Do Magnetic Fields Do Nonzero Work on Moving Objects?

[lugita15]

I've been following the recent thread about work done by magnetic fields, and I'm more confused than ever. I have a few questions about the subject. I have phrased them as true/false statements.
Consider Statement A: If an object X moves in any direction which is not perpendicular to some force F, then the work done by F on X is nonzero.
Is Statement A true or false?
Consider the situation where there are two parallel current-carrying wires separated by some distance d, each having a current of magnitude I and pointing in the same direction. For simplicity, let us assume that the currents are going from the bottom of the page to the top of the page, and that the first wire is to the left of the second wire.
Now consider Statement B: By the Biot-Savart Law, the magnetic field due to the second wire at any point on the first wire is directed out of the page.
Is Statement B true or false?
Now consider Statement C: Since the magnetic force on a current-carrying wire is proportional to \vec{I}\times\vec{B}, by the right hand rule the magnetic force on the first wire due to the magnetic field of the second wire is directed to the right (that is, towards the second wire).
Is Statement C true or false?
Now consider Statement D: As a result of the rightward force it is experiencing, wire 1 will move to the right, i.e. closer to wire 2.
Is Statement D true or false?
Now consider Statement E: The direction in which wire 1 is moving, which is to the right, and the direction of the magnetic force acting on it, which is also the right, are parallel, which obviously means they are not perpendicular.
Is Statement E true or false?
Finally consider Statement F: Since wire 1 is moving in a direction which is not perpendicular to the magnetic force acting on it, by Statement A the work done by the magnetic force acting on wire 1 is nonzero.
Is Statement F true or false?
If you think that Statment F is false please point to the earlier step in which I made a mistake.

Any help would be greatly appreciated.
Thank You in Advance.

 

[Longstreet]

There is a missing statement that the current I is held constant. If you have two free interacting currents, say both I_{z}, they will move toward each other. But now the z component is different for each: I_{z}^{'} < I_{z}. Kinetic energy is not changed. What changes is the distribution of EM field. If you want to keep I_{z} fixed you have to supply an emf in z direction. So, you'll find that the emf is what is doing the work to drive the wires together.

 

[lugita15]

There is a missing statement that the current I is held constant. If you have two free interacting currents, say both I_{z}, they will move toward each other. But now the z component is different for each: I_{z}^{'} < I_{z}. Kinetic energy is not changed. What changes is the distribution of EM field. If you want to keep I_{z} fixed you have to supply an emf in z direction. So, you'll find that the emf is what is doing the work to drive the wires together.

Yes, let us assume that the current in each wire does not change. Basically the assumption is that the distance between the wires is sufficiently great, and consequently the magnetic field strength is sufficiently low, that there is no significant change in the currents.
Out of the six statements I listed, which ones do you agree with and which one do you disagree with, and why?

 

[Longstreet]

If I had to pick one it would be statement E. Once the wires are moving toward each other then jxB (or vxB) no longer points toward the other wire (to the right).

 

[lugita15]

If I had to pick one it would be statement E. Once the wires are moving toward each other then jxB (or vxB) no longer points toward the other wire (to the right).

Obviously the direction of the magnetic force will change as a function of time. But the important thing is that, at least initially, the wire will move in a direction that is not perpendicular to the magnetic force acting on it. Therefore SOME amount of work, however small, must be done by the magnetic force due to the second wire.

 

[Bob S]

Statement F is true.
Suppose the two wires are in the x y plane, and the currents are in the y direction, and wire 1 moves in the x direction.
The stored energy per unit length in the system is

W = (1/2)LI², where L is the inductance per unit length.

The force F_x= dW/dx = (1/2)d/dx( LI²) = (1/2) I² dL/dx + LI dI/dx.

Since I is a constant, the second term is zero, so we have

F_x = (1/2) I² dL/dx

So the motion of the wire is reducing the stored inductive energy.

The electrical energy was due to a voltage pulse V = I dL/dt + L dI/dt , where the second term is zero.

Statements A through E are also true.

Bob S

 

[Longstreet]

So how do you explain jxB and j*E at the fundamental level.

 

[Bob S]

j x B refers to the vector cross product of a current density and a static magnetic field, resulting in a force F on the current density. This can be Lorentz transformed to a force (density) j'*E +j' x B', where the force now comes from both electric and magnetic fields. The force can be completely transformed to electric fields if the particles in j are completely relativistic.
Bob S

 

[Hootenanny]

Electric fields are neutralized by protons, two wires do not attract or repel until we pass the current and create magnetic fields.

Bob S' point is that it depends on your reference frame, or point of view. Suppose you have a distribution of charges that is stationary relative to you. You see an electric field, but no magnetic field. Now if I'm moving relative to you, I see a magnetic field. The two are difference aspects of the same object rather than distinct objects in themselves.

This point is emphasised when we use the electromagnetic tensor to write Maxwell's equations

F_{\left[\alpha\beta,\gamma\right] = 0

{F^{\alpha\beta}}_{;\beta} = \mu_0J^\alpha

Here, there is no distinction between electric and magnetic fields, we simply have the electromagnetic field.

