# Why this "floating magnet" fallacy?

Discussion of maglev transport over in GD prompts this long-time unexpressed question.

Let’s say you have a flat “roadway” in which are embedded some huge number of hyper-powerful permanent magnets, all of them with the same pole, let’s say N, pointing straight upward.

Now you take a flatbottomed platform constructed of similar magnets, all with their N poles pointing downward toward the road surface.

Like poles repel. Seems to be that if the magnets were indeed “hyper” enough, and the combined weight of platform-and-magnets low enough (which could still be as heavy as one needs), said platform would float above the roadway at a certain height. Put more weight on it and it descends; put a lot of weight on it, and it finally hits the road, Jack.

So–why all the electromagnetic maglev-type induction stuff–at least for the vertical element?

But somewhere I read a reference to this idea as a famous fallacy. What’s fallacious? I can see that the stability of the platform will be an issue, but an irresolvable one?? Is there some law of physics that precludes such a system, maybe requiring that the platform flip over no matter what?

In any event, couldn’t there be guiderails or something similar to prevent this–with minimal friction? Or a segway-type gyro?

Well… just try laying a magnet on top of another, same poles facing. It’ll just move off, as opposed to floating. Perhaps that’s not what you’re asking, but…

So change the roadway from a flat surface to something more like a channel (not too narrow) - The vehicle would tend to sit in the middle.

That’s not to say that it could actually be inplemented though.

Simple - hyper-powerful permanent magnets that could do the job don’t exist.

I think - and I could be mistaken - that all the “induction stuff” is for efficiency, allowing one set of magnets to be used to both levitate and propel the train. I don’t think it has much to do with stability.

The killer for the idea is Earnshaw’s Theorem (for instance, here). This summarises as proving that there can be no local minima in combinations of inverse-square law fields. That is, however you set things up, there can be no stable position where something will sit levitated using a static combination of permanent magnets (i.e. ferromagnets) and gravity. Guide rails would work, as with conventional maglev, but then you get into the further difficulty that yoyodyne mentioned: that there’s a limit to the strength of permanent magnets.

But the link you site mentions the Levitron, which appears to be a counterexample to this (here’s a picture). I have one of these, and it really does work. (But do a Google on Levitron for some interesting info on patent infringement.)

Make that “cite.”

So just out of interest, if I construct a slightly dished surface (let’s say an inch deep and a yard across) and stud it densely with magnets all with the same pole facing upwards, then I take a piece of light balsa, octagonal in shape and maybe a foot across - at each of the vertices, I mount a magnet (again all in the same orientation) - I place the object in the centre of the dish (so that the facing poles repel).

What will happen? - it’s too wide to flip over, surely.

Xema:
the Levitron, which appears to be a counterexample

Earnshaw talks about static combinations. The getout is that the Levitron isn’t static, and gyroscopic effects provide forces that stabilises it.

Right - the Levitron only works when its spinning (and only between certain rates).

Mangetout:
What will happen?

Good question. My suspicion is that the disk would find some way to slide sideways off the field, while tipping up.

Earnshaw’s Law certainly “sounds” like the basis of the fallacy as I read it in a brief reference, and I do believe there was something to the effect that: “Nobody will believe it, but no matter how wide the thing is, it will just flip over.”

But like Mangetout, it’s a hard proposition to make sense of in terms of “surely THAT can’t be true”.

Take a bar magnet, N pole upwards. Attach an ultra-fine, well-lubricated wire to that pole, and extend it upward as high as you wish. Now take another bar magnet, and drill a narrow-diameter hole through its middle along its length–that is, the hole opens at the N and S poles. Thread it onto the wire, N pole downward, and let it go. Doesn’t it fall a ways, slow, and finally (after a little oscillation due to acquired momentum) come to a stop some ways above the lower bar magnet? AND IF SO, doesn’t that show that a point of stability DOES exist “in space”–the problem being how to keep the magnet from drifting and flipping without a wire, which would seem solvable by a Mangetout trough and onboard gyro (which I guess HAS been demonstrated).

