What is a magnetic field? (fun mental exercise)

[meBigGuy]

Think of a charged particle moving parallel to a wire carrying a constant current. The magnetic field caused by the constant current exerts a force on the moving particle (say it moves towards the wire).

Now, think of the same thing from a different reference plane. Think of a still particle near a parallel moving wire (same distances, charges, current, and relative velocities). In other words, shift from the reference plane of the wire at rest to the reference plane of the particle at rest.

The particle must be affected by the current in the same way. It must move toward the wire. So, how does that happen? Where does that force come from?

It's an interesting problem, and leads to the conclusion that a magnetic field in one reference plane is an electric field in the other, brought about by relativistic motion. In reality they are the same thing.

COOL

http://www.feynmanlectures.caltech.edu/II_13.html Section 13.6

 

[anorlunda]

Bingo, you got it. In different inertial reference frames, electric becomes magnetic, and magnetic becomes electric.. The are actually the same thing, called electromagnetic fields.

 

[Baluncore]

You cannot have magnetic fields without electric fields. They are quite dependent on each other.

Consider a length of link chain made of a conductive magnetic material. Pass a wire carrying AC current through the end link.
That will create a magnetic flux in the end link which will then induce an electric current in the next link. The process repeats along the chain in alternate links.

At the far end of the chain you hang a detector on a small loop of wire.
Depending on whether there is an odd or even number of links in the chain, the detector may or may not detect the input signal.

Now add an extra link somewhere in the chain that circles the junction of two links.
The detector response is now independent of the number of links, every link has both a magnetic flux and an electric current flowing.

 

[meBigGuy]

Your example is about electric currents (I) and magnetic fields (B), not electric fields (E).
The point is that electric fields and magnetic fields are not different things, but rather, different views of electromagnetic fields.

To a stationary electron, a moving wire, conducting current, appears positively charged.
(There is a relativistic change in charge density relative to the stationary electron caused by the moving wire.)
To a moving electron, the magnetic field produced by a current in a wire causes it to arc toward the wire.

Have you read the Feynman link?

"magnetism and electricity are not independent things—that they should always be taken together as one complete electromagnetic field. Although in the static case Maxwell’s equations separate into two distinct pairs, one pair for electricity and one pair for magnetism, with no apparent connection between the two fields, nevertheless, in nature itself there is a very intimate relationship between them that arises from the principle of relativity."

and

"We have found that we get the same physical result whether we analyze the motion of a particle moving along a wire in a coordinate system at rest with respect to the wire, or in a system at rest with respect to the particle. In the first instance, the force was purely “magnetic,” in the second, it was purely “electric.”

I was unaware of the role relativity plays in the character of electromagnetic fields.

It's also interesting that the introduction of relativity didn't change Maxwell's equations.

 

[jim hardy]

hmm

Think of a still particle near a parallel moving wire (same distances, charges, current, and relative velocities). In other words, shift from the reference plane of the wire at rest to the reference plane of the particle at rest.

The particle must be affected by the current in the same way. It must move toward the wire. So, how does that happen? Where does that force come from?

i'm hung on the thought the moving wire must carry its magnetic field along with it. So the QV cross B term in Lorentz doesn't change - you said relative velocities are the same.

I won't say any more until i make it through that Feynman lecture.

 

[stedwards]

Faraday Tensor

 

[anorlunda]

hmm
i'm hung on the thought the moving wire must carry its magnetic field along with it. So the QV cross B term in Lorentz doesn't change - you said relative velocities are the same.

I won't say any more until i make it through that Feynman lecture.

Jim,

Visualize yourself riding on a train with a trapped charge in a balloon. Are you electric or magnetic? You on the train has a different answer than you on the platform.

Learn it best from the master teacher Leonard Susskind

 

[Baluncore]

Visualize yourself riding on a train with a trapped charge in a balloon. Are you electric or magnetic? You on the train has a different answer than you on the platform.

But you cannot be in two different places at one time, so it must appear as magnetic or electric depending on where you really are and what it really is. That does not make it both at the same time to you. Sitting on the fence is not an option here.
When you toss a fair coin it comes down, (static), heads or tails, (electric or magnetic?). But if you rest or spin the coin on it's edge, how it appears will depend on your viewpoint.

