Permanent Magnets and Maxwell's Equations

[MisterPants]

How do you predict the interaction of two permanent magnets using Maxwell's Equations?

 

[AbsolutDealage]

*sniff* *sniff*.... I smell homework.

 

[TuxDave]

Wow... how vague of a question...

 

[eLiu]

Uh...? You don't need equations to say 'they attract' or 'they repel.' What, specifically, are you looking for...?

 

[MisterPants]

This isn't homework. I know it doesn't have a nice analytic solution, so it wouldn't be in a textbook.

Let me clarify my question. If I had a speaker magnet, I could run a current through a wire and measure the force to determine the strength of the magnetic field at any point around it. How can I use this to predict (quantitatively) what would happen if I put another identical speaker magnet near it?

I assume there is some way to do this using Maxwell's equations because classical electromagnetism would have been a pretty dissatisfying theory if it couldn't predict something so common.

 

[TuxDave]

So... your question is more of a, how can I quantitively predict the direction and strength of a magenetic field at a certain point given some magnets at some position. Well... here's my best guess.

If you were able to do measurements with the copper wire and all. I have a belief that if you measure the direction and strength of the magnetic field that each magnet individually contributes, you can just vector add the two together to get the resultant magnetic field. This is under the assumption that the individual magnetic fields will not interact with the cores of the magnets.

 

[MisterPants]

That is not my qusetion. How can I quantitatively predict the force one permanent magnet exerts on another?

 

[TuxDave]

Originally posted by: MisterPants
That is not my qusetion. How can I quantitatively predict the force one permanent magnet exerts on another?

Well why didn't you just say that in the first place? I need some time to formulate an answer.

 

[TuxDave]

*raises hands in defeat* Maxwell's equations were a set of elegant equations that could describe interactions between electric and magnetic fields. I'm not sure how to apply it in this case. Heck, I don't even know if the Lorentz force (what you described in the original post) was derived from Maxwell's equations.

Regardless, it's not a stupid theory. It's like saying a gasoline is a crappy source of energy since I can't use it to help me wake up (short of setting myself on fire). Maybe it wasn't written for this context. I don't know of any equation that could describe the force a magnet will exert on a metal, let alone another magnet.

 

[eLiu]

The lorentz force is prescribed in Einstein's Special Relativity...using something called the "electromagnetif field tensor." Don't ask me what a tensor is--part of some higher math that I don't know anything about. Search on like mathworld for more info. But the results of this tensor-thingy make quasi-sense...as does the lorentz force (F = q(E + v X B), X being cross-product).

I don't believe Maxwell's Eqns can be used to describe the interaction btwn 2 magnets. IIRC, you need much much much more complicated math/physics to figure that one out. Methinks it's not so much how the magnets interact, but how their fields interact...and how pressures/stresses are transmitted by the field (somethign tells me this has got to have somethign to do with tensors). I mean, that's how the the interaction between a magnetic dipole & a uniform B-field were described to me...which can be kinda related to the topic at hand (i.e. if the dipole were extremely small and placed extremely close to a permanent magnet where the B-field is *nearly* uniform).

Of course, I don't really think that's what you're looking for...

Another thought is that the interaction may exist at the quantum level...i mean, 'dipole groupings' (i forgot the real name) within ferromagnets is a product of quantum mechanics that isn't fully understood...*shrugs*

I'm just kinda thinking out loud here--maybe something I said is useful? lol...my experience w/e&m is pretty limited, lol.

-Eric