Mentor

## Can a magnetic fields/forces do work on a current carrying wire?!

 Quote by vanhees71 I do not need to copy the already cited very well written paper, where it has been demonstrated on simple examples that magnetic fields do no work as predicted by Maxwell electromagnetics.
Thanks for posting that paper. I have gone over it quite a bit and found it very persuasive. Here is my current thought process:

1) Let's use the definition of work as energy transfered to or from a system by any mechanism other than heat.
2) Only external forces can do work on a system since internal forces cannot transfer energy in or out of the system.
3) A system's KE may change without work being done on the system, provided there is some compensatory change in some other form of energy for the system. (this is what I neglected in my example)
4) If the paper represents some specific examples of a general principle, then in all situations where the magnetic force is the only external force, any change in KE must be accompanied by a corresponding change in some other internal form of energy.

So, in my example, an external magnetic field can accelerate (increase KE) a superconducting loop. This must be accompanied by a decrease in internal energy. The only available energy is the energy density of the magnetic field, which depends only on the current. Therefore, the current in the loop must decrease as the loop accelerates. Although I didn't calculate it explicitly, this makes sense to me.

A motor is easy to explain since the magnetic field is not the only source of energy transfer.

However, the one thing that makes me hesitate to adopt this principle wholeheartedly is that it is not always clear what internal energy is being used. For example, consider a permanent magnet being accelerated in an external magnetic field. What is the internal energy that is being used in the permanent magnet? Any ideas?

 Quote by vanhees71 I can only repeat that Maxwell's equations hold in a very large range of applicability. QED effects are negligible in everyday applications, and Maxwell's equations clearly say that the power (work per time) done on charge distributions by the electromagnetic field is given by $$P=\int_{\mathbb{R}^3} \mathrm{d}^3 \vec{x} \; \vec{E}(t,\vec{x}) \cdot \vec{j}(t,\vec{x}).$$ Note that the current also contains the effects of magnetization through the corresponding part $\vec{j}_{\text{mag}}=\vec{\nabla} \times \vec{M}$. I do not need to copy the already cited very well written paper, where it has been demonstrated on simple examples that magnetic fields do no work as predicted by Maxwell electromagnetics. It is also demonstrated that this picture also applies to the pure quantum phenomenon spin and the corresponding magnetic moment within semiclassical Dirac theory (semiclassical here means that the electron is treated as a quantum particle and the em. field as classical, an approximation valid for the nonrelativistic realm of the electron's motion, i.e., in atomic, molecular and solid-state physics for not too large charge numbers of the involved atomic nuclei). I take the freedom to cite this paper again, including the abstract, which already explains it very clearly: PHYSICAL REVIEW E 77, 036609 (2008) Dipole in a magnetic field, work, and quantum spin Robert J. Deissler* Physics Department, Cleveland State University, Cleveland, Ohio 44114, USA ͑Received 28 February 2007; published 21 March 2008 The behavior of an atom in a nonuniform magnetic field is analyzed, as well as the motion of a classical magnetic dipole ͑a spinning charged ball and a rotating charged ring. For the atom it is shown that, while the magnetic field does no work on the electron-orbital contribution to the magnetic moment ͑the source of translational kinetic energy being the internal energy of the atom, whether or not it does work on the electron-spin contribution to the magnetic moment depends on whether the electron has an intrinsic rotational kinetic energy associated with its spin. A rotational kinetic energy for the electron is shown to be consistent with the Dirac equation. If the electron does have a rotational kinetic energy, the acceleration of a silver atom in a Stern-Gerlach experiment or the emission of a photon from an electron spin flip can be explained without requiring the magnetic field to do work. For a constant magnetic field gradient along the z axis, it is found that the classical objects oscillate in simple harmonic motion along the z axis, the total kinetic energy—translational plus rotational—being a constant of the motion. For the charged ball, the change in rotational kinetic energy is associated only with a change in the precession frequency, the rotation rate about the figure axis remaining constant. DOI: 10.1103/PhysRevE.77.036609
The key is the dot product inside the integral, i.e. E⃗ (t,x⃗ )⋅j⃗ (t,x⃗)

Work done on charges according to this dot product is that of the E field along the direction of charge motion. We know that J = sigma*E, so that J & E are generally in the same direction. J dot with E is simply sigma*E2. But this work being done on the charges is that of conduction current. The current in the loop consists of charges acted upon by E force so that the current density J is along the direction of E force per Lorentz law.

We already knew that. Again, let us convey an example. An induction motor is a good case to examine. The stator is connected to an ac power source, constant voltage, 60 Hz, etc. A rotating field is established. Current in the stator results in a mag field which revolves about the stator axis linking the rotor bars, for a squirrel cage type rotor. This rotating B field is accompanied by a rotating E field.

