Why Maglev

Why Maglev . . .
MagLev technology is entirely different from any form of transportation in operation today, but the basic principles that lie at the foundation are not beyond the understanding of the beginning electricity and magnetism student. It is in the application of these principles to design and optimize an actual train that things get hairy. The basic idea has been researched since the mid-sixties, but it is only now that economically feasible prototypes are being built and governments are seriously looking towards magnets to propel us into the next century. Leading the race is Germany. Their design, the Transrapid 07, is ready for commercial production. It utilizes conventional electromagnets and forces of attraction to levitate the train. A good web site to find out more about German plans for their design is http://transrapid.simplenet.com/index-e.htm

The Japanese are investigating an entirely different design involving superconducting magnets to generate huge repulsive forces which levitate the train. However, their MLU002N is still in experimental stages. For more information, check out http://www.rtri.or.jp/rd/maglev_E.html

With a little stretching, the average physics student should be able to comprehend the principles of magnetic levitation and propulsion through synchronous linear motors. To facilitate the process of understanding this complex material, we suggest that the student go through this web site in order. Make sure you understand the basic physics before moving on to the page which applies these principles to magnetically levitated vehicles.

Moving Charge --* Magnetic Field
Intro
We know from experiment that a moving charge exerts a force on other moving charges; we call this effect magnetism. The magnetic force is a field force, meaning that a moving charge sets up a field which in turn exerts a force on other moving charges. The field set up by a given moving charge is found to be perpendicular to its velocity, and to decay with distance from the charge:

First, we will examine how magnetic fields are created, then we will calculate their magnitude and direction.
Permanent magnets
Some materials can be said to be natural magnets. These magnets don\'t appear to have any moving charge, so how can they set up magnetic fields? The answer is found at the atomic scale:

Electrons circling an atom set up small magnetic fields. In most materials, these fields are aligned in a fairly random manner, so that all of these small fields cancel each other. In a magnet, however, these fields line up to create a net magnetic dipole, so that the object sets up a magnetic field in the surrounding space.
Current
A current is a moving charge. Moving charges set up magnetic fields. Thus, a current seems the logical way to create a magnetic field. There are two basic setups which can be used for this purpose:

Calculating Magnetic Field Strength
Equations
The Biot-Savart Law: in order to find the magnetic field (denoted by the symbol B) produced by a given current distribution, we have to integrate the field at a given test point, P, due to individual current displacements, ids:

The equation for the field integral turns out to be a rather complicated one, known as the Biot-Savart Law:

Ampère\'s Law: in cetain situations, this integral can be simplified by symmetry. In these situatins, we can use a more fundamental law, known as Ampère\'s Law. This law allows the calculation of the field from the amount of current enclosed by an arbitrary closed loop:

The equation for the magnetic field in such a case turns out to be:

Long, straight wire
One of the two most commonly used magnetic field equations is that for a long, straight wire. This equation can be determined from Ampère\'s Law through the following setup:

The equation is then derived as follows:

Solenoids
A solenoid is a tightly wound coil of wire carrying a uniform current i : The field inside a solenoid is approximately as shown in the following diagram:

We can calculate the field inside a solenoid with n turns per unit length using Ampère\'s Law:

Summary:
We have now examined how magnetic fields are created, and how to calculate their magnitude. Next, we will examine the force felt on moving charges and currents due to magnetic fields.
Field --* Force on moving charge
We know that a moving charge sets up a Magnetic Field. We also know that this field sets up a force on other moving charges. This