 

[meBigGuy]

whether it APPEARS magnetic or APPEARS electric, it is electromagnetic. Of course it can also APPEAR as a combination of both magnetic and electric. it just depends on your frame of reference. You say it depends on "what it really is", as if it is "really" electric or "really" magnetic. What it is is "really" electromagnetic.

 

[anorlunda]

But you cannot be in two different places at one time, so it must appear as magnetic or electric depending on where you really are and what it really is. That does not make it both at the same time to you. Sitting on the fence is not an option here.
When you toss a fair coin it comes down, (static), heads or tails, (electric or magnetic?). But if you rest or spin the coin on it's edge, how it appears will depend on your viewpoint.

Where analogies fail, resort to the math. Stedwards posted the true answer, the Farsday Tensor. I also posted the video lecture that will teach you about the Faraday Tensor.

 

[meBigGuy]

"The electromagnetic tensor is completely isomorphic to the electric and magnetic fields, though the electric and magnetic fields change with the choice of the reference frame, while the electromagnetic tensor does not."

The thing about the 4 Maxwell equations is that their conditions are such that the reference plane is fixed.

"This tensor simplifies and reduces Maxwell's equations as four vector calculus equations into two tensor field equations."

Regarding what Jim said about the magnetic field "moving" with the wire. That's an obvious and intuitive way to consider it, but I wonder how the moving wire would affect a compass? Is there actually a moving magnetic field? Can a magnetic field "move" in that sense (along an infinite wire moving along the axis of current flow)?
After all, the electron's displacement is such that a moving magnetic field would describe it exactly.

BTW, this is all new to me and I am not a mathematician. I'm not a fields guy either.

 

[stedwards]

The fields don't move, by definition. Amplitudes can decrease in some places, and increase in others. An electromagnetic wave is an example.

Spacetime is four dimensional. So one has to wonder why electromagnetism, as commonly expressed, has these 3 dimensional vectors E=(Ex, Ey, Ez) and B=(Bx, By, Bz). You can think of these two 3 dimensional vectors as the space-like and time-like parts of the same thing. Like this: E=(Ext, Eyt, Ezt) and B=(Bxy, Byz, Bzx). These are the elements of the Faraday tensor.

But there is a simple 4 dimensional vector associated with electromagnetism. It's called the 4-vector potential, A=(At, Ax, Ay, Az). The component At is the familiar electric potential phi, expressed in volts. The remainding three are called the magnetic potential.

The electric field is due to the change in electric potential over a distance, combined with the change in the magnetic potential over time. Ex = d(Ax)/dt + d(At)/dx. For Bx, it's like a cross product. Bx = d(Ax)/dy - d(Ay)/dx.We're dealing with 4 dimensions instead of three. A reference frame in motion with respect to another reference frame is comparable to one coordinate system rotated with respect to another in 3 dimensional space. It's called a "boost". During any rotation or boost the length of the vector A doesn't change, but the values of the components do. This is why an electric field in one frame of reference can look like both an electric and magnetic field in another reference frame; the components of A are different, as well as the components of spacetime.

 

[jim hardy]

i found a printable copy of that Feynman magnetostatics page.

Will be back. Dont want you folks to think I'm not interested .

Faraday Tensors look really fearsome. I don't have the vocabulary to handle the link you posted.

And this

The fields don't move, by definition.

is counter-intuitive to me. A magnetic field must accompany whatever is producing it - else marine compasses wouldn't have compensating magnets.

Thanks, guys

 

[Jony130]

 

[stedwards]

And this [...] is counter-intuitive to me. A magnetic field must accompany whatever is producing it - else marine compasses wouldn't have compensating magnets.

Thanks, guys

By example of fields that don't move, there are surface waves on water. The wave itself propagates, but the water itself is relatively fix (a particle of water driven by a series of waves moves in small circles). The question never seems to come up in engineering setting where either concept seems to work just as well as the other.

A magnet itself seems to carry it's field with it, but if it's in relative motion it would have an accompanying electric field.