 

[Longstreet]

j x B refers to the vector cross product of a current density and a static magnetic field, resulting in a force F on the current density. This can be Lorentz transformed to a force (density) j'*E +j' x B', where the force now comes from both electric and magnetic fields. The force can be completely transformed to electric fields if the particles in j are completely relativistic.
Bob S

I mean in terms of work. obviously jxB does no work because j*(jxB) = 0. So magnetic force does no work, in only changes momentum. Mechanical power transfer comes from J*E at a fundamental level so saying the power comes from magnetic force is misleading it comes from the electrical force. Transforming frames doesn't get around the fact because j*(jxB) is zero by definition in every frame.

Also, looking at the divergence of the poynting vector \nabla \cdot S = \nabla \cdot (E \times B) = B \cdot (\nabla \times E) - E \cdot (\nabla \times B)

you find

\frac{\partial u}{\partial t} + \nabla \cdot S + J \cdot E = 0

where u is electromagnetic field energy density.

So by this energy can only be exchanged between EM field and matter through the electric field and current. So I ask again, how do you say magnetic field does work, at the fundamental level.

 

[Longstreet]

A square looks rectangular in another frame but its the same object. Just because they look different doesn't mean they are different. It's called lorentz covariance. You can describe an object and what it looks like in every frame.

And no I did not even write field potentials (phi and A I presume) in my post. And yes, but what is a) causing the force b) direction of force and c) what causes the work is being obfuscated. All you are saying is that work is done. Yes, well duh, if I may be frank. But not saying WHAT does the work, which is the initial question.

 

[Longstreet]

How is it causing work when v*vxB = 0. just answer that.

 

[Bob S]

You are confusing FIELD POTENTIALS and direction of the FORCE.

Can you calculate the force between two wires and realize the direction?

Hi Drum-

The stored magnetic energy per unit length is

W= (1/2) LI²

where L is the inductance per unit length, also known as the stored magnetic energy per unit length.

L = (1/I²)∫B·H dV_volume

the force F_x is given by

F_x = dW/dx = (1/2)d(LI²)/dx = (1/2) I² dL/dx + L dI/dt, (but dI/dt =0 at constant current),

where x is the separation between the two wires.

A reduction dx of the wire separation at constant current is producing a voltage pulse

V = L dI/dt + I dL/dt = I dL/dt

and removing stored magnetic energy between the two wires.

Bob S

 

[Longstreet]

x: displacement

dx/dt = v: displacement/time

So rate of work, also known as power, from the lorentz force: v \cdot (q v\times B)= 0.It's zero.

 

[Hootenanny]

"Two different aspects" actually does mean "two different things".

No it doesn't. If I'd have meant "two different things" I would have said that.

As long as they are different, they are not the same, and that's all I'm saying.

But I am saying that they are the same thing. Whilst this may be a matter of taste with no 'practical' significance, I think it's a discussion worth having. As I said in my previous post, in relativity there is no difference in magnetic and electric fields, it is simply a matter of reference frames. If a choice of reference frames determines whether we observe a magnetic field or an electric field, then it is obvious that the distinction between electric and magnetic fields is an artificial one, imposed by us, rather than one imposed by the underlying laws. In other words, there is no difference between electric and magnetic fields.

The problem is that means you are wrong since two different things can not transfer from one to another, you can not mathematically equate apples and oranges, right?

The difference here is that an apple remains an apple irrespective of your relative velocity. If the apple changed to an orange if you move relative to it, then we would have a situation which was analogous to EM fields. If this would be the case, it wouldn't make any sense to have apples and oranges since whether you observe one or the other depends on how you are traveling relative to them. Therefore, we would be forced to conclude that apples and oranges are in fact the same objects and we would work with apple-oranges.

 

[Bob S]

No it doesn't. If I'd have meant "two different things" I would have said that..

Your statement paraphrases Humpty Dumpty in Alice in Wonderland:
‘When I use a word,’ Humpty Dumpty said, in a rather scornful tone, ‘it means just what I choose it to mean, neither more nor less.’

‘The question is,’ said Alice, ‘whether you can make words mean so many different things.’

‘The question is,’ said Humpty Dumpty, ‘which is to be master – that’s all.’

Bob S

 

[Hootenanny]

The magnetic field resulting from a current is nothing else than an application of length contraction applied to the distance between the positive ions in the wire.

A single current carrying wire: http://galileo.phys.virginia.edu/classes/252/rel_el_mag.html

The result for two generalises in an obvious manner for two wires.

As for my motivation for making this point, it is simply that I think it a nice result. By combining special relativity and the electric field, we can arrive at electromagnetism. Do you not agree that this is a nice result?

 

[Longstreet]

What are you talking about? What equations are those?

Do you mean to say when el. current in these two wires gets turned off wires would get back to original position and so the total work done would be zero, or something? Lorentz force (magnetic force) acts in the direction of the displacement, that's all that matters here.

Those are the equation of motion for charged particles and power delivered to them. Why would they go back to original positions? Work has to do with change of ENERGY, not position. The magnetic force is not a conservative force, for no other reason that it does no work in the first place. The magnetic field cannot change the mechanical energy of the system. That is what work is.

The magnetic force is NOT in the direction of displacement. You are being confused by saying that current is in one direction, and then saying that it's moving in a different direction. It's redundant to say a current is moving. Current IS movement (of charges).

