MadSci Network: physics |
Hi Radu, I would express the balance of forces as: Force_magnetic - Force_gravity = 0
Or in otherwords, the magnet levitates because the force from the magnetic field - superconductor is enough lift to cancel gravity. This is done when the superconductor prevents the magnetic field from penetrating its surface. The magnetic field lines bend around the superconductor, but for this to happen the superconductor has to generate surface currents which requires no voltage in a superconductor. The net surface current over the entire super-conductor will be zero.
Now this surface current will generate a magnetic field that will repel the floating magnet. This magnetic force is a often a complicated formula for systems with complex geometry. I would start from the assumption that the surfaces of the magnet and the superconductor are flat and parallel. And that the surface current of the superconductor is uniform. The value it has is enough to create zero magnetic field at the surface. One way you might imagine this is to create a virtual magnet within the superconductor that is a mirror image of your real magnet. If it is aligned oppositely, then the plane equi-distant to each magnet will have zero magnetic field. So if you now the strength of your floating magnet as a function of distance you can figure out at what distance the magnetic field is just strong enough to repel itself by stacking two magnets on top of each other and restricting there motion to verticle only.
This is a simple way to get an order of magnitude calculation. The next level of complexity is painful enough to be a tricky advanced physics/graduate school problem.
Sincerely,
Tom "Virtual Magnet" Cull
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