The current induced into the rotor consists of charges acted upon by Lorentz force. What force is doing the work of moving e- around the rotor loops resulting in a rotor generated revolving magnetic field? The only answer is the E force. The equation you gave is applicable here. The B force acts radially to the rotor bar electrons, E force moves them around the loop.

I doubt that anyone here would dispute that the rotor charges moving in the rotor loop are motivated by the revolving E force, not the B force. Hence the work done on the rotor charges moving in the rotor loop is done by E force. Pretty obvious.

But now that rotor current is realized, a revolving rotor magnetic field exists. This field interacts with the stator field & a torque is produced. As the rotor is moved towards the stator, energy is expended, & the mag field must be replenished. The ac power mains source does just that.

Your integral shown above relates the work done on charges to the dot product of E & J. Draw a diagram & it is plain as day that that is the work establishing rotor current, not the work done turning the rotor through an angle. E is in the direction of J, if E is normal to J, dot product goes to 0. The force on the rotor is not along the direction of J. It is normal to J.

The "E dot J" in your integral is not what you think it is. I will accept correction if I erred, but please give us references as to the orientation of B force, E force, J, etc. Thanks for your interest.

Claude

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 Quote by DaleSpam However, the one thing that makes me hesitate to adopt this principle wholeheartedly is that it is not always clear what internal energy is being used. For example, consider a permanent magnet being accelerated in an external magnetic field. What is the internal energy that is being used in the permanent magnet? Any ideas?
There's no general difference to the examples given in the paper! The magnetization of the permanent magnet is equivalent to a current density (using Heaviside-Lorentz units)
$$\vec{j}=c \vec{\nabla} \times \vec{M}.$$
Now, the permanent magnet is accelerated by the external magnetic field and according to Faraday's Law this induces an electric field which in turn leads to a current counteracting the change (Lenz's Rule). So again you have an change of intrinsic energy, and the work done is solely due to the induced electric field as it must be according to Poynting's Theorem!

Mentor
 Quote by vanhees71 Now, the permanent magnet is accelerated by the external magnetic field and according to Faraday's Law this induces an electric field which in turn leads to a current counteracting the change (Lenz's Rule).
So you think that the acceleration actually reduces the atomic currents? Is there any study that would support that. I mean, it makes sense for the big picture, but I don't see how the atomic level currents can be reduced without causing problems or at least changes in the atoms.
 Recognitions: Science Advisor The induced current is a usual conduction current (caused by the conduction electron's motion in your metal permanent magnet). There's nothing exotic in this. There's a lot of confusion on this issue, because many textbooks still use the pretty vague ideas of 19th century electromagnetism, where the inner structure of matter hasn't been as well understood as nowadays. The best introductory book about a more modern point of view on "macroscopic electrodynamics" is vol. II of the Feynman Lectures. In fact it has been 19th century electromagnetism that paved the way to gain this understanding. A first highlight was the development of (special) relativity (which you can still count as 19th-century physics although it was finished only 1905 with Einstein's famous paper and the 1907 paper by Minkowski on covariant macroscopic electromagnetics). Another one the development of "classical electron theory" by Lorentz, Abraham, et al. Finally the many contradictions and problems in the description of atoms lead to the main achievement of 20th century physics, namely quantum theory, which again was triggered by a purely electromagnetic problem, namely the problem of the spectrum of thermal radiation, which lead to the discovery of the "action quantum" $\hbar$ by Max Planck in 1900 and the development of "old quantum" theory, again by Einstein with his "heuristic point of view" of electromagnetic radiation as light corpuscles (1905) and Bohr's and Sommerfeld's quantum model of the atom (again a work on electromagnetism, namely the motion of electrons around a nucleus, 1912-1916). Finally it lead to the development of modern quantum mechanics (Heisenberg, Born, Jordan, Pauli; Dirac; Schrödinger 1925-1927) and quantum electrodynamics and finally relativistic quantum field theory. BTW: Physicswise we still live in the 20th century, because there's no new big paradigm change at the horizon yet. To the contrary: The preliminary discovery of hints for a (quite boring form of a minimal standard-model) Higgs again confirms the good old Standard Model of elementary particle physics :-(.

Mentor
 Quote by vanhees71 The induced current is a usual conduction current (caused by the conduction electron's motion in your metal permanent magnet). There's nothing exotic in this.
I am not sure that works. Suppose that the magnet is in a region of non-uniform magnetic field, and therefore accelerates, gaining KE. During the acceleration the magnet sees a changing B field and therefore there is an induced current, which acts to reduce the magnet's own field and therefore the magnet's internal energy. So far so good.