Ok. So, let's use this very example then.

How do you explain magnetic force is the same as electric force when:a.) Electric force is neutralized due to protons in these two wires.

b.) We get repulsion with reversed current in one of the wires.

c.) Attraction/repulsion between wires varies with velocity.These are not the properties of electric fields, especially if we neutralized them to start with, so the force we observe here seem very independent, separate and different to the force of the electric fields. Can you explain how they can transform to each other in different reference frames, and why, I mean WHY, would you be compelled to be proving so?

Compelled by the fact that electromagnetism makes no sense unless you do this. Take the magnetic force qv\times B. Now change your reference frame x' = x - vt. v' = v - v = 0. So qv'\times B = 0. The particle no longer has an acceleration of any kind. Physics has apparently CHANGED just by switch reference frames, which makes no sense.

 

[Longstreet]

The shape of the magnetic field lines has nothing to do with this. I will try to explain this without vector algebra. Your picture is only valid for a static situation which by definition has no work associated with it. To understand what happens when the wire actually moves, you need to look at the forces internally.

If we assume electrons are the source of current, then in wire 1 they will be moving up and to the left. This causes a force up and to the right, toward wire 2. No work has been done yet though because nothing has moved. Now, if the wire starts moving up and to the right , then the electrons are not moving in the same direction they were. They have a net motion more directly upward, slightly toward wire 2. But they are not moving directly toward wire 2 either. Also, because of this motion toward wire 2, there is an additional force down and to the right. So the net force is no longer pointed directly toward wire 2 either. It turns out that since the electrons are being displaced more to the up, and the force is more to the right, that force and direction are perpendicular still. No work has been done by magnetic force even when moving.

And no we do not agree. You cannot have a *complete* description of the electromagnetic field with only electric, or only magnetic fields. They are two properties of the same field. Properties are different, yes, but they are still part of the same entity. The maxwell equations even have what is called duality. They are completely symmetric and you can interchange electric and magnetic fields and electric and magnetic charges or have combinations of them and you will get the same equations. This has been well understood classically far 100 years. If you are really interested in understanding it there are many sources etc available.

 

[Nirgal]

Do we agree magnetic fields are separate and different from electric fields, or not?

The question is ambiguous. From a certain philosophical point of view you could say that the Electric and Magnetic fields are different, in the sense that the different phenomena you observe can be understood by invoking the idea of an Electric field or a Magnetic field. Again, as iterated many times by previous posts, observation is what distinguishes the two.
The Electric and Magnetic fields are just conceptualizations to understand problems. They do not exist. What actually exists is the Electromagnetic field. Call it what you will, the point is that Electrical phenomena and Magnetic phenomena all come from the same source. That "source", the Electromagnetic field, is a real thing that exists at every point in space. Electricity cannot exist without Magnetism and vice versa. This means the two phenomena are two sides of the same coin.

Think about light. As I said before, the Electromagnetic field exists at every point in space, when you move a charge then you have changed the local electric field in your region. But regions far from you still experience the "old" electric field. You can think of a discontinuity in the field that spreads out from the charge at the speed of light, allowing regions far from the charge to experience the new structure of the field. This is a simple description of an Electromagnetic wave. But wave propagation cannot occur without the both fields, because a time changing magnetic field induces a time changing electric field and vice versa. The E-field and the B-field create each other in a kind of self-referential tango.

You might be tempted to say "wait a minute, all you have are two fields interacting to create light!" But you arrive at paradoxes in other areas of physics when you assume independence of one another. Really think about their relative nature. If you ride with an electron you will not experience the magnetic field due to the current. Suddenly you stop riding with it and you experience a magnetic field. Where did it come from?

I think the root of your confusion is philosophical. How humans classify things. What words to give phenomena.

 

[Born2bwire]

DRUM, you need to brush up on the basics of electrodynamics. First, work is defined as the application of force over a distance, the integral quantity
W = \int \mathbf{F}\cdot d\mathbf{\ell}
When the path of displacement is not along the force vector, then the work done is zero. It is obvious from the Lorentz force that the contribution from the magnetic field gives rise to zero work. The displacement is along the velocity vector yet the cross product of the velocity and magnetic fields means that the force vector will be normal to the velocity vector. This can be seen most easily in cyclotron motion. If I have a charge moving at some velocity v in a constant magnetic field applied perpendicular to the velocity, then the charge will be induced to move in a circular orbit. And just like a mass on a string being revolved in a circular orbit, the force on the charge is always pointing towards the center of the orbit, causing the work done over any length of path to be zero.

Maxwell's equations satisfy special relativity, indeed they helped to directly precipitate the derivation of the theory. As such, we are often at home working with electromagnetic fields in the Minkowski space through the use of four-vectors, covariants, tensors and such. In this respect we see that electric and magnetic fields are purely a matter of reference frames. They are equivalent to each other in the respect that they always exist together (I just mentioned Jefimenko's equations in another thread that gives one insight into this) and that by manipulating the reference frames one can induce the magnetic field from a electric field. The calculation of the magnetic field from a line of current using Lorentz transformations on the electric field of the charges in their frame is a common undergraduate physics problem in electromagnetics. I am sure you can find the appropriate derivations in say Jackson or Griffiths.

