| MadSci Network: Physics |
Hello, Abdul.
You’ve asked a rather tough question. There is a textbook answer which is easy. Then there are the answers that have to take reality into account. Those are harder. For an ideal superconductor much bigger than your magnet, the equilibrium height in the Meissner effect is due only to the levitating magnet – not the superconductor. Therefore, the height would be the same for all superconductors. (For those interested in the Meissner effect, see the references included below.) For real-world superconductors the heights can be different. Here are a few things that could affect the outcome – there may many more that I haven’t thought of: 1) the size of the superconductor relative to the size of the magnet, 2) the material quality of the superconductor, 3) the surface morphology of the superconductor, and 4) the thermal conductivity around the superconductor. 1) A magnet has a finite-sized magnetic field. If your superconductors are all much bigger than this size then the heights will be the same. As the superconductor gets smaller, its ability to balance the magnet’s field is compromised. Once your superconductors approach the size of the field, things will change even for perfect superconductors. Eventually, the superconductor gets too small to support the magnet. 2) Real superconductors have defects, which can impair the current flow and alter the ability to repulse magnetic fields. Plus, many superconductors (especially the high temperature ones) have varying abilities to incorporate magnetic fields in the form of vortices. The number and distribution of these defects and vortices will alter the details of a superconductor’s current flow. This will have a small effect on the exact height of a levitating magnet. In the extreme case where you have enough defects that the superconductor’s resistance to magnetic field is low, you may find that the same magnet levitates over a good superconductor while it hits the surface of a poor superconductor. This would happen if the magnetic field of your magnet was high enough to exceed the critical field of the superconductor; above the critical (magnetic) field a superconductor reverts to its normal, resistive state. 3) If your superconductor surface is anything but flat, you’ll obviously have different behavior depending on the shape of the surface. 4) If you have two superconductors with different thermal behavior at their surface, you may see differences in the heights. There is quite a bit of current that builds up in a superconductor, particularly at the surface. Every real material has some defects and discontinuities that will heat up when exposed to this kind of current. The surrounding medium must pull the heat away to keep the superconductor below its critical temperature. Details of the temperature distribution around the edges of your magnet may alter the equilibrium position of the magnet. REFERENCES Meissner effect =========== Here’s a good general reference. They point out that if you stack two superconducting disks on top of one another, a magnet is levitated higher. I think that this is because of the geometry of the disks versus the magnets (point (1), above): General Meissner Effect Here’s another, more technical reference, with links to a bunch of the sub- topics that comprise the Meissner effect: Technical Meissner Effect Superconductivity ============= While the following reference doesn’t address your question directly, it does have a lot of information about superconductors. It was from reading this site that I understood some non-ideal behaviors of superconductors: Superconductor Tutorial This is a full-on reference for all things superconductive: Full Superconductor Reference
Try the links in the MadSci Library for more information on Physics.