Taken to it's conclusion, the field of electric charge density doesn't move either, but most people would hesitate to adopt this point of view, insisting that charge moves, or something similar. This goes for electric current density as well.

 

[meBigGuy]

Again, think of an infinite wire carrying a current. It has a magnetic field radiating out from the wire that attenuates with distance. But, there is nothing to distinguish the field along the axis of the wire at a given distance. It is of fixed intensity, the same all along the wire. If the field is moving, what is it that is moving? If a put a wire (not carrying a current) perpendicular or parallel to the moving wire, what would it detect? It would see a fixed magnetic field. I don't think it can tell the wire is moving.

 

[anorlunda]

Again, think of an infinite wire carrying a current. It has a magnetic field radiating out from the wire that attenuates with distance. But, there is nothing to distinguish the field along the axis of the wire at a given distance. It is of fixed intensity, the same all along the wire. If the field is moving, what is it that is moving? If a put a wire (not carrying a current) perpendicular or parallel to the moving wire, what would it detect? It would see a fixed magnetic field. I don't think it can tell the wire is moving.

Yes but also think of the looped magnetic lines we see at the surface of the sun. They are made visible by the plasmas they carry. Those lines move and grow and shrink as we watch. Isn't that a moving field?

 

[Baluncore]

Yes but also think of the looped magnetic lines we see at the surface of the sun. They are made visible by the plasmas they carry. Those lines move and grow and shrink as we watch. Isn't that a moving field?

Is it the path taken by the current through the plasma that is moving and so dragging the magnetic field with it? Or is it the magnetic field that is driving the plasma? MHD says it is both. Every current is intimately looped by a magnetic field and every magnetic field is intimately looped by a current.

You cannot have E without M in our finite impedance Universe.

 

[meBigGuy]

I can't really comment on the specifics of plasma flows on the sun, but I didn't say (or mean to imply) that fields, in any general sense, don't move.
If you move the wire laterally, the magnetic field strength in space changes. That would be a "moving magnetic field". If you move it along the axis of the current carrying wire, there is no magnetic field strength change laterally from the wire or anywhere in space, so how can you tell the wire is moving by the magnetic field? (but when it is moving along the axis of current flow it displays an electric charge)

 

[stedwards]

Fields don't move.

There are no associated velocities in Maxwell's equations. In the Lorentz force equation, the velocity is associated with electric charge.

 

[jim hardy]

By example of fields that don't move, there are surface waves on water. The wave itself propagates, but the water itself is relatively fix (a particle of water driven by a series of waves moves in small circles). The question never seems to come up in engineering setting where either concept seems to work just as well as the other.

A magnet itself seems to carry it's field with it, but if it's in relative motion it would have an accompanying electric field.

Taken to it's conclusion, the field of electric charge density doesn't move either, but most people would hesitate to adopt this point of view, insisting that charge moves, or something similar. This goes for electric current density as well.

Fields don't move.

There are no associated velocities in Maxwell's equations. In the Lorentz force equation, the velocity is associated with electric charge.

you fellows are causing me to re-consider my most fundamental concepts.

Might all of space then be considered an electromagnetic field through which disturbances propagate like ripples on the surface of or sound through the bulk of , water ?

What i thought of as the "field" surrounding a bar magnet, or around earth, or is just a local distortion ?

 

[meBigGuy]

The magnetic fields of bar magnets are explained nicely in
That guy has some interesting, simple, videos.

As for magnetic fields "moving". If the source of the magnetic field moves, the field strength in space changes (most of the time). That could be considered as moving. It is not propagating.

 

[Baluncore]

Might all of space then be considered an electromagnetic field through which disturbances propagate like ripples on the surface of or sound through the bulk of , water ?

All of space, free or occupied, has a finite impedance that determines the ratio of E/M and the speed of propagation of an EM disturbance. In (linear) space, the field at any fixed point is the sum of all the EM influences, delayed by their propagation time from their origin to that point.

Engineers and technicians like to think that translation of a “field generator” drags magnetic “field lines” through the variable impedance of our “engineered space”. Physicists only see changes in field magnitude and direction at fixed points in space.