 

[Born2bwire]

Displacement is not along the force vector. The force vector is the direction of acceleration. As I mentioned previously, if you take the electron in a cyclotron you can see most clearly that the force vector is normal to the path of displacement at any point. And again, we can see that the magnetic field's contribution to the force does no work because of this. We can even see this explicitly with the wires, the movement of the charges are perpendicular to the force for our given static initial condition. In this case, it is apparent that the work at the initial condition is zero since the force is being applied normal to the path of displacement of the charges at that moment.

And no, there is nothing where classical electrodynamics can explain a phenomenon where relativistic electrodynamics cannot. First, classical electrodynamics satisfies special relativity already, there is no modification needed to the theory for them to agree. As such, careful examination of classical electrodynamics will give rise to the Lorentz transformations (as they did originally for Lorentz when he derived them) and you can then apply them to show the equivalence between the electric and magnetic fields. Once again I can only implore you to pick up an undergraduate electrodynamics textbook and familiarize yourself with relativistic electrodynamics. However, your confusion of acceleration with the path of displacement also suggests that you may want to also work out a few simple trajectory problems to refamiliarize yourself with the basic mechanics of the problem. Force only points along the path of displacement for special conditions, the primary one being when the current velocity of the mass is zero.

 

[Born2bwire]

I simply can't believe this. Displacement we are talking about here is not displacement of electrons along the wire, but displacement of two wires that come closer or repel themselves further away. So, do we finally agree that this displacement of wires IS in the direction of Lorent force?

Oh no, I wouldn't make such a prediction off-hand. First off there are two things to discuss here. The first is that the Lorentz force is not acting on the wire, it is acting on the charges confined to the wire. In this case, the wire is made up of a lattice of atoms which we can freely strip the valence electrons off of in reaction to fields and forces leaving behind positively charged, but largely immobily tied to the lattice, ions. Now the Lorentz force acting on the moving electrons displaces them and the displaced electrons pull the wire's lattice with them from their own Coulombic attraction (via electric fields), in a very brief hand-wavy kind of explanation. So it is not meaningful to talk about the Lorentz force working on the wire, it is only working (if at all) on the moving charges. So we have to take into account that the charges are moving normal to the direction of force acting on them.

The second point is that once we allow time to progress, we no longer have a magnetostatic problem. The movement of the wires now means that we have time varying magnetic fields, which invariably means we also have time varying electric fields. So now we have Lorentz forces from electric and magnetic fields. And with electric fields we now have Lorentz forces capable of performing work on the charges.

So does the Lorentz force point along the path of the wire's displacement? Most likely I am sure though it isn't a simple problem but I would expect one could easily use Lagrangian physics, assuming a plasma or electron gas in place of the wires. But that doesn't matter, the Lorentz force isn't acting on the wire, it is acting on the charges in the wire.

EDIT: In response to your edit, I am not really interested in the OP as I am sure that the previous posters were able to address that. In addition, this is a thread that seems to pop up constantly and so there are a multitude of previous threads that have already explained this. I am more concerned about what I feel are misconceptions in your posts about the physics of the forces and interactions and your comments in response to Hootenanny's and Bob S' posts.

 

[Born2bwire]

The point of contention is stating that the magnetic fields are doing the work. There is nothing wrong with the magnetic fields being a source of a Lorentz force, however, they act on the charges in a manner that does not expend work. However, in this case the actual trajectory of the system, over which we would calculate the work done, causes an electrodynamic problem, not a magnetostatic problem. So one of the problems here is assuming that we only have a force that arises from the magnetic field. So assuming a force arising from the magnetic fields is fine, but it is a different problem when we start talking about the work done in the dynamic system.

And again, the displacement here is not along the direction of the force. The force is not acting on the wire, it is acting on the charges that make up the currents in the wire which have an initial non-zero velocity which makes the path of displacement not the same as the direction of force. The mention of special relativity allows us to look at the problem in a different manner. We can work the problem using Lorentz transformations and Coulombic attractions, in which case there are no magnetic fields.

 

[Hootenanny]

Born2bwire has already addressed the majority of your comments, so there may be some overlap here. However, I would like to respond to the comments you directed at me.

Can you find any other example of anything like that?

Yes, the electro-magnetic field. Why do you think we call it the electro-magnetic field?

Why equations for E and B are different then, describing different properties?

You are probably used to seeing Maxwell's equations as a set of four differential vector equations. However, as I said in one of my earlier posts, we can write Maxwell's equations in covariant form as a set of two tensor equations. In this form there is no distinction between magnetic fields and electric fields. Since you seem to require a reference for every statement I make, see here: http://en.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism. Although, I note a distinct lack of references on your part.

Magnetic and electric fields are different, otherwise we would just have electric fields

That is precisely my point, we can just have electric fields. It is possible to make a coordinate transformation such that the magnetic field disappears, leaving us only with the electric field. See for example, Grant & Philips; Electromagnetism, or Griffiths as Born2bwire suggests. Indeed, most undergraduate physics texts on electromagnetism will at least mention this.

That's incomplete and terrible attempt at explanation.

As opposed to your well written and logically consistent arguments?

Can you find some more "authoritative" source on the subject, some papers or even Wikipedia article? That article there says crazy things and sets some weird experimental setups

Yes. See the texts I mentioned above. I was trying to be helpful by providing a website, since I assumed that you wouldn't have access to any physics texts.

