# Magnetic levitation

Magnetic levitation is the process by which an object is suspended above another object with no other support but magnetic fields. The electromagnetic force is used to counteract the effects of the gravitational force.

Earnshaw's theorem proved conclusively that it is not possible to levitate using static, macroscopic, "classical" electromagnetic fields. The forces acting on an object in any combination of gravitational, electrostatic, and magnetostatic fields will make the object's position unstable. However, several possibilities exist to make levitation viable, by violating the assumptions of the theorem.

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## Methods

### Diamagnetism

A 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 μr < 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 pyrolitic 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.

### Superconductivity

Due to the Meissner effect, a superconductor also expels magnetic fields (μr = 0), much better than a diamagnet. Due to this (and flux pinning) the magnet is held at a fixed distance from the superconductor or vice versa.

This is the principle in place behind EDS (electrodynamic suspension) magnetic levitation trains.

### Feedback control systems

If the position and trajectory of the object to be levitated can be measured, the field of nearby electromagnets (or even the position of permanent magnets) can be continuously adjusted via feedback control systems to keep the levitated object in the desired position.

This is the principle in place behind common tabletop levitation demonstrations, which use a beam of light to measure the position of an object. The electromagnet (arranged to pull the ferromagnetic object upwards) is turned off whenever the beam of light is broken by the object, and turned back on when it falls beyond the beam. This is a very simple example, and not very robust. Much more complicated and effective measurement, magnetic, and control systems are possible.

This is also the principle upon which EMS (electromagnetic suspension) magnetic levitation trains are based. The train wraps around the track, and is pulled upwards from below.

### Oscillating fields

A 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 materials, as the ferromagnetic ones are attracted to the electromagnet.

### Halbach arrays

Another way of stabilizing the repulsive effect is to use fields that move in space, rather than just time. This effect can be demonstrated with a rotating conductive disc and a permanent magnet, which will repel each other.

This is the principle of the Inductrack maglev train system, which avoids the problems inherent in both the EMS and EDS systems. It uses only permanent magnets (in a Halbach array) and unpowered conductors to provide levitation. The only restriction is that the train must already be moving at a few km/h (about human walking speed) to levitate. The energy for suspension comes entirely from forward motion, efficiency is good, and no extremely low temperature suspension magnets are required.

Halbach arrays are also well-suited to magnetic levitation of gyroscope, motor and generator spindles.

### Gyroscopic motion

The reason a permanent magnet suspended above another magnet is unstable is because the levitated magnet will easily overturn and the force will become attractive. If the levitated magnet is rotated, the gyroscopic forces can prevent the magnet from overturning. This is the principle behind the Levitron toy.

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