Earnshaw's theorem proved conclusively that it is not possible to levitate using static, macroscopic, "classical" electromagnetic fields. A forces acting in an object in any combination of gravitative, static, & magnetostatic fields will make a object's position unstable. All a same, many possibilities survive to produce levitation viable, by violating the assumptions of the theorem.

Methods
Diamagnetism

The substance which is diamagnetic repels a magnetic field. Earnshaw's theorem does not apply to diamagnets since they behave in the opposite manner of a typical magnet (relative permeability μ_r < 1). All materials have diamagnetic properties, but the effect is very weak, and usually overcome by the object's paramagnetic or ferromagnetic properties. A material which is predominantly diamagnetic will be repelled by a magnet, although typical objects only feel a very small force. This can be used to levitate light pieces of pyrolytic graphite or bismuth above a moderately strong permanent magnet. As water is predominantly diamagnetic, this property has been used to levitate water droplets and even live animals, such as a grasshopper and a frog. The magnetic fields required for this are very high, however; in the range of 16 teslas, and create significant problems if ferromagnetic materials are nearby.

See also: Diamagnetic levitation

Superconductivity

Due to the Meissner effect, a superconductor also expels magnetic fields (μ_r = 0), much better than a diamagnet. Due to this (& flux pinning) a magnet is held at the fixed few feet away from either the superconductor even or the other way around.

This is the principle in situ behind EDS (electrodynamic suspension) magnetic levitation trains. A select few how else a actual understanding is unknown.

Feedback control systems

In case a position and trajectory of a object to be levitated may be measured, the field of nearby electromagnets (or even a position of permanent magnets) can be day and night adjusted via feedback control systems to keep the levitated object in the desired position.

This is a principle in situ behind most common tabletop levitation demonstrations, which utilize the beam of weak to measure the position of an object. A electromagnet (intended to pull a ferromagnetic object upwards) is turned off anytime a beam of weak is broken per object, & turned back in once it lessens beyond a beam. This occurs as super elementary case, & does'nt super robust. Lot other complicated & effectual measure, charismatic, & control systems come imaginable.

This is too a principle upon which EMS (electromagnetic suspension) magnetic levitation trains are depending. A train diapers in a area of the track, & is pushed upwards from either beneath.

Oscillating fields

The conductor may be levitated above an electromagnet using the high frequency alternating todays flowing across it. This induces any regular conductor to behave such as the diamagnet, due to the eddy currents generated in the conductor. Since a eddy currents produce their have fields which oppose a magnetic field, a conductive object is repelled from either a electromagnet.

This result takes high frequencies & non-ferromagnetic materials, when a ferromagnetic ones come attracted to the electromagnet.

Halbach arrays

A second way of stabilizing a repulsive consequence is to utilise fields that move inside space, like than merely instance. This consequence may be demonstrated by having the rotating conductive disc & the permanent magnet, which might repel every more.

This is the principle of the Inductrack maglev trawithin system, which avoids a problems inherent in two a EMS & EDS systems. It utilizes merely permanent magnets (within the Halbach array) and unpowered conductors to provide levitation. A lone restriction is that a train must already exist as moving at two or three kilometres per hour (all about homo walking speed) to levitate. A energy for suspension comes totally from either forward motion, efficiency is adept, & there is no pleasantly online temperature suspension magnets come expected.

Halbach arrays come likewise easily-suited to magnetic levitation of gyro, motor & generator spindles.

Gyroscopic motion

a cause a permanent magnet suspended above a second magnet is unstable is because a levitated magnet may easy overturn & the inflict might get attractive. In case a levitated magnet is rotated, a gyroscopic forces from spinning and precession can prevent a magnet from either overturning. This is a principle behind the Levitron toy. Look at external links for further details.