 

[Born2bwire]

At this point there is nothing more than I can say about the matter. Again, I can only reiterate that you should take the time with some reference materials to learn about the subtleties of this problem.

The Lorentz force does not act on the wire because it only acts on charges. This means that the displacement over which the Lorentz force acts is not the direction that the wire moves. The displacement is determined by the trajectory of the charges that represent the currents in the wire. The wire moves because the displacement of the currents causes a Coulombic attraction between the static ions of the wire's lattice (since the ions do not move they are not affected by the initial magnetic field).

The question here is whether or not magnetic fields do any work, and the attraction and repulsion of wires is a common example brought up in regards to this question. In this case, we can see that in the initial conditions, there is no work being done by the Lorentz force. This is because the magnetic fields are applying a force that is normal to the path of displacement of the moving charges.

However, there is work done because the problem is not a static problem, since the magnetic fields are time-varying we introduce time-varying electric fields which we can trivially show that the Lorentz force from an electric field can perform work on a charge.

Classical electromagnetism follows special relativity. This allows us, by judicious choice of reference frames, to work a problem only involving electric fields. With the insights from special relativity, or other formulations of classical electromagnetics, we see that we can think of having an electromagnetic field, as Hootenanny put it, as opposed to electric and magnetic fields.

As for your repeated requests for explanations, if you take a look at any reference material you should see examples addressing these situations. Indeed, in the Griffiths text that I suggested earlier he deals with the problem of two lines of current and reformulating it as a purely electric field formulation.

 

[Hootenanny]

DRUM, I simply reiterate what born2bwire said. There is nothing more that either of us can say until you review elementary electromagnetism. Both Griffiths and Grant & Phillips deal with this precise problem explicitly.

 

[Hootenanny]

Why do you pretend as if it was me lacking some understanding, when, in fact, it is you who is failing to provide reference and answers to questions.

Both I and Born2bwire have given you two references many times. See Grant & Phillips or Griffiths on Electromagnetism.

Now, I have (yet again) provided you with two references. Can you now show explicitly how the Lorentz force acts on the wire? Alternatively, can you provide a reference which explicitly shows how the Lorentz force acts on the wire?

 

[Doc Al]

Try to use Lorentz force equation and you can find for yourself that is all it takes to accurately predict the attraction OR repulsion of the wires.

The Lorentz force doesn't act on 'wires', it acts on charges. The magnetic force acts on moving charge. Note that for ordinary current-carrying wires the bulk of the mass in is the positive lattice, which is stationary. What do you think exerts the force on those stationary charges to move the wire?

 

[Born2bwire]

These are 100 or more years old theories and equations, there should be more accessible and more public reference like Wikipedia articles or whatever on the Internet so everyone can see if it makes sense or not.

By some chance, I know books you are referring to, none of that can substitute Lorentz force equation, ergo it can not explain why would different current directions in two parallel wires cause wires to repel and why would current in the same direction make wires attract. I'm asking you if you have read that book yourself and if you can be more specific what exactly do you think can explain that? Also, in what kind of reference frame electric fields can cause charges to spiral like magnetic fields do?

Since when has anyone here said that the Lorentz force was not the force acting on the charges? The point is that the magnetic field contribution to the Lorentz force is not doing the work.

I don't see what is the problem?

It is the same thing as when two permanent magnets get closer to each other, they do not fly apart to electrons and protons, even though most of the attraction comes exclusively from electrons spin. So, electrons pull protons, protons pull electrons and all that chemical, molecular and structural stuff is going on, yes, but the net effect is that the whole wire is moving. I thought this was obvious. Do we agree finally?

What other force, what equation do you suggest?

So you should be able to understand that the path of displacement over which the Lorentz force is acting is not the path of displacement of the wire.

 

[Hootenanny]

These are 100 or more years old theories and equations, there should be more accessible and more public reference like Wikipedia articles or whatever on the Internet so everyone can see if it makes sense or not.

The theories and equations are available from many resources, Wikipedia included. However, this particular application is not.

By some chance, I know books you are referring to,

Do you indeed? Do you happen to have them to hand?

none of that can substitute Lorentz force equation, ergo it can not explain why would different current directions in two parallel wires cause wires to repel and why would current in the same direction make wires attract.

You seem to be clinging onto the Lorentz force for dear life, yet you have no idea how to apply it! As I, Born2bwire and Doc Al have said: The Lorentz force doesn't act on the wire, it acts on charges. Furthermore, the magnetic force only acts on moving charges. To a good approximation, all the mass of the wire is contained within the positive lattice. This lattice is stationary. Would you kindly explain how a magnetic force can act on a stationary positive lattice?

I'm asking you if you have read that book yourself and if you can be more specific what exactly do you think can explain that?

I have 'read' (meaning read the relevant sections) of both texts. Indeed, I have a copy of Grant & Phillips. If you turn to section 14 (pages 451 - 477), you will find a discussion on SR & EM which deals with this specific problem.

 

[Hootenanny]

You are wrong. Why do you hesitate to make citation here so everyone can see?

What do you mean "I am wrong"? Can you not locate the relevant subsection?