When you gradually translate a magnet or a current filament sideways, the strength and direction of an initial field gradually changes to that of a final field. That gradual change propagates outwards from the field generator at the speed of light. The field strength at fixed points in space has changed. It may appear that the field has moved because the same field pattern has been translated with the generator, but the new pattern has arisen by the progressive removal of the initial field generator and it's replacement by the final field generator. Hence, the field does not move, it is the vector field that has changed.

We live in a universe of incompatible interfaces. It is characterised by it's impedance variations. We can only perceive our universe some time after a poynting vector encounters an impedance mismatch, where energy is reflected or scattered, to be poynted our way.

 

[anorlunda]

Thanks for that Baluncore. It is a radical view, yet perfectly logical. I guess, that the problem is that our understanding is warped by natural language self-centric descriptions of nature. We can be trained to think mathematically, but we speak naturally.

What you said about electomagetic fields could also apply to any other field. The gravitational field of Earth doesn't move around the sun annualy, it's manitude at certain coordinates changes as the Earth passses by. It is very difficult to think of it that way.Thanks to you too meBigGuy, that video was very clever in presentation.

 

[jim hardy]

Engineers and technicians like to think that translation of a “field generator” drags magnetic “field lines” through the variable impedance of our “engineered space”. Physicists only see changes in field magnitude and direction at fixed points in space.

Thanks. I spent a lifetime around electrical machinery where that version of electromagnetics sufficed quite nicely for understanding the equipment and keeping it in good running order. I was after all a maintenance man.

All of space, free or occupied, has a finite impedance that determines the ratio of E/M and the speed of propagation of an EM disturbance. In (linear) space, the field at any fixed point is the sum of all the EM influences, delayed by their propagation time from their origin to that point.

As a maintenance engineer i didn't really have to worry about the workings of the universe, for its maintenance falls to a power greater than myself.
I always was curious though about the nature of electromagnetic fields and what it is about "the universe" that gives it permeability and permittivity in peculiar proportions that determine speed of light.
I'm plodding along - thanks guys for sharing your insights. All is not lost.

old jim

old jim

 

[stedwards]

you fellows are causing me to re-consider my most fundamental concepts.

Might all of space then be considered an electromagnetic field through which disturbances propagate like ripples on the surface of or sound through the bulk of , water ?

What i thought of as the "field" surrounding a bar magnet, or around earth, or is just a local distortion ?

I'd been uncertain how to answer this.

The map is not the territory: The classical models of electromagnetic fields and charge are not the objective physical reality, but a map to it. In any case, someone might be able to come up with a mathematical model of electromagnetism where the fields have associated velocities, just as charged particles. They wouldn't be the same fields as we learned about, but there would obviously be some relationship, if both models worked, so you could translate from one to the other.

This can be made more concrete. We have an example of fields of charge and current within Maxwell's equations--actually the density of charge and the current density. These fields have no velocities. But the Lorentz force equations describe fields acting on charges, and charges in motion, instead; F = q(E + BxV). V is the velocity of the charge, q. The standard classical theory is schizophrenic concerning charge.

However, there's a fields model for the Lorentz force using what's called the Lorentz 4-Force (in Wikipedia). Now charge and current can both be treated as fields. In this case, it's the Lorentz 4-force density, but that's more detail than is necessary.

Applying this particle-field duality (not the quantum duality) to electromagnetic fields might be feasible, although of what value, I don't know.

Thank you, Jim. You've certainly got me thinking about this in more detail than before.

 

[the_emi_guy]

I think that sometimes these EM concepts are viewed as consequences of relativity when they are in fact historically the source of special relativity:

"What led me more or less directly to the special theory of relativity was the conviction that the electromotive force acting on a body in motion in a magnetic field was nothing else but an electric field" Albert Einstein, 1952.

As we know, in relativity there is no special, unique "at rest" frame of reference. This is a philosophical concept.

On the other hand, in classical electromagnetics one could discover the unique "at rest" frame of reference by simply observing a charged particle. If it is emitting a magnetic field than it is moving. If not, then it is in this singular "at rest" frame. This is the dilemma that Einstein solved with SR.