However, then suppose the magnet transitions to a region with a uniform field. At this point there is no more flux and therefore no more induced current. The magnet's internal field is no longer partially canceled so its internal energy returns to normal, but it still has KE.

I think the change in energy must be more than just a conduction current in this case. I am just not sure what else it could be.

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 Quote by Miyz BRAVO!!! BRAAAVO!!! The best answer so far the SHUTS every thing down! I totally agree again and again with Claude! Well said there sir! Common sense everyone: Bring a loop connect it to a battery = nothing, Bring a magnet = MOTION! Also! magnetic force on the wire = IL x B!!! Magnets do work on this system and its all because of the INPUT POWER(battery etc...) Again if you do say that magnets do no work please bring something NEW to the table! To support you're claim! Thanks again everyone for you're efforts! Good discussion!
I don't like to participate in this kind of discussion anymore but I would point out that this isn't a case of just a magnetic field. One thing to note here is that if we have two stationary wires, then in the lab frame where the wires are stationary we only have magnetic fields and currents. So in this snapshot it would appear that if the wires move away or together that the magnetic field is doing the work. However, we are looking at a static picture where we only have forces. The work is done over the dynamic picture of the wires actually moving. Once the wires begin to move, then we invariably have an acceleration of the charges that make up the currents and therefore have an electromagnetic field. So over the displacement of the wires over which the work is done, there exists electric and magnetic fields.

Another thing to consider is that in the situation where the wires are held stationary and we only have magnetic forces, from the rest frame of the charges in the wires there only exists an electric field. This is a common problem that is worked in texts like Griffiths. So from the electron's point of view, it only sees an electric field and not the magnetic field. In that case why not conclude that it is still the electric field that does all the work?

So the take away point that I would make is that with the wires, we need to keep in mind that it isn't an electric or magnetic field but an electromagnetic field. You can't conclude that the magnetic fields do the work from the face of it.

 Quote by Born2bwire I don't like to participate in this kind of discussion anymore but I would point out that this isn't a case of just a magnetic field. One thing to note here is that if we have two stationary wires, then in the lab frame where the wires are stationary we only have magnetic fields and currents. So in this snapshot it would appear that if the wires move away or together that the magnetic field is doing the work. However, we are looking at a static picture where we only have forces. The work is done over the dynamic picture of the wires actually moving. Once the wires begin to move, then we invariably have an acceleration of the charges that make up the currents and therefore have an electromagnetic field. So over the displacement of the wires over which the work is done, there exists electric and magnetic fields. Another thing to consider is that in the situation where the wires are held stationary and we only have magnetic forces, from the rest frame of the charges in the wires there only exists an electric field. This is a common problem that is worked in texts like Griffiths. So from the electron's point of view, it only sees an electric field and not the magnetic field. In that case why not conclude that it is still the electric field that does all the work? So the take away point that I would make is that with the wires, we need to keep in mind that it isn't an electric or magnetic field but an electromagnetic field. You can't conclude that the magnetic fields do the work from the face of it.
1st bold: No. Charges do indeed move when wires move, but net charge motion is 0. Acceleration of charges refers to charges acquiring KE. When an entire wire moves, the e- as well as stationary p+ move. I don't think this motion of equal & opposite charges can be treated the same as "conduction current".

2nd bold: "From the electron's point of view ---". We understand that when we view a motor spinning, we are viewing it from our static reference frame. We have already conceded that a free e- in conduction cannot have work done upon it by a B force, only an E force. You keep rehashing isolated particle physics & emphasize facts I've already conceded to. Nobody is disputing that. Also, the electron sees a static E field from the other loop's stationary lattice protons. But it sees a B field due to the other loop's electrons in motion. The electrons moving in the other loop undergo a Lorentz-Fitzgerald contraction, so that mere E force is not adequate to explain the force here.

3rd bold: "we need to keep in mind that it isn't an electric or magnetic field but an electromagnetic field". What on earth is an "electromagnetic field"? Please enlighten me. There are magnetic quantities B & H, electric quantities E & D. Just how do you describe this "electromagnetic field"? Please enlighten me.

So far the naysayers have produced nothing. They talk a big game about Einstein, reference frames, etc., but cannot show me the fields working in a simple induction motor. Show me, please, how it is E force, & not B force that spins the rotor. So far all I get is people blowing smoke. Not 1 naysayer has addressed the motor operation question.