 

[Born2bwire]

What is the direction of Lorentz force then?


What force do you suggest is responsible?

Please see the attached picture. The trajectory is just off the top of my head so it should not be taken to be exact but this is the general shape of the path as I see it. The Lorentz force due to the magnetic field is shown in the thin arrows (magnitudes not to scale). The thick line is the displacement path.

This ignores the Lorentz force component from the resulting electric fields though. Perhaps it would be more instructive of you to ignore the actual physical wire. Treat the problem as I suggested earlier, as a stream of electron gas. Just assume that we have a line current of free flowing electrons. What is the displacement path of one of the electrons or current elements? Why don't you draw that out?

 

[Born2bwire]

Yes, it is plain to us that you do not understand what is going on with this problem.

If you do not understand how the trajectory that I drew arises with an electron gas then you sorely need to brush up on your mechanics. Once again, you should sit down and work out the cyclotron problem and from that realize how the trajectory arises and why there is no work done in that situation. The same situation is applicable here though there are additional caveats that can be ignored for the current purposes of teaching the basic electrodynamics.

There is nothing that we can do for you until you take the time to learn basic electrodynamics. Your refusal to to look at the problems that we have suggested and looking at the reference materials that have been suggested to you in many of the previous posts is preventing you from understanding this discussion.

 

[lugita15]

Just to clarify, the whole point of my thread is to try to understand whether or not the work done by the magnetic force on an object can ever be nonzero. Usually, people say that the work done by magnetic forces is always zero. But if statements A through E are true, then the work done by magnetic forces CAN be nonzero. So I am trying to find out which, if any, of the statements A through E are true.

 

[Born2bwire]

Just to clarify, the whole point of my thread is to try to understand whether or not the work done by the magnetic force on an object can ever be nonzero. Usually, people say that the work done by magnetic forces is always zero. But if statements A through E are true, then the work done by magnetic forces CAN be nonzero. So I am trying to find out which, if any, of the statements A through E are true.

Work is not done by the magnetic contribution to the Lorentz force. This is because the Lorentz force is directly acting upon the currents, not the wire. The wire is moved in reaction to the wire's ionic lattice being attracted via Coulombic forces between the displaced currents. That is, the Lorentz force displaces the electrons in the wire, the movement of the electrons causes them to pull the wire with them via electric fields (to first order). So when we are talking about the path of displacement over which the Lorentz force is acting, it is not in say the x direction (assuming that our wires run in the z direction). That is the direction of the movement of the wires but since the force is not acting on the wires it is not relevant. The force is acting on the moving charges that make up the current, now these charges had an initial velocity so they are actually going to be moving in a circular trajectory in response to the magnetic field. But as their velocity vector changes, so does the force from the magnetic field. The Lorentz force from the magnetic fields always changes its direction as the direction of the charge's movement changes too.

This circular trajectory is not noticed because the movement of the electrons is not impeded along the wire, so there is no movement in the wire along its axial direction. In addition, the wire is infinitely long, so we are looking at a superposition of charges that are all moving and reacting identically. On the whole, what we see is a line current moving together in one direction towards to the other wire.

But the other point to note is that if we allow the wires to be attracted over a distance, then we now have a changing set of magnetic fields since the currents are moving in space. This means that we now have a set of electric fields. So we need to now take into account the force that will arise from these electric fields. It actually becomes a complicated problem that is not apparent from the static force problem.

EDIT: I would say that statements A-E are correct. It is just when you assume that the path that we take our integral for the force is not the path that the wire moves. Ignore the wire, think of what would happen if we just had lines of electrons that were moving in place of the wires and currents. What happens to just one electron in response to the magnetic fields from the other wire? Keep in mind that when start the problem off, the electron already has an initial velocity, corresponding to being a current.

 

[Longstreet]

That is precisely my point, we can just have electric fields. It is possible to make a coordinate transformation such that the magnetic field disappears, leaving us only with the electric field. See for example, Grant & Philips; Electromagnetism, or Griffiths as Born2bwire suggests. Indeed, most undergraduate physics texts on electromagnetism will at least mention this.

I just wanted to state one last thing here. You cannot *always* completely transform away magnetic field. This is one situation where that is true, because you cannot take a pure magnetic field, and turn it into a pure electric field, by lorentz transformation. However, you can always transform so that vxB = 0, at least for one specific v.

 

[Per Oni]

It’s probably not going to be a popular move around here but I am going to drum up some support for DRUM.
I am not going to plough through 4 pages of statements but here are my thoughts.

A magnetic field of a source will:
1: only react with a magnetic field and 2: store energy.
Exactly the same can also be said of an electric field. Both are on an equal footing.

Now regarding of post #26: http://galileo.phys.virginia.edu/cla...el_el_mag.html
I have raised this subject here a couple of times without much reply.

The logic put forward in this paper (and similar) to explain the (cause of) magnetic field as a result of relativity is this:

The space between conduction electrons in a current carrying wire is length contracted for an observer stationary with the +ve lattice of this wire. However this would result in the wire to become negatively charged wrt the observer. It is therefore necessary that these electrons move a little further apart length ways, because in reality this stationary wire is neutral even when carrying a current. Therefore according to this theory the combination of length contraction and “spreading out” results in the wire being neutral.