I have always felt that it is unfortunate that SR is often first introduced with images of trains being struck by lightning at each end and such. I think it would be better if it were taught in a manner parallel to Einstein's own thinking.

Another (maybe random) point: post-relativity electromagnetism only includes one physical constant: vacuum permittivity. (vacuum permeability is not a physical constant but a defined number). If electric and magnetic phenomena were independent they would each have their own physical constant.

 

[meBigGuy]

I just dug out my old Scientific Basis of Electrical Engineering. No mention of relativity. First 150 pages on Electric Fields, next 150 on Magnetic Fields. Maxwell-Free to boot, so to speak.

At least they do pin down the reference frame in which the charge is moving.

 

[anorlunda]

I just dug out my old Scientific Basis of Electrical Engineering. No mention of relativity. First 150 pages on Electric Fields, next 150 on Magnetic Fields. Maxwell-Free to boot, so to speak.

At least they do pin down the reference frame in which the charge is moving.

No. Not the basis of EE, the basis of SR. Below is the opening paragraph of Einstein's paper where he first announced special relativity. As you will see, his attention was focused on the electromagnetic problem.

ON THE ELECTRODYNAMICS
OF MOVING BODIES
By A. Einstein
June 30, 1905
It is known that Maxwell's electrodynamics—as usually understood at the present time—when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion. For if the magnet is in motion and the conductor at rest, there arises in the neighbourhood of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated. But if the magnet is stationary and the conductor in motion, no electric field arises in the neighbourhood of the magnet. In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise—assuming equality of relative motion in the two cases discussed—to electric currents of the same path and intensity as those produced by the electric forces in the former case.​

 

[jim hardy]

On the other hand, in classical electromagnetics one could discover the unique "at rest" frame of reference by simply observing a charged particle. If it is emitting a magnetic field than it is moving. If not, then it is in this singular "at rest" frame.

still plodding along... (got back from that trip which interrupted my studies here, though i did muse a lot while driving cross country)

I'm okay with:
Take one charge and one observer. If there's relative motion between them then there's a magnetic field surrounding the charge. So two observers might report differently on the presence of said magnetic field.
But--
When i tried to work the positively charged cat video in my alleged brain, i got a "runtime error".
Here it is.
We have negative charge in motion due to the electron borne current in the wire, so a magnetic field surrounds it
When wire is stationary and +cat moves along it, there's relative motion between him and the field surrounding the wire's moving negative charge.
So +cat experiences F=QVcross B.
But when in the video, Mr +cat moves along in step with the negative electron borne charges in that wire, he no longer has relative motion wrt that negative charge.
Narrator asserted that in +cat's frame of reference, the magnetic field disappears because the relative motion disappeared.
I counter assert that +cat now has motion relative to the positive charges inside the wire which are moving wrt +cat from his nose toward his tail as he progresses along the wire.(or as it progresses under him).
Mr +cat sees j dot ds for positive and negative charges inside the wire that are not equal because of the tiny electron drift velocity, which narrator emphatically quantified as tiny relative to c.
By right and left hand rules, the magnetic field experienced by +cat from +charge (inside the wire) moving in direction from from his head to his tail
is the same as that experienced from -charge(inside the wire) moving opposite way in other reference frame.
The two reference frames yield the same magnetic field.

SO - i was unable to accept that cat video.
For me it's QV cross B in both cases. What'd i miss ??

Is there a handy link to that Einstein introduction, anorlunda ?

ALERT edited a bit to improve clarity

 

[anorlunda]

SO - i was unable to accept that cat video. For me it's QV cross B in both cases. What'd i miss ??

Is there a handy link to that Einstein introduction, anorlunda ?

Too bad about the video, analogies are always imperfect. I couldn't follow your verbal thought exercise.

Jim, I think you would do better with the Susskind video linked in post #7. Susskind makes even the most exotic mathematics understandable by mere mortals. I learned it from Susskind; you can too.

Whoops, I forgot the Einstein link. Here it is.
http://www.fourmilab.ch/etexts/einstein/specrel/www/

Einstein wasn't the only one studying the EM riddles. There were many others. But he was the first to succeed because he abandoned the common sense definition of simultaneity. You must bring time into it to understand SR.

 

[jim hardy]

Thanks.. i made note of Susskind before we left but the laptop refused to connect to wifi until it got back home, will look at him tonight.

Sorry my words weren't clear. If Susskind doesn't clear it up i'll try to make a picture in Paint...

 

[meBigGuy]

If susskind clears it up, with all the 4-vectors. etc, then you are a batter man than I.

anorlunda:
My comments were not a comment on what you said about SR (which I accept wholeheartedly, since that's why I started the thread) but a comment on the "Scientific Basis of Electrical Engineering" not even mentioning SR.

 

[the_emi_guy]

still plodding along... (got back from that trip which interrupted my studies here, though i did muse a lot while driving cross country)

I'm okay with:
Take one charge and one observer. If there's relative motion between them then there's a magnetic field surrounding the charge. So two observers might report differently on the presence of said magnetic field.
But--
When i tried to work the positively charged cat video in my alleged brain, i got a "runtime error".
Here it is.
We have negative charge in motion due to the electron borne current in the wire, so a magnetic field surrounds it
When wire is stationary and +cat moves along it, there's relative motion between him and the field surrounding the wire's moving negative charge.
So +cat experiences F=QVcross B.
But when in the video, Mr +cat moves along in step with the negative electron borne charges in that wire, he no longer has relative motion wrt that negative charge.
Narrator asserted that in +cat's frame of reference, the magnetic field disappears because the relative motion disappeared.
I counter assert that +cat now has motion relative to the positive charges inside the wire which are moving wrt +cat from his nose toward his tail as he progresses along the wire.(or as it progresses under him).
Mr +cat sees j dot ds for positive and negative charges inside the wire that are not equal because of the tiny electron drift velocity, which narrator emphatically quantified as tiny relative to c.
By right and left hand rules, the magnetic field experienced by +cat from +charge (inside the wire) moving in direction from from his head to his tail
is the same as that experienced from -charge(inside the wire) moving opposite way in other reference frame.
The two reference frames yield the same magnetic field.

SO - i was unable to accept that cat video.
For me it's QV cross B in both cases. What'd i miss ??

Is there a handy link to that Einstein introduction, anorlunda ?

ALERT edited a bit to improve clarity

Jim,
In order for magnetic force to act we need both magnetic field (moving charges) and another charge moving relative to that field.
In the scenario: "cat moving and cat's frame of reference", you are right, the cat would see a magnetic field from the moving (+) charges (not mentioned by narrator) but there is no force because there is no charge moving relative to this field. Remember, from the cat's frame of reference his own charge is not in motion.

 

[jim hardy]

the cat would see a magnetic field from the moving (+) charges (not mentioned by narrator) but there is no force because there is no charge moving relative to this field. Remember, from the cat's frame of reference his own charge is not in motion.

Thanks !

i'm toggling that picture in my mind.
+cat sees the wire moving backward with respect to himself, because he and his reference frame are moving forward with the electron drift which is admittedly small but finite.
So - does +cat see those "Maxwell halos" of mmf (and flux) encircling the wire as stationary, or moving backward with the wire?

I know why I'm hung up - read Flatland as a kid.
Viewed from above those circles would appear straight lines , as do the men in Flatland
and the initial analogy of riding in a train planted the visual image of railroad tracks, where the ties are straight lines as are circles viewed from their own plane...
Viewed from a locomotive windshield the rail looks stationary(only because it's smooth) but the ties shoot by backward
and that's the visual image i affixed to those flux halos surrounding a wire..

So my question becomes
do those red B circles move along in direction of I with the moving +charges they encircle ? If so, they're moving backward in +cat's frame.
It would seem at first that they must - a single charge in motion would surely find itself surrounded by an accompanying "Maxwell Halo" .

Edit - added :
If that's so, then +cat sees relative motion between himself and those B circles ??

I'm sorry to appear stubborn - its just i need to reconcile this little point in order to progress. No mischief intended.