## Senin, 29 November 2010

### Magnetic levitation

Lift
Magnetic materials and systems are able to attract or press each other apart or together with a force dependent on the magnetic field and the area of the magnets, and a magnetic pressure can then be defined.
The magnetic pressure of a magnetic field on a superconductor can be calculated by:

where Pmag is the force per unit area in pascals, B is the magnetic field in teslas, and μ0 = 4π×10−7 N•A−2 is the permeability of the vacuum.[1]
Stability
Static stability means that any small displacement away from a stable equilibrium causes a net force to push it back to the equilibrium point.
Earnshaw's theorem proved conclusively that it is not possible to levitate stably using only static, macroscopic, paramagnetic fields. The forces acting on any paramagnetic object in any combination of gravitational, electrostatic, and magnetostatic fields will make the object's position unstable along at least one axis, and can be unstable along all axes. However, several possibilities exist to make levitation viable, for example, the use of electronic stabilization or diamagnetic materials (since relative magnetic permeability is less than one[2]); it can be shown that diamagnetic materials are stable along at least one axis, and can be stable along all axes.
Dynamic stability occurs when the levitation system is able to damp out any vibration-like motion that may occur.
Stability methods
For successful levitation and control of all 6 axes (3 spatial and 3 rotational) a combination of permanent magnets and electromagnets or diamagnets or superconductors as well as attractive and repulsive fields can be used. From Earnshaw's theorem at least one stable axis must be present for the system to levitate successfully, but the other axes can be stabilised using ferromagnetism.
The primary ones used in maglev trains are servo-stabilized electromagnetic suspension (EMS), electrodynamic suspension (EDS), and experimentally, Inductrack.
Mechanical constraint (pseudo-levitation)
With a small amount of mechanical constraint for stability, pseudo-levitation is relatively straightforwardly achieved.
If two magnets are mechanically constrained along a single vertical axis, for example, and arranged to repel each other strongly, this will act to levitate one of the magnets above the other.
Another geometry is where the magnets are attracted, but constrained from touching by a tensile member, such as a string or cable.
Another example is the Zippe-type centrifuge where a cylinder is suspended under an attractive magnet, and stabilized by a needle beading from below.
Direct diamagnetic levitation

A live frog levitates inside a 32 mm diameter vertical bore of a Bitter solenoid in a magnetic field of about 16 teslas at the High Field Magnet Laboratory of the Radboud University in Nijmegen the Netherlands. Direct link to video
A substance that is diamagnetic repels a magnetic field. All materials have diamagnetic properties, but the effect is very weak, and is 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.