My main argument against this logic is this: where are these electrons going to spread to? Don’t imagine an infinite long wire but think of a real circuit. Spreading out of sight of an observer in one place only means heaping more electrons up somewhere else so that somewhere else the problem becomes worse.

Btw a slightly different explanation put forward sometimes is that the electric field of the electrons perpendicular to the current increases. However this also results in electrons having to spread out.

Now also look at a different aspect. In reality conduction electrons move randomly at a Fermi velocity which is 10 orders of magnitude higher then your average current drift velocity. Fermi velocity is of course in all directions but length contraction should be the same whether left, right up or down. Now how far are these electrons going to spread out for the wire to remain neutral? Where to?

 

[burashka]

I have read some of the posts in this thread but not all. However, it appears to me that some important but rather elementary facts are being lost sight of.

First, an electric wire is made of charged particles. When these particles move, as the wire moves as a whole, there might be some work done on each of these particles. When summed over all particles of the wire, it yields the total work done on the wire. According to the Lorenz law, the magnetic field does no work on every particle in particular and, consequently, no work on the wire as a whole.

Second, the work which is being considered in the first post (the example with two wires) is done by the electric field. The field originates from the elementary charged particles which make up the wire. In a sence, the wire is "pulling itself up by the hair". This is, in fact, possible when the motion is constrained, and the magnetic field provides such a constraint.

Third, a relevant mechanical example of constrained motion in which you can literaly pull yourself up by the hair is a man on a swing. If you stand on a swing, you can swing yourself up by periodically bending your knees and moving your center of gravity up and down relative to the base of the swing. Since your velocity is always perpendicular to the force of reaction that the swing exerts on your feet, the swing (more specifically, the force of reaction) does no work at all. Nevertheless, when you swing yourself up, you gain some potential energy. Who then made the work? The answer is simple: you did. You have used your internal chemical energy to make your muscles flex and to pull yourself up in the air, and the swing has provided a useful constraint to your motion without which such a "self-lift" would be impossible. Nevertheless, the swing has done no work at all.

Same with the two wires. The energy is supplied by the source of the current and converted into mechanical energy by means of electric force between the charged particles of the wire. The magnetic field provides a useful constraint.

 

[Longstreet]

DRUM, if magnets did work then motors would not require any electrical energy to run, except for a small resistance in the wire, and conversely a permanent magnetic would lose all magnetism almost instantly because its magnetic energy would be consumed in doing work on the rotor. People have tried to make perpetual motion machines by doing this over and over and no one has succeeded. Why? Because magnets can't do work.

Motors do consume electrical power, which is actually MORE then the measured output power because of losses, and the permanent magnets retain their strength for the entire life of the motors. This is verified every day in millions of motors.

 

[Per Oni]

DRUM, if magnets did work then motors would not require any electrical energy to run, except for a small resistance in the wire, and conversely a permanent magnetic would lose all magnetism almost instantly because its magnetic energy would be consumed in doing work on the rotor.

Does such a motor consume electric field? Does it consume electrons? Of course not. Such a motor consumes energy supplied via a net work of electrical and magnetic fields. Most likely this energy comes from coal, gas or nuclear power stations.

 

[Longstreet]

It does consume electrical fields, because that is what you put into move the electrons. That's why you need to supply power to maintain the electric field. Otherwise it would be used up, disappear, and work would cease to occur.

 

[Longstreet]

You need to be a student of this instead of an authority. You are the one who is wrong. I am trying to make this simple because you have no background in physics. But I can see there is no point in trying to explain it further. Please try to study electromagnetism for yourself in the texts already listed.

 

[Born2bwire]

Same with the two wires. The energy is supplied by the source of the current and converted into mechanical energy by means of electric force between the charged particles of the wire. The magnetic field provides a useful constraint.

Yes, exactly, it would not surprise me if we could find that the energy is sourced from the fact that we have to maintain the currents for the problem to remain the same. That is, the magnetic fields divert the trajectory of the currents, normally they would run along the z direction but the force from the magnetic fields would, without changing the magnitude of v, change their direction. The loss of velocity in the z direction would mean that the current now has changed. But since we have hooked our wire up to some kind of voltage source, we would inject energy to maintain the same currents. I wonder if that can be used to show the same change in energy that we expect from the movement of the wires. I think though that it would be a very convoluted means to do so, plus it ignores the work done to pull the wire with it. That would be a lateral force due to the invariance in the z direction. Well, perhaps it would at least be a means of finding the energy expended in moving the charges themselves. Hmmm... interesting ideas.

 

[Longstreet]

you can integrate vxB (where v is the velocity of the wire) along the wire to find the motional emf which will oposes the emf put into the wire to drive it forward.

 

[Per Oni]

It does consume electrical fields, because that is what you put into move the electrons. That's why you need to supply power to maintain the electric field. Otherwise it would be used up, disappear, and work would cease to occur.

The motor is supplied with energy which comes in a combination of E and H, as given in the Poynting vector S=E x H.

 

[burashka]

Lorentz law is not about fields, but about FORCE, which is why it is called 'Lorentz force law'. Why do you even mention FIELDS? Where did you ever hear fields do work? Why not talk about how unicorns do no work? What is this? FORCE DOES WORK, NOT FIELDS.

