It is proved that magnetic levitation cannot be obtained just by using static ferromagnetism, as the object would tend to gain instability. In order to create proper magnetic levitation condition, diamagnetic materials or superconductors have to be used. But in all these cases a little help from pseudo-levitation needs to be taken. Pseudo-levitation is a system that provides stability to the levitated object using a magnetic mechanism. For light objects, magnets made of diamagnetic materials are sufficient.
Diamagnetic substance
The atoms of a diamagnetic substance such as silver and bismuth, doesn't have a specific dipole moment. When these objects are brought under the influence of a magnetic field, a dipole moment is induced in the direction opposite to that of the field applied. Because of this a repulsive force is generated that creates the desired levitation.
Another way of obtaining magnetic levitation is by using electromagnetism. Electrodynamic fields are created when electricity is passed through a conductor. The moving charges that are created as a result of the magnetism, provides a vertical push that is equal to the gravitational pull, which in turn help to produce a stable levitation condition. Heavier objects are generally levitated by this method.
Apart from these main methods, eddy currents or electrodynamic suspension, oscillating magnetic fields and permanent magnet suspension are also used.

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