconductors), or an interface forms, between an enclosed resistive region (in a tube like shape), and the surrounding superconducting region. The resistive region lets flow a quantum of magnetic field (h/e_s, where e_s is the charge of the superconducting pair, usually 2*e, twice the electron charge), while the current to confine it flows in the nearby superconducting surrounding. These "quantum vortices" multiply to let flow the excess magnetic field, until their density is again too high for the whole superconductor to keep beeing superconducting: again a question of lower energy. Too many interfaces, too few bulk superconductor to lower the overall energy, and the whole superconductor transits to resistive state. This field, linked with the too high density of vortices, is Hc_2. It is of the order of 10-20 Tesla in best cases (Nb3Sn, Niobium-Tin: 15 Tesla), usually much less.

The "floating" of magnets above superconductors, are due to these vortices, which cannot move in space as freely as usual magnetic flux lines in vaccuum can. This phenomenon "traps" the field exactly as it is, and the magnet with it, and only a force above a certain threshold (usually higher than the weight of the magnet used for the demonstration) can move the magnetic flux lines inside the superconductor.

This "floating" is the only difference in principle between superconductors and usual conductors.

One last thing: you can have objects, even living creatures like frogs, floating inside a copper coil, but this happens only with very high fields (more than 10 Teslas for water, see http://en.wikipedia.org/wiki/Magnetic_levitation#Diamagnetism)