Do you realize Lorentz force acts exactly in the direction of wire displacement?

At any rate, there is no need to shout or be impolite. Of course I understood your argument the first time I saw it. I've heard it many times before from students. You should not assume that you are the first to come up with this great counterexample.

The Lorenz Force on a point particle of electric charge q, moving in electric field E and magnetic field B with the velocity v is F=qE + (q/c)v\timesB. The second term in this formula is the force due to the presence of magnetic field, and it is always directed perpendicularly to the particle velocity, v. This is why people say that the magnetic field does no work: because the force which arises due to the presence of the magnetic field does no work. No unicorns needed to understand that, I hope.

Now since the magnetic field does no work on any charged particle of the wire, it does no work on the wire as a whole, either.

The mistake you have made is that the force apparently applied to the macroscopic wire is not by any means the magnetic part of the Lorentz force. Indeed, the wire is electrically neutral, and the Lorenz force, as defined above, needs a net charge (or charge density).

In reality, the magnetic part of the Lorenz force is applied ONLY to the free electrons which drift inside the wire. The effect of the magnetic field is to curve the electron trajectories (without doing any work!) and to make electrons bump onto the wore wall from inside. This deviation of electron motion from straight trajectories creates local deviation from electric neutrality inside the wire and, as a result, gives rise to some macroscopic electric field. This electric field does the work when the wire is mechanically accelerated as a whole.

This may seem to be impossible: the wire literally accelerates itself, as if in violation of the Newton's third law. And it would be impossible without the presence of the magnetic field. The latter constrains the motion in such a way that the Newtons third law is no longer applicable. The two subsystems of the wire (the negatively charged conductivity electrons and the positively charged ions) exert on each other a net total force. This is the force that is observed macroscopically and makes the wire accelerate.

In general, the third law in electrodynamics should be applied only with extreme caution. There are many instances when it breaks.

Think some more about the example with the swing; it may be useful to gain some understanding of what's going on.

What formulas do you use to model this interaction?

How do you explain wires repel if we change direction of the current in one wire?

A) The Columb law of electrostatics.

B) Because the electrons, when they deviate from straight trajectories inside the wire, can go either to the left or to the right, depending on the direction of the external magnetic field, and they would push the wire either to the left or to the right.

Finally, why is it such a big topic? I've noticed that general public (by that I mean nonphysicists) are most interested in the subjects which are abolutely inconsequential and can not be even considered as part of theoretical physics.

How does it matter whether the magnetic field does work in this situation or not?

Can you offer an experiment in which your understanding of this phenomenon would lead to a different observable? Can you predict a new effect? If not, this discussion has no relation to physics whatsoever and should be moved to philosophy or linguistics forum.

 

[SystemTheory]

Comment on my philosophy. Galileo, who is recognized as a pioneer of empirical methods, said the (untested) ideas of the philosophers gave him a great pain! Now this flies in the face of conventional "wisdom," which regards emotion as playing no part in theoretical science! I have discovered it is impossible to reason without first forming emotions, which Spinoza defines as "a feeling accompanied by an idea about its cause." He also said the greatest good is for men to join, one with another, in bonds of common reason. However there is a great challenge with joining in bonds of common reason, stated in a song lyric from the 1980s, "Communication is the problem to the answer."

 

[burashka]

Comment on my philosophy. Galileo, who is recognized as a pioneer of empirical methods, said the (untested) ideas of the philosophers gave him a great pain! Now this flies in the face of conventional "wisdom," which regards emotion as playing no part in theoretical science! I have discovered it is impossible to reason without first forming emotions, which Spinoza defines as "a feeling accompanied by an idea about its cause." He also said the greatest good is for men to join, one with another, in bonds of common reason. However there is a great challenge with joining in bonds of common reason, stated in a song lyric from the 1980s, "Communication is the problem to the answer."

I am not sure about Spinoza and emotions, all this is totally above my pay scale. But one thing seems to be certain. There is a big difference between "untested" and "untestable" and the great lesson that Galileo has taught us is that we should not spend energy thinking about things or theories which are in principle untestable. The philosophers of the antiquity all seed to had notions of absolute rest and absolute motion, but Gallileo has posed the question: how do you distinguish between these two states experimentally? If there is no way to do that, then there is no reason to try to answer the question whether the ship moves forward or the ocean moves backward. It's just an idle question.

It's OK to set up "thought experiments" which so far can not be implemented in iron. But theories or propositions which are in principle untestable do not belong in physics or (in my humble opinion) in science in general.

 

[Per Oni]

the Lorenz force, as defined above, needs a net charge (or charge density).

Nope. Any moving charge in a neutral wire will do.

This may seem to be impossible: the wire literally accelerates itself, as if in violation of the Newton's third law. And it would be impossible without the presence of the magnetic field. The latter constrains the motion in such a way that the Newtons third law is no longer applicable.

What nonsense.
I just can't believe anybody around here wrote this.

From Wikipedia:

Whenever a first body exerts a force F on a second body, the second body exerts a force −F on the first body. F and −F are equal in magnitude and opposite in direction

I can assure you that this law is not violated as any engineer knows who’s job it is to calculate forces exerted by magnetic fields eg in motors.

I got this feeling that w're slowly going to coocoo land with this thread.