# Conclusion

Initially, I sought out to study the interaction of magnetic fields and moving charges that allows Maglev trains to function as one of the world’s leading competitors in future transportation. Conceptually, their supposed high efficiency was not something unclear or doubtable: through magnetic levitation, the methods involved in EMS and EDS virtually eliminate all ground drag forces that moving vehicles typically face. However, though these machines seem to be “free of all forces,” it now seems that forces – and the delicate balance of interacting forces – is extremely important in determining whether or not a maglev system will work properly and efficiency.

I found that there are many variables that influence how a maglev system will function, and that different types of variables affect different types of magnetic levitation. Although the levitation force in the EMS system is entirely attractive and not very dependent upon the speed of the moving train, the EDS system relies upon repulsive forces and speed drives the levitation. I’ve revisited inductance and its quantitative – rather than qualitative – value beyond the simplicities of Lenz’s Law. In the non-ideal physics world, there are real forces that affect our system that we can’t always “assume away.” Although I did approximate the superconducting coil configuration with that of a magnetic dipole, I would have compared my outcome with that of a real rectangular coil with finite dimensions if an equation for the magnetic field or force was available.

To extend upon this project, I would like to do several things: (i) determine an exact analytical equation for the magnetic force that would allow a superconducting coil with physical dimensions to levitate; (ii) compare my result with similar results, and vary some other values besides speed (current, number of loops, area of loops, etc.); (iii) determine which settings are optimal for a real maglev train to attain maximum efficiency; and (iv) introduce the concept of a guidance force (the force that stabilizes the train in the horizontal direction), and analyze how this additional force impacts the lift, magnetic drag, and the ratio between the two.

Lastly, I think it would be most valuable to conduct experiments on my own, testing the relationships proposed by physicists in the past, and searching to develop a model to describe the exact relationship between the speed of the train (or some scale model) and the levitation force, magnetic drag force, and aerodynamic drag force that result. Ideally, then, I could derive an expression for the ideal height (the height that maximizes ) of the maglev train at any given speed.