[Atomic-S (OP)]

Consider two dielectric plates, each given a static charge, one negative and one positive, and mounted a fixed distance apart to create a field between them.  Now consider a ring made of superconductor and carrying a current that travels tangentially around the ring the way a normal current loop travels, thereby becoming a magnet.  Under ideal conditions (0 g,  vacuum),   the ring is propelled rapidly but without rotating into the space between the plates, moving, at the time of entry,  parallel to them and half way between them.    What  happens to the ring as it continues on its journey?

Consider the same plates and ring, only this time the ring is caused to spin rapidly as it drifts slowly from the outside into the space between the plates on, like before, a parallel trajectory.  The tangential speed of the ring is much greater than the drift speed of its center. What happens to the ring once it gets between the plates (assuming that it does)?
 

[acsinuk]

Yes. wish we knew the answer to that.  A great university project for someone.   But what do you think would happen if the magnet tumbled through the gap??

[Atomic-S (OP)]

the behavior while tumbling will be more complex, and more easily answered if we first know the behavior when not tumbling.

[acsinuk]

Yes, first things first.  If the magnet was rolled up in an epoxy resin ball and we use a plastic tube to roll it down.  A model can be constructed with your two conducting plates stuck on with cellotape.   Use an oscilloscope on the DC source to the plates and watch as the ball rolls down the tube.   If you manage to get it to work please forward a youtube of the experiment so we can all see.  Thanks

[PmbPhy]

What happens to the ring once it gets between the plates (assuming that it does)?

I'm not precisely clear as to what you're asking. Can you please clarify your question for me please? Why are the charges on a dielectric rather than a conductor? Using two conductors makes it a lot easier to set up in the lab since all you'd need to do is get two conducting plates such as steel or copper and then apply a difference in potential across the plates using either a battery or a power supply, depending on what kind of field strength that you'd like.

If you're looking for the exact equation of motion then this becomes a very complex question. If you're merely looking for a qualitative response then its a bit easier. If you're not familiar with relativistic electrodynamics then you should look into that. It will give you an idea of what you want to know.

The textbook Classical Electricity and Magnetism by Panofsky and Philips is a superb text for these kinds of scenarios, i.e. moving magnetic dipoles. That's essentially what you have here, i.e. the current loop is a magnetic dipole. Due to relativistic effects, when it's in motion its also an electric dipole. This is due to the fact that what is a pure electric field in one frame becomes a mixture of an electric and magnetic field in a frame moving relative to the original frame. Also, what is a pure magnetic field in one frame becomes a mixture of an electric and magnetic field in a frame moving relative to the original frame. Almost all textbooks on special relativity (SR) have the transformation equations for the EM field in them. Their easy to derive if you note that the EM field is describe by a tensor called the Faraday tensor and that the components of tensors in SR transforms using the Lorentz transformation. You can find the EM field transformations on the internet. You can also download Panofsky and Philips from the following URL: http://bookzz.org/book/2058380/30648b
You have to register first but its free and very easy to do. It's a wonderful website. I highly recommend it.

It's been a while since I've worked with these equations. Do you really need help or can you find it yourself with the information that I've just given you?

[Atomic-S (OP)]

PmbPhy: Your info looks useful. I do have a book on electromagnetism but it does not seem to cover these kind of questions.  The reason for using dielectric rather than conducting plates is so that the field, insofar as dependent on the plates, will remain invariant under the influence of the flying ring.  An exact equation of motion is not currently sought, just a qualitative description. Your statement about the moving magnetic dipole becoming also an electric dipole agrees with what I had expected, in that if the observer moves along with the ring (in the irrotational scenario), then to him the plates are moving in the opposite direction. But being charged, they are also carrying a current, and this current must create a magnetic field between them that lies at right angles to the direction of motion but parallel to the plates. In such an environment, the magnetic ring would be expected to experience torque about the direction of motion, thereby tending to flip to a position 90 degrees from its original plane. That result agrees with what one would expect in the other frame of reference when an electric dipole oriented at right angles to both the electrostatic field and the direction of flight was acted upon by the electrostatic field.

Things get more complicated, however, in the second experiment, in which the ring's motion is primarily rotational rather than translational.  In this scenario, an ant sitting on the ring would experience motion through the external field very similar to what the ant would experience in the first experiment (when positioned on a part of the ring that paralleled the motion), in that the ant would percieve the external field  as having a magnetic component, which acts upon the current under the ant's feet in such a way as to push that spot toward one or the other of the plates.  But unlike in the first experiment, in which this effect existed in opposite directions on opposite sides of the ring, when the ring spins rather than moves linearly  the displacement force is, it seems, in the same direction for every part of the ring, causing the ring to be propelled in its entirety toward one of the other plate.  That result seems to run into some significant conceptual problems, making me wonder if there must be something else going on that has not been accounted for, but if something else is going on, what is it, and what is the final answer toward how the ring moves when in the spinning mode?