Some good stuff..

Some time back I happened to write this technical paper for a competition at our institute; although it ain't any great piece of research, the topic is something which deeply interests me. So, here's some of it..

Magnetic Levitation also known as “Maglev” is the process or technique by which an object can be suspended or made to ‘hover’ over another object without any support barring magnetic fields. There is no physical contact between the objects. Gravity is defied using electromagnetic forces.

Stability

Very often, stability in magnetically levitated systems is difficult to attain; this is further proved by Earnshaw’s Theorem which states that a set of point charges cannot be maintained in a stationary equilibrium solely by the electrostatic interaction of the charges. A corollary of this theorem is that forces acting on an object in any combination of gravitational, electrostatic and magnetostatic fields will make the object’s position unstable. However this theorem can be violated by usage of diamagnetic materials and electronic stabilization.

Methods

There are many ways of obtaining magnetic levitation of which the commonly used ones are EMS - Servo stabilized electromagnetic suspension, EDS – Electrodynamic Suspension and Inductrack, they are used specially in Maglev Trains.

Mechanical Stabilization:

This is the simplest way to attain levitation; by using two magnets which are constrained along a single axis facing their like poles towards each other. This will act to levitate one magnet over the other.

Direct Diamagnetic Levitation:

A diamagnetic substance is one which repels a magnetic field. Earnshaw’s theorem is not applicable to diamagnets because their behaviour is completely opposite to that of normal magnets due to their low relative permeability. This method was predominantly used to levitate water and animals.

The condition for this is given by, B*dB/dZ = μ₀ρg/χ, where

χ - magnetic susceptibility

ρ - density of the material

g - local gravitational acceleration

μ₀ - permeability of free space

B - magnetic field

dB/dZ - rate of change of magnetic field along the vertical axis
Assuming ideal conditions along the z- direction of solenoid magnet:

Water levitates at: B*dB/dZ >> 1400 T^2/m

Graphite levitates at: B*dB/dZ >> 375 T^2/m

Superconductors and EDS:

Superconductors act as perfect diamagnets (μ_r = 0) due to Meissner Effect. For type-II Superconductors, the levitation is stabilized due to flux pinning. This method, also known as EDS(Electrodynamic Stabilization) is used in some magnetic levitation trains. In trains where the weight of the electromagnet is a major issue(a stronger field is required to levitate the huge mass of the train), superconductors are used for the electromagnet, since they can produce stronger fields for lesser weight.

Rotational Stabilization:

A magnet can be stabilized by spinning it in a radial field created by other magnets. Stability is guaranteed only as long as the rate of precession slows below a threshold value. This method was used in the Levitron toy.

Servo Stabilization EMS:

Dynamically stabilized levitation is achieved by measuring the position and path of the magnet being levitated and depending on the motion of the object adjusts the magnitude of the field. This is the principle which is responsible for the demonstrations of levitation where a electromagnet or a beam of light is used to record the position and velocity of the object and depending on the proximity of the object to the magnet the field is adjusted so as to maintain a constant distance. This is exactly what happens in the maglev trains where the locomotive wraps around the track and is pulled upward by magnets, which helps in maintaining a constant height above the track.

Rotating conductors beneath magnets:

This is based mainly on the concept of electromagnetism where a conductor when rotated in the field of another magnet has a current induced in it and this causes the magnet to be repelled, if the speed of rotation is sufficient enough it results in achieving levitation of the magnet.

(The main source for this paper was Wikipedia, I'd like to acknowledge it...)

Rest of the stuff in the next post....