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

[truesearch]

Cabraham:
from post 171:We need to do work on the e- to transition it from valence to conduction band. Only E can do that.
Can you give me some idea of the width of the energy band between Valence and conduction bands in something like copper that you would use in any analysis?
From most recent post: But the input supply is providing current as well as voltage. The product times the power factor times the efficiency is the amount of power processed by the fields, B as well as E.
I am fimiliar with the concept of power factor in the analysis of AC circuits containing R, L and C but I have not met the idea applied to DC electric motors... Can you amplify on this or quote a reference that I could access?
And... how do you define efficiency in your analysis.
Looking forward to any explanations you feel able to give.

 

[cabraham]

Cabraham:
from post 171:We need to do work on the e- to transition it from valence to conduction band. Only E can do that.
Can you give me some idea of the width of the energy band between Valence and conduction bands in something like copper that you would use in any analysis?
From most recent post: But the input supply is providing current as well as voltage. The product times the power factor times the efficiency is the amount of power processed by the fields, B as well as E.
I am fimiliar with the concept of power factor in the analysis of AC circuits containing R, L and C but I have not met the idea applied to DC electric motors... Can you amplify on this or quote a reference that I could access?
And... how do you define efficiency in your analysis.
Looking forward to any explanations you feel able to give.

For metals, the valence & conduction bands actually overlap. Some e- are already in conduction band. Those in valence that require a little work to move into conduction get this work from E, not B. For a good conductor, like Cu, E is small, since J = sigma*E. Since the bands overlap, many e- are already in conduction band & need no work from E. Those e- in valence need a small amount of work to transition up into conduction band.

I was referring to ac motors as far as power factor goes. For dc motors, power factor can still have meaning. For example, if the input is a pure dc voltage source, but the current is a square wave, I've heard "power factor" defined as "pi/4". The dc pedestal current times the dc voltage is the continuous average power we are familiar with. But the ac ripple current times the voltage integrates to zero real power. Thus the ripple component of current does not contribute to motor output mechanical power.

Again, I was implying ac motors whenever PF is computed. But with dc motors, or other types of load, the term "power factor" can still have meaning. It differs from the R-L-C definition of power factor. With R-L-C networks, PF is cos of phase angle between I & V. However, in switching power converters, a rectified waveform has a power factor involving fundamental line frequency & all harmonics. I.e. a full wave bridge rectifier outputs fundamental & harmonic frequencies, current & voltage.

Power factor is defined as real power over total power. Reactive power is due to products of I & V of differing frequency. Or it can be due to same frequency I & V with 90 degree phase difference. I hope I've answered your question. BR.

Claude

 

[truesearch]

You have 'answered' my questions but not completely satisfactorily...sorry.
'Most electrons are already in the conduction band and need no work done on them'...that is what I thought. How does this affect your presentation?
A lot of confusion regarding power factor !...you have 'heard it defined' as pi/4... definitions are not communicated by hearsay... where is it published as pi/4
I did not realize that AC motors were implied in what you have produced...sorry.
Also, I am not certain what is meant by this phrase: ' & energy maxes out when the poles are 90 degrees apart'...is this a recognised technical term?

 

[vanhees71]

To make it clear once again: I never denied that magnetic fields cause forces and also torques, but what has this to do with the fact that the magnetic field does not do work on charge and current distributions (including magnetization currents)! I think, in principle we agree now on this simple fact.

BTW: I don't like to draw diagrams but to use vector calculus since this is far more save.

 

[Dadface]

The original question enquired as to whether a magnetic field or force can work on a current carrying wire and the answer is yes it can.The answer is nicely illustrated in the labelled sketch(in the opening post) which shows a force(F=BIL) on each of the two opposite sides of the coil.F=BIL is found by using F=BeV and calculating the total force on all of the current carrying electrons in the length of conductor under consideration.In fact it is the total magnetic force.
If memory serves correctly F=BIl is used to define magnetic flux density which is used to define the Tesla which,in turn,is used to define the Ampere.
The motion of the electrons within the conductors is affected by the B field as is evidenced by the Hall voltage which is set up if there are constraints to the movement of the coil.
It should be remembered that the B field is not just that due to the permanent magnets or field coils only.There is also a major contribution to the field because of the current flowing through the coil.The resultant field is sometimes referred to as the "catapult field".

 

[Dale]

E dot J is the work done by E. But why do you say that this work is split between rotor conduction thermal loss & mechanical energy? You're making a pure assumption. E dot J is the conduction loss, thermal, of the rotor.
...
Where it went is into rotor loss, conduction current squared times resistance. That is all of it.

It looks like we have a disagreement of fact. I believe that E.j is greater than the Ohmic losses, you believe it is equal.

If you are correct on that fact, then I agree with your reasoning.

If I am correct on that fact, do you agree with my reasoning?

 

[Miyz]

Hmmm, 3 good questions. Here are 3 good answers.

1st bold: Agreed. E dot J is the work done by E. But why do you say that this work is split between rotor conduction thermal loss & mechanical energy? You're making a pure assumption. E dot J is the conduction loss, thermal, of the rotor. The current in the rotor is needed or else there is no B force to spin the rotor.

2nd bold: Where it went is into rotor loss, conduction current squared times resistance. That is all of it. "E dot J" cannot be what produces torque. Torque acts radially to the loop, whereas E dot J is tangential. Refer to my picture. I made it clear that E and J are in the wrong direction to produce torque. To produce torque we need a radial force, i.e. normal to current density J. E is along the J direction. Any component of E normal to J has ZERO dot product with J.

3rd: Agreed. The energy B used to do the work had to come from somewhere. We are in agreement thus far. Hopefully we are still in agreement when I say that the independent power source driving the motor (battery, wall outlet, car alternator, etc.) is replenishing the B energy.

No field, E, B, whatever, can supply energy long term. Just as the input power source replenishes the B field energy, it also replenishes E field energy as well. As the B magnetic poles align, energy is minimum, & energy maxes out when the poles are 90 degrees apart. But the input supply is providing current as well as voltage. The product times the power factor times the efficiency is the amount of power processed by the fields, B as well as E.

Like I said, E & B both do short term work. But the input power supply is doing the long term work. The energy from the supply is stored in B & E fields, transferred to charges & torque*angle, then said E & B field energy is replenished by the power source. Ultimately all the energy is provided by this input power source.

But fields such as B & E provide us with a means of focusing & controlling the energy & transfer. The winding length, number of turns, air gap, core shape, etc. allow us to modify the motor behavior based on the application. But in all cases the power source driving the input does all the work. BR.

Claude

The problem to me this is another higher level of my education but you made sense to me there.

The original question enquired as to whether a magnetic field or force can work on a current carrying wire and the answer is yes it can.The answer is nicely illustrated in the labelled sketch(in the opening post) which shows a force(F=BIL) on each of the two opposite sides of the coil.F=BIL is found by using F=BeV and calculating the total force on all of the current carrying electrons in the length of conductor under consideration.In fact it is the total magnetic force.
If memory serves correctly F=BIl is used to define magnetic flux density which is used to define the Tesla which,in turn,is used to define the Ampere.
The motion of the electrons within the conductors is affected by the B field as is evidenced by the Hall voltage which is set up if there are constraints to the movement of the coil.
It should be remembered that the B field is not just that due to the permanent magnets or field coils only.There is also a major contribution to the field because of the current flowing through the coil.The resultant field is sometimes referred to as the "catapult field".

Thanks Dadface, for that I think other then Darwin123, no one mentioