Force/ enegry equations for maglev (electromangetism)

[richard cash]

i am having a few problems with a project I am doing for university. The basics of which are force/energy/field size needed to lift magnets.

Basically, i need to show some calculations for the repulsion/attraction forces etc and my knowledge on electromangetism is limited.

For the first system of electromangetic attraction (EMS maglev suspension) we have a mass(train) being suspended above a track and the vehicle curls round the track. Under the track the electromagnet on the train is attracted to a permanent magnet. I have tried to get some equations relating the field strength, current, turns in the wire etc but just can't seem to get any equations right.

also, there is a repulsive system (EDS) whereby an electromagnet (usually a superconductor) is above a track on a train and induces currents in the track that repel the train. I can't figure out and sort of equation for the field strength, energy used or force required to left the train here either.

Could someone please help me out.

 

[Crosson]

Hmm, if you assume the bottom of the train is flat, and that the track is flat, you may as well use this formula.

The pressure on the bottom of the train will be:

P = \frac{B ^2}{2\mu_0}

Assuming equal currents in the train and track. The expression above, is true for pressure, and for energy density (joules per cubic meter) so if you multiply the pressure by the total volume in which B is significant, you get total energy.

To find the current required to produce this B, use:

B = \frac{\mu_0 i}{A}

where i is current and A is cross sectional area.