I was reading some of the stuff about the coin shrinking from that link I posted in the LHC accident thread, and noted the author mentioned something about "anomalous" longitudinal magnetic forces (basically this is the idea there are longitudinal forces on current elements, not predicted by
v x B). That reminded me about that particular controversy.

In the 80s with rail-gun type experiments, along with other advances of the high current discharge variety, produced some results that seemed to indicate a straight wire carrying a large current experienced internal axial tension. For example, shoot enough current through a long wire, and it will break in two, sometimes into several pieces.

It was thought this was just a melt and pinch effect, but some people did experiments designed to keep the wire from melting, and demonstrated it was tensile fracture in the solid state. It's a long controversy -- some even suggested it was *Lorentz contraction* that caused the tensile stress. That was a bit of a "stretch"....

Well, this is long convoluted thing, but another interesting experiment is the "mercury submarine". Place a pencil-like piece of copper, one end with a sharp point and the other with a blunt end in a vat of mercury. It floats normally. Now, pass a large enough current through the mercury and the copper pencile will sink (this is due to "pinch forces"), and it will propel itself backwards, blunt end first through the mercury. There is a net translational force on it, always toward the blunt end regardless of current direction. The assymetry in shape is what gives rise to this (this is sort of like tidal forces, depends on gradients in the field......)

Anyway, all that gave rise to renewed interest in these "longitudinal" forces. Here is a very nice, very readable paper on the subject:

http://www.df.lth.se/~snorkelf/LongitudinalMSc.pdf

The author demonstrates, at least to my sastification, that these longitudinal forces are *predicted by the Maxwell stress tensor* (well, he doesn't use the actual tensor formulation, just its vector resultant). IOW,
F = qE + v x B works as point function thing, but it has consequences beyond what you'd think.

Anyway, the above is a good read if you're into this stuff. I'd have to dig around in Jackson and some others, but I do recall some commentary about the Maxwell stress being "weird" in some cases. Maxwell and others originally thought of what we would call the stress tensor as the actual stress in the ether. IOW, "tension" in the "medium". However, there is no medium in that classical sense, so what it really represents is sort of funny. It does indeed represent the momentum density and transport of the EM field. And it does indeed give the forces on material objects when properly done, but there are some oddities there about media.

-Richard

That looks interesting. Wish I understood more than half of it.

Have to read it again (probably a couple of times...)

Thanks for the post.

There is an old question of mine here, are
magnetic lines of force real or an artifact of
the iron filings? I believe now that lines are
real but the iron filings are showing a
conglomerate of billions of such lines! Now if
you could make the circular lines visible
around a current carrying wire, would you see
more lines form as the current increases or
would you see the lines becoming larger with
more inner lines forming? Such an experiment
may be possible with iron colloids in a
transparent liquid. Get two magnets and feel
the repulsion from the like poles. It is still
a marvelous mystery what is happening no matter
how familier!

That really reminds me a lot of Hannes Alfven's work with plasma and the way he describes z-pinches or Bennett pinches in plasma. The plasma forms filaments that more or less resemble a tornado or twister, or the kind of thing you see form in a common plasma ball. There is an inward pressure from the magnetic fields that constricts the plasma flow into densely wound filaments. If there is enough current flow, the result in plasma can be explosive.

One starts to wonder is the electrons flowing inside the wire aren't acting in a similar way?

Also, having a large current flowing in a thin wire and seeing the wire go bang is popular in physics classes.

__________________
papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

Well, first of all, field lines are not real, they are a mathematical conception, just like altitude lines on a map are not real. The magnetic field is a vector field, which means that at every location in space the magnetic field has a direction and a magnitude. Now, also the magnetic field is continuous-differential in all space, which means that you can follow the direction of the magnetic field in space, by taking tiny steps in the direction of the local field. This is what is being done by looking at fieldlines, these things follow the directoin of the field. Now, interestingly enough in the special case of a magnetic field, we can show the field using magnetic material. The shavings align with the direction of the field, and thus act like the mathematical field lines.

The funny thing is that the field lines can actually be used to visualize things more easily. For example, what you said about the strength of the field. Take a bar magnet and your shavings. Now, you will see that taking an area on the side of the magnet, and following taht to the pole of the magnet that the area gets smaller. So, in science we say that the field strength is determined by the number of field lines through a square meter. But this is only qualitatively, because we cannot put a real value on the number of field lines, as the magnetic field is a continuous field and basically there are an infinite number of field lines.

You can do the same experiment with a current carrying wire. Take a non-conducting plate and make a hole. Put a wire through it and have a current flow. Now take your filings and put them on the plate, you will find (if your wire is long enough, don't make it too short) that the filings will align themselves in concentric circles, which is the magnetic field you would expect from a wire current.

Basically, the number of "field lines you can see" is dependent on the size of the filings you use. And as I just explained that there are actually an infinite number of field lines, your filings must be infinitely small to be able to see them all, but then your table will be just a grey area and you will not see any structure anymore.

If I recall correctly, for a dipole (a bar magnet, but then you have a slight error which can be neglected) the mathematical equation for a magnetic field line is:

R / cos²(theta) = constant

Where R is the distance to the center of the dipole and theta is the angle with respect to the direction of the dipole.

BTW, Publius thanks for the paper, I downloaded it but have not read it yet, but it looks interesting.

__________________

Any comments in orange are to be considered in ModeratorMode, when not already specifically mentioned.