In a motor, we are not simply moving electrons from valence to conduction. We are exerting forces on wire loops resulting in torque & work being done. Making a loop spin involves more than conduction current. A B force acting on free electrons in a loop producing torque is more involved than simply inducing a loop current. The B force yanks on the e-, but the p+ & n0 get tethered as well. These e-, p+, & n0, all moving together in unison constitute zero current. Of course the current in the rotor loop is non-zero. There is more than 1 thing going on here.

Claude

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 Quote by DaleSpam However, then suppose the magnet transitions to a region with a uniform field. At this point there is no more flux and therefore no more induced current. The magnet's internal field is no longer partially canceled so its internal energy returns to normal, but it still has KE.
Ok, then there is no more magnetic force, and the magnet stays moving with a constant velocity (at least after some transition time, when all the dynamics of the currents and fields are damped). In the rest frame of the magnet, its magnetization and magnetic field is then that of the magnet at rest and its electric field is 0. What's left in the original reference frame is the static electric and magnetic field you get by a Lorentz boost with the appropriate velocity of this situation in the rest frame.

Mentor
 Quote by vanhees71 What's left in the original reference frame is the static electric and magnetic field you get by a Lorentz boost with the appropriate velocity of this situation in the rest frame.
Yes, that is correct too. So not only does some unknown (to me) energy store inside the permanent magnet need to compensate for the increased KE, it also needs to compensate for the increased energy of the permanent magnet's E and B fields.

 Quote by cabraham 1st bold: No. Charges do indeed move when wires move, but net charge motion is 0. Acceleration of charges refers to charges acquiring KE. When an entire wire moves, the e- as well as stationary p+ move. I don't think this motion of equal & opposite charges can be treated the same as "conduction current". 2nd bold: "From the electron's point of view ---". We understand that when we view a motor spinning, we are viewing it from our static reference frame. We have already conceded that a free e- in conduction cannot have work done upon it by a B force, only an E force. You keep rehashing isolated particle physics & emphasize facts I've already conceded to. Nobody is disputing that. Also, the electron sees a static E field from the other loop's stationary lattice protons. But it sees a B field due to the other loop's electrons in motion. The electrons moving in the other loop undergo a Lorentz-Fitzgerald contraction, so that mere E force is not adequate to explain the force here. 3rd bold: "we need to keep in mind that it isn't an electric or magnetic field but an electromagnetic field". What on earth is an "electromagnetic field"? Please enlighten me. There are magnetic quantities B & H, electric quantities E & D. Just how do you describe this "electromagnetic field"? Please enlighten me. So far the naysayers have produced nothing. They talk a big game about Einstein, reference frames, etc., but cannot show me the fields working in a simple induction motor. Show me, please, how it is E force, & not B force that spins the rotor. So far all I get is people blowing smoke. Not 1 naysayer has addressed the motor operation question. In a motor, we are not simply moving electrons from valence to conduction. We are exerting forces on wire loops resulting in torque & work being done. Making a loop spin involves more than conduction current. A B force acting on free electrons in a loop producing torque is more involved than simply inducing a loop current. The B force yanks on the e-, but the p+ & n0 get tethered as well. These e-, p+, & n0, all moving together in unison constitute zero current. Of course the current in the rotor loop is non-zero. There is more than 1 thing going on here. Claude

"Not 1 naysayer has addressed the motor operation question." THANK YOU!
I really like were you're going with this Claude + Agree with you're argument all the way!

Magnetic forces generated on the current loop/stator etc... Is all due to the magnetic field! THE MAGNETIC FIELD CAUSES THE ROTATION and WORK TO BE DONE!(Not it alone by has a primary key role in this whole process).

Many keep denying that fact WHY?! What give you that idea? Even when you deny it you'd refere to a single charge... Well read the thread topic... Were talking about the effect thats present within a motor! Why include that law that is irrelevant to it?

That law is based on "A" charge...

Please state you're opinion or idea based on the "motor effect". Not one the quantum scale of things where everything's different.

Mentor
 Quote by cabraham 3rd bold: "we need to keep in mind that it isn't an electric or magnetic field but an electromagnetic field". What on earth is an "electromagnetic field"? Please enlighten me. There are magnetic quantities B & H, electric quantities E & D. Just how do you describe this "electromagnetic field"? Please enlighten me.
The electromagnetic field is usually described using tensors. The Wikipedia page on the topic is actually quite good:

http://en.wikipedia.org/wiki/Covaria...ectromagnetism

With this formulation the separation of the EM field tensor into an E field and a B field is seen as a simple artifact of the coordinate system chosen. Since the choice of coordinate system is arbitrary, so is the distinction between E and B.

Regarding naysayers, I haven't yet made up my mind. I came into the thread quite convinced that magnetic fields do work, but I am no longer so certain after having read the paper referenced above. Did you read it? If so, did you find any specific errors?

