This constraint to zero magnetic field inside a superconductor is distinct from the perfect diamagnetism which would arise from its zero electrical resistance. Zero resistance would imply that if you tried to magnetize a superconductor, current loops would be generated to exactly cancel the imposed field (Lenz's law). But if the material already had a steady magnetic field through it when it was cooled trough the superconducting transition, the magnetic field would be expected to remain. If there were no change in the applied magnetic field, there would be no generated voltage (Faraday's law) to drive currents, even in a perfect conductor. Hence the active exclusion of magnetic field must be considered to be an effect distinct from just zero resistance. A mixed state Meissner effect occurs with Type II materials.
One of the theoretical explanations of the Meissner effect comes from the London equation. It shows that the magnetic field decays exponentially inside the superconductor over a distance of 20-40 nm. It is described in terms of a parameter called the London penetration depth.
A superconductor is fundamentally different from our imaginary 'perfect' conductor. Contrary to popular belief, Faraday's Law of induction alone does not explain magnetic repulsion by a superconductor. At a temperature below its Critical Temperature, Tc, a superconductor will not allow any magnetic field to freely enter it. This is because microscopic magnetic dipoles are induced in the superconductor that oppose the applied field. This induced field then repels the source of the applied field, and will consequently repel the magnet associated with that field. This implies that if a magnet was placed on top of the superconductor when the superconductor was above its Critical Temperature, and then it was cooled down to below Tc, the superconductor would then exclude the magnetic field of the magnet. This can be seen quite clearly since magnet itself is repelled, and thus is levitated above the superconductor. For this experiment to be successful, the force of repulsion must exceed the magnet's weight. This is indeed the case for the powerful rare earth magnets supplied with our kits. One must keep in mind that this phenomena will occur only if the strength of the applied magnetic field does not exceed the value of the Critical Magnetic Field, Hc for that superconductor material. This magnetic repulsion phenomena is called the Meissner Effect and is named after the person who first discovered it in 1933. It remains today as the most unique and dramatic demonstration of the phenomena of superconductivity.
On account of the polycrystalline nature of a typical ceramic superconductor, the Meissner Effect appears to be a bulk phenomena. This can be demonstrated by stacking two or more superconductor disks. With the addition of each disk, the magnet will be levitated higher. This result is particularly advantageous if the Meissner Effect is being demonstrated to an audience with the help of an overhead projector.
Another interesting observation is that the levitated magnet does not slide off the superconductor. This seemingly stable equilibrium is actually a manifestation of Flux Pinning, a phenomena uniquely associated with Type II superconductors, of which our high temperature ceramic superconductors are examples. Here lines of magnetic flux associated with a magnet can penetrate the bulk of the superconductor in the form of magnetic flux tubes. These flux tubes are then pinned to imperfections or impurities in the crystalline matrix of the superconductor thereby pinning the magnet.
In other words, what is happening is that you are initially forcing the magnetic field to exist in these non superconducting regions, by "squeezing" it though the cracks between the superconducting crystals. These regions of the material are surrounded by superconducting material. Think of a gallon jug, filled with water, that has a small pin hole in the bottom. The jug is the superconductor, the water is the magnetic field. This superconducting material will not allow a magnetic field to pass though it, in much the same way the jug will not allow the water to pass though it. However, the tiny non superconducting regions will allow the magnetic field to pass though, in the same way the pin hole in the jug allows the water to pass though. When you lift the magnet up, the force of gravity acting on the pellet (F=ma first semester physics stuff), is not great enough to force the trapped magnetic field to pass though the superconducting material, hence, like a weight on a string, you can lift the pellet. The string in this case is the magnetic field, and the weight is the superconductor.
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