Optimism does not change the laws of physics. (T'Pol)
A good scientist has freed himself of concepts and keeps his mind open to what is. (Dao De Jing 27)
Martin ( http://www.geocities.com/DrMartinV )

Thanks for that tusenfem. Its a throwback to
physics instruction many years ago with talk
of conductors cutting magnetic lines of force.
And yet, and yet...we accept that at the atomic
level things are "granular" so why not magnetic
fields as well? This has been the confusion.
Going into pure speculation I could visualise
little twirly thingies in the vacuum that are
aligned by moving charge. A bar magnet would
be causing billions of "lines" each a string of
twirleys twisting in unison. And when opposing
lines meet, they interfere and repel but lines
twisting in the same direction merge. Oh this is
fun! And remember that Maxwell in creating his
great theory is said to have used the idea of
little spinning things to try and give an
insight into the physics! Some say to forget
this, just regard the great mathematical
structure. But I wonder. If my experiment is
feasible to some extent, I thought it might give
a pointer.

When I first posted that, I didn't notice, but this paper is the author's (Lars Johannsen) master's thesis. And again, his conclusion (which seems sound to me, but no Jackson am I), is that the Maxwell Stress Tensor does indeed predict longitudinal forces in these situations. It is thus "regular ol' EM", just doing things sort of unexpected from elementary considerations.

I have seen that before. Someone finds something he thinks goes beyond EM theory (I forget, but there was something about the vector potential itself having some force; ie no B field, just A). But upon careful analysis, it turns out it was regular, known EM all along, just sort of coming out in unexpected ways.

I've always been fascinated by the Maxwell Stress tensor. The 3 x 3 version of that is just the momentum transport, just like any other "pressure" or stress tensor. In the ether days, it was thought this was really the stress in the medium. IOW, E and B were stresses in the ether.

But, without an ether, just what the heck does it represent for the vacuum, or space-time. Going to the 4-vector formulation, the 3 x 3 part are the ij components, and the Poynting vector becomes the 0i components (00 is the energy density as always). The 4-vector version is indeed the EM stress-energy tensor.

And that does indeed go right into the Einstein Field Equation as a source of gravitation. Here's what fascinates me to no end.

Take a capacitor and a C-clamp magnet and make a small region with E and B at a right angle to each other. You have non-zero Poynting,
E x H. You also have momentum density. But, if you integrate that Poynting vector over any closed surface, you get zero. This seems to say that while there is no transport of energy anywhere, there is still a "current" of energy. Energy is circulating around, but the density at any one spot is constant.

That fascinates me. And while it gets more complex, there are similiar things going on with the momentum. The field has momentum density, and can even have momentum transport. The analysis of this can get dizzingly complex, but you can show that the work you do with the sources to produce the field has momentum involved, which exactly agrees with the momentum density. IOW, push these charges and currents together however you have to, and you see that mechanical momentum "went somewhere".

It went into the field. And you can even have angular momentum in the field as well. That is, building up the field, you had torques you had to work against and indeed you put angular momentum in the field too in such cases.

So we have the odd situation that perfectly static EM field seems to have "flows" of energy and momentum all through the vaccum -- or at least, that's what the equations and our interpretation of their meaning seem to say. And indeed, electrovacuum solutions of the EFE indicate this a well. Indeed, as far as the EFE is concerned, that simple magnet and capacitor will be frame dragging.

Unfortunately, since gravity is so weak (G*Energy/c^2, and a 1/c^4 dependence for energy current frame dragging effects) these effects are well below the practical threshold of measurement. Look up the space-time solution of a propagating EM wave. Einstein and Rosen did this way back (and it was a doozie), solving the fully coupled Maxwell and GR equations for the space-time of a propagating plane EM wave. It was most fascinating. An EM wave makes a gravitational wave. But it again, unless the EM energy density was ridicioulously high, the effect on space-time is vanishingly small.

But is there. My own wild-eyed side says that any "warp drive" or other fancy effects is going to come from EM field effects on space-time. Figure out a way to amplify the effect, and you can do some fancy things with space-time.

Quantum "stuff" may be the key to that amplification. Tajmar and deMattos seem to have found that certain types of rotating superconductors makes a much larger B_g field that predicted by the EFE. There's some sort of "amplification" afoot.

Dr. Ron Mallet thinks a Bose-Einstein condensate will amplify the frame dragging effects of EM radiation. Mallet things he can make a tiny region of space-time in the lab with closed time-like curves, and something weird will happen, and he can make a time machine

-Richard

This discussion reminded me of something I came
across that is worth looking up. Chapter 28 of
the Feynman Lectures on Physics, vol 2. Here is
the lowdown on difficulties with classical
electromagnetism. So any suspicions you may have
had about the mainstream are laid out The
skeptic could have been one of the co-authors
Leighton or Sands or all of them! Dont pretend
to understand much myself but here it is.

Pete,

There is a quantum theory of EM, called Quantume Electrodynamics (QED). And the weak force has been unified with EM, so you can call it the Electroweak field, really.

Anyway, in QED, the fields themselves are indeed quantized, coming in little chunks so to speak. QED, as Feynman always like to brag, is the most successful physical theory to date in terms of the agreement of its prediction with experiment.

-Richard

I was looking through a slim paperback on QED
some ten years ago. Wondered if this calculation
on the gyro something ratio accurate to
umpteen decimal places was a fluke. Or maybe
not.

What kinds of tech could exploit such effects.