Hyperpowerful permanent magnets? I recall a photo of a little round wafer about the size of a quarter holding up a pile of lead weights–and this was in the late 60’s! Is it perhaps a problem of expensive, exotic materials? (As opposed to fundamental physics?)

Billy Rubin, you must know about this. Why ARE we lifting our trains by induction, not permies?

Well, IANAE or a physicist, but heres a thought. So called ‘permanent magnets’ are not really permanent. They are created when certain materials are exposed to high magnetic fields, which essentially coerces the electrons in the material to ‘flip’ to the opposite magnetic state. When you take the material out of the field, the electrons will stay… but not forever. They are in an unnatural position. I’d also expect that exposing this material to another magnetic force … i.e. north pole pointed at north pole… would speed up the decay. So,eventually a train build with permanent magnets would need maintenence… probably new magnets, where as one using inductance doesn’t.

Scott Dickerson - that proves only that a point of stability exists in one dimension - not in space as a whole.

Soctt Dickerson
Hyperpowerful permanent magnets? … Is it perhaps a problem of expensive, exotic materials?*

Certainly there are many exotic materials that make far stronger permanent magnets than, say, iron; and I’ve no doubt that they’ll continue to tweak these. However, they’re still not in the same league as electromagnets (and of course superconducting electromagnets). Electromagnets also have the advantage of controllable field, so that it’s easy to use feedback systems to stabilise the levitation.

Darn me! I take back my previous post. This is fascinating: the Inductrack maglev system, under development at Lawrence Livermore National Laboratory. Maglev for trains using permanent magnets is feasible, but not by repulsion of opposed permanent magnets. Instead, the train’s motion causes one set of permanent magnets to induce current in coils, and these fields oppose to produce the lift. The magnets are arranged in a ‘Halbach array’, which somehow - I haven’t read the details - achieves very high field strength (something like a third that of superconducting magnets) just by virtue of configuration. A Google search for “Inductrack” finds tons of stuff about this; the cited papers explain how it’s side-stepping Earnshaw by being, essentially, a passive feedback system.

Here’s some more stuff about Halbach arrays, and a Scientific American reprint on how Inductrack works.

A snippet from the SciAm article:

“…In the past, engineers believed permanent magnets could not be used in maglev systems, because they would yield too little levitating force relative to their weight. The Inductrack’s combination of Halbach arrays and closely packed track coils, however, results in levitation forces approaching the theoretical maximum force per unit area that can be exerted by permanent magnets. Calculations show that by using high-field alloys-neodymium-iron-boron, for example-it is possible to achieve levitating forces on the order of 40 metric tons per square meter with magnet arrays that weigh as little as 800 kilograms per square meter, or one fiftieth of the weight levitated…”

So–the main issue never was the Earnshaw Theorum after all, but a “mere” problem of finding, or producing, sufficiently strong and lightweight permanent magnets.

A few more questions to tie it up:

1. What is the reason that there is a “theoretical maximum force per unit area” for permanent mags, though evidently not for mag fields in general?

2. One article mentions that the Halbach array makes use of the “Lorentz force,” which I’ve heard of but can’t find in my Oxford Dictionary of Physics. What is it?

3. Given all the above–including, BTW, a sort of vindication of the Mangetout “trough”–let me restate the thing I have in mind. “Is it possible in principle to arrange two sets of Halbach-type magnets in a configuration such that one set will float above the other (vertical dimension) AND will be restrained from sideways motion AND will NOT be restrained from forward motion; without actual physical contact (rails, etc) and without the use of nonpermanent magnets (ie, induction coils)”–?

This is slim, but it’s pretty much the limit of my understanding. If you put a wire in a magnetic field and run a current through it, there will be a force applied to the wire that is perpendicular to the current flow and to the magnetic field.