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Just look up maglev (not to be confused with MalÚv).
High-frequency oscillating electromagnetic fieldsA conductor can be levitated above an electromagnet with a high frequency alternating current flowing through it. This causes any regular conductor to behave like a diamagnet, due to the eddy currents generated in the conductor. Since the eddy currents create their own fields which oppose the magnetic field, the conductive object is repelled from the electromagnet.This effect requires high frequencies and non-ferromagnetic conductive materials like aluminium or copper, as the ferromagnetic ones are also strongly attracted to the electromagnet. The effect can be used for stunts such as levitating a telephone book by concealing an aluminium plate within it.
Diamagnetically-stabilized levitationA permagnet can be stably suspended by various configurations of strong permanent magnets and strong diamagnets. When using superconducting magnets, the levitation of a permanent magnet can even be stabilized by the small diamagnetism of water in human fingers.
Direct diamagnetic levitationA substance which is diamagnetic repels a magnetic field. Earnshaw's theorem does not apply to diamagnets; they behave in the opposite manner of a typical magnet due to their relative permeability of μr < 1. All materials have diamagnetic properties, but the effect is very weak, and usually overcome by the object's paramagnetic or ferromagnetic properties, which act in the opposite manner. Any material in which the diamagnetic component is strongest will be repelled by a magnet, though this force is not usually very large. Diamagnetic levitation can be used to levitate very light pieces of pyrolytic graphite or bismuth above a moderately strong permanent magnet. As water is predominantly diamagnetic, this technique has been used to levitate water droplets and even live animals, such as a grasshopper and a frog; however, the magnetic fields required for this are very high, typically in the range of 16 teslas, and therefore create significant problems if ferromagnetic materials are nearby.
The response of a metamaterial, consisting of a 3D lattice of lossy capacitively loaded metallic loops is studied theoretically when it is inserted into a homogeneous harmonically varying magnetic field. The current distribution is found by taking into account the magnetic coupling between any pair of loops in the approximation of no retardation. It is shown that in a frequency range above its resonant frequency the metamaterial behaves as a diamagnet expelling the applied magnetic field. As the resonant frequency is approached the magnetic field is shown to be expelled not only from the volume of the metamaterial but from a larger zone which in the vicinity of the resonant frequency takes the form of a sphere. In the lossless case the radius of this exclusion sphere tends to infinity. In the presence of losses the maximum radius is limited by the quality factor of the individual elements. The response of a single element is shown to be analogous to that of a sphere of magnetic material, an analogy that leads to an alternative definition of effective permeability.
Figure (9) demonstrates what occurs as a superconductor is placed into a magnetic field. When the temperature is lowered to below the critical temperature,(T_c), the superconductor will "push" the field out of itself. It does this by creating surface currents in itself which produces a magnetic field exactly countering the external field, producing a "magnetic mirror". The superconductor becomes perfectly diamagnetic, canceling all magnetic flux in its interior. This perfect diamagnetic property of superconductors is perhaps the most fundamental macroscopic property of a superconductor. Flux exclusion due to what is referred to as the Meissner Effect, can be easily demonstrated in the classroom by lowering the temperature of the superconductor to below its T_c and placing a small magnet over it. The magnet will begin to float above the superconductor. In most cases the initial magnetic field from the magnet resting on the superconductor will be strong enough that some of the field will penetrate the material, resulting in a nonsuperconducting region. The magnet, therefore, will not levitate as high as one introduced after the superconductive state has been obtained.