However, the reason that I used a superconducting loop in my example rather than a motor is the obvious weakness of the motor argument: specifically, the motor has a large amount of E field energy going into the system on the wires. I wanted a "cleaner" system where the only possible work was done by the B field, which is not the case with a motor.

 Quote by DaleSpam The electromagnetic field is usually described using tensors. The Wikipedia page on the topic is actually quite good: http://en.wikipedia.org/wiki/Covaria...ectromagnetism With this formulation the separation of the EM field tensor into an E field and a B field is seen as a simple artifact of the coordinate system chosen. Since the choice of coordinate system is arbitrary, so is the distinction between E and B. Regarding naysayers, I haven't yet made up my mind. I came into the thread quite convinced that magnetic fields do work, but I am no longer so certain after having read the paper referenced above. Did you read it? If so, did you find any specific errors? However, the reason that I used a superconducting loop in my example rather than a motor is the obvious weakness of the motor argument: specifically, the motor has a large amount of E field energy going into the system on the wires. I wanted a "cleaner" system where the only possible work was done by the B field, which is not the case with a motor.
You avoided the question. If E & B has arbitrary distinction, how can you claim that E does work, B does not? Also, they are in different directions, & that is not arbitrary. Show me an illustration where E exerts force on the loop/rotor. Every machine text shows B/H doing the force on the rotor. E exists, it has to along with B/H, but its direction is not oriented so as to turn the rotor.

Now when it comes to moving e- through the loop, work is needed. As electrons collide with the lattice, losing energy & radiating photonic emission (heat which is I2R), they need to have work done on them to replenish said energy. This work is done by E, not by B. Thus the work done on the charges in the loop(s) maintaining the current, is done only by E, not by B force. Fair enough?

Claude

Mentor
 Quote by cabraham You avoided the question.
Yes, I still haven't made a conclusion, so I cannot answer. I was only pointing out what I feel is an obvious weakness of the motor example in deciding the answer to the question either way.

 Quote by cabraham If E & B has arbitrary distinction, how can you claim that E does work, B does not?
Work and energy also depend on the arbitrary choice of coordinate system.

 Quote by DaleSpam Yes, I still haven't made a conclusion, so I cannot answer. I was only pointing out what I feel is an obvious weakness of the motor example in deciding the answer to the question either way.
Ok, that's fair enough. Please keep us posted when you have something to share.

 Quote by DaleSpam Work and energy also depend on the arbitrary choice of coordinate system.
Fine. Please refer to the coordinate system of a stationary observer watching the motor spin. What force is doing the work? Please give illustration including direction of force vector. Thanks in advance.

Claude

Mentor
 Quote by cabraham Please refer to the coordinate system of a stationary observer watching the motor spin. What force is doing the work?
Not until I have gotten to the point that I can analyze a simpler system and make up my mind on the general question based on that analysis. Once I can analyze a simpler system where there is only B then I can attempt systems with E and B.

Btw, did you read the paper? What did you think?

 Quote by DaleSpam Not until I have gotten to the point that I can analyze a simpler system and make up my mind on the general question based on that analysis. Once I can analyze a simpler system where there is only B then I can attempt systems with E and B. Btw, did you read the paper? What did you think?
Good paper, no denying that. But it does not deal with the interaction of 2 magnetic fields. It does state that under specific conditions, that mag force can do work. It does not deal with the forces of 2 current carrying loops.

The wiki link gives a good primer as to how special relativity relates to e/m field theory. Both references are very useful & well written. But we already have many text books written on motor operation. Do we really need to examine the OP question from the viewpoint of reference frame other than a stationary observer watching the motor spin? We seem to have gone off on a tangent.

This weekend I will create a sketch & post it. Based on Ampere's Law, Faraday's Law, the magnetic vector potential A, E field, B/H field, etc., the only logical conclusion is that to turn the rotor, a force must exert a torque on said rotor. Only B/H seems to have the correct direction to do that. E acts tangential to the loop. resulting in induced current as Lorentz force describes.

To get a torque you need a B force. But to have a B force you need 2 currents. Each current is established & maintained by E forces. But those E forces rely on B fields as well. The E field in the rotor maintains rotor current. But the rotor E is due to the stator B field. Stator B is due to stator I, which is related to stator E.

I think I'm on solid ground when I say that E, B, V, I, torque, & speed are very interactive. No single entity is responsible for motor action. But B produces the torque. But w/o E, I, V, etc., there wouldn't be any B. Likewise B only yanks on electrons, then the protons & neutrons are tethered via E & SN forces. B cannot do it alone.

That has been my position w/o wavering.

Claude