magnetic potential

trivial.

See

Johan E. Mebius

Magnetic strength is equal in the field.

Mitch Raemsch

One reason is that the vector wave equation takes a familiar form in terms of the vector potential. Writing it out in terms of the E and B field components is much much uglier.

Cheers

Phil Hobbs

I take the magnetic vector potential, A, as being the irrotational part of a magnetic field. Using the Potential Formulation of EM, one can write Maxwell's equations in two equations instead of four. See Griffiths' "Introduction to Electrodynamics" for that and where it is used and why. Or any similar EM textbook.

Best,

Fred Diether Co-moderator sci.physics.foundations

Magnetic strength is equal in the field.

Mitch Raemsch

that makes no sense.

I'm reminded of a figure somewhere in the Feynman lectures on physics. He's showing two slit interference of an electron beam. There is a magnetic field confined to the space between the two slits. (If you are looking down on the two slits (one north and the other south), and the e beam is traveling west to east the magnetic field is coming out of the page.) There is a phase shift in the interference pattern formed by the electron beam that depends on the amount of magnetic flux enclosed between the two paths. In principle you can imagine a magnetic field that is totally contained to a space through which the electrons do not pass. So how do the electrons know about the field? Well, the magnetic potential (what I call the vector potential) is non zero in the path of the electron beam. What's more fundamental the field or the potential?

George H.

PS. There may be some error in the above... go to the source and read for yourself.

I am not an expert on the problem.

To solve quantum mechanical problems, a suitable hamiltoninan is needed. For that a potential term is required. If the electric effects are not predominant, but magnetic effects are, the hamiltonian includes a term in A. I am not an expert in this.

The classical approach is in Classical Mechanics by Goldstein. When it comes to developing equations of motion for continuous media such as fields in space and the vibrations of strings and bodies, you start with expressing kinetic and potential energy integrated over the volumes. Then variational methods can be used to get the equations of motion. If there is an electromagnetic field present, its energies must be included. 30 years ago, I did use the kinetic and potential energies with variational methods to get the equations of motion for a flyline or bullwhip.

There have been experiments inspired by David Bohm that clearly show that it is the potentials in quantum mechanics that count. IIRC, electrons were diffracted around magnetized iron whiskers. The electrons were never in a magnetic field but the diffraction pattern depended upon the magnetization of the whiskers and the change in consequent vector potential.

Bill

The magentic field is always of the same strength. Play with some magnets. Do they get stronger when they are close? No. The force remains the same though the range may change.

Mitch Raemsch

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I learned E&M using J. D. Jackson and Vector potential A was a major part of it. Oddly, never used it in real life applications of magnetism and have totally forgotten it.

Right, "Mitch". Play with some magnets and win two Nobel Prizes!

Idiot.

The reference is The Feynman Lectures Vol II section 15-5. It's called the Aharonov-Bohm effect. And Feynman argues the point that A (magnetic vector potential) seems somehow more "fundamental" than B (magnetic field).

The interesting thing is that there are a lot of obvious cases where magnetic induction occurs where there is no magnetic field such as outside a solenoid (as in the Aharonov-Bohm effect) or outside a toroid, or self-induction down a straight wire.

In the old days, the magnetic vector potential was pretty much regarded as only a mathematical "trick" used to solve problems that were difficult when using only B fields. But today there seems to be some evidence that it is A rather than B that is the more fundamental field as Feynman suggests.

For example take the case of magnetic induction. The classic story is that a changing magnetic field induces an emf in space that can cause a current to flow in a conductor. It's called Faraday's Law. But the problem is that somehow emfs are induced even though the B field is not present at the wire! Now that's a mystery! But it turns out that the whole classical idea is not only wrong, it was never stated in that manner by Faraday in the first place!

The true law of induction is that a changing CURRENT induces an electric field in space around itself, falling off as 1/R for short elements, and that electric field is either parallel or anti-parallel to the current vector. And the sign of this law is such that it it creates a direction that complies with Lenz's law. No magnetic fields in sight! Of course the catch is that the current ALSO creates a magnetic field AT THE SAME TIME, which is related to the induction, so one is (usually) able to use the magnetic field as a "measure" (Maxwell's word) of the induction. However, the magnetic field (flux) does NOT cause the induction! Faraday's law as usually understood is bogus.

So what about "A"? Well if you rewrite induction in terms of A you find a very simple relation ship where E induction vector is simply equal to the negative of the time rate of change of the A vector. This explains the mystery of induction where there is no B field. As Feynman notes, even though B is zero in lots of places mentioned above, A is NOT zero there! Zero A implies a zero B, but a zero B does not imply a zero A!

So it seems that A is more fundamental than B, but the problem is we have lots of "model" for B with flux lines and so forth but A does not (as yet) seem to have such an easily comprehended physical model. That is probably the reason why people prefer to think of B as being the quantity doing everything.

The reference is The Feynman Lectures Vol II section 15-5. It's called the Aharonov-Bohm effect. And Feynman argues the point that A (magnetic vector potential) seems somehow more "fundamental" than B (magnetic field).

The interesting thing is that there are a lot of obvious cases where magnetic induction occurs where there is no magnetic field such as outside a solenoid (as in the Aharonov-Bohm effect) or outside a toroid, or self-induction down a straight wire.

In the old days, the magnetic vector potential was pretty much regarded as only a mathematical "trick" used to solve problems that were difficult when using only B fields. But today there seems to be some evidence that it is A rather than B that is the more fundamental field as Feynman suggests.

For example take the case of magnetic induction. The classic story is that a changing magnetic field induces an emf in space that can cause a current to flow in a conductor. It's called Faraday's Law. But the problem is that somehow emfs are induced even though the B field is not present at the wire! Now that's a mystery! But it turns out that the whole classical idea is not only wrong, it was never stated in that manner by Faraday in the first place!

The true law of induction is that a changing CURRENT induces an electric field in space around itself, falling off as 1/R for short elements, and that electric field is either parallel or anti-parallel to the current vector. And the sign of this law is such that it it creates a direction that complies with Lenz's law. No magnetic fields in sight! ============================================

Idiot.

Stop sniffing glue, likewise your friends' replies.

It's like saying the meaning & usefulness of the magnetic force is unclear.

The magentic field is always of the same strength. Play with some magnets. Do they get stronger when they are close? No. The force remains the same though the range may change.

Mitch Raemsch

troll. go twiddle with your own magnets

ery...

Wonderful "show and tell" experiment there Andro! I'll bet your teacher was really impressed with it and told you that you might grwo up to be a scientist some day! She lied.

Idiot.

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om...

I would strongly recommend any of the papers of that grand old man of EM, C. J. Carpenter, who wrote many papers on the use of the vector potential in real world problems of electro-magnetism. Several of these can be found on Kirk McDonald's invaluable archive site on EM at Princeton University:

Incidentally, the vector potential is the PHYSICAL basis for EM as it is directly related to the exchange of momentum between two moving charges - all the rest is just math.

Maxwell's Equations can be written as ONE single quaternion equation using the quaternion form of the EM potential.

Exactly so, Benj. Once an idea gets accepted into the canon of science (in this case, FIELDS) it becomes "anti-scientific" to criticize the concept. Real theologians mastered this technique hundreds of years ago. In the case of EM, Maxwell focused on the vector potential (as did Lorenz, a little earlier) in his famous 1864 paper where he analyzed the physical nature of his proposed EM aether model. Maxwell changed to the more mathematically elegant 'field' approach in his 1873 "Treatise" after he gave up on any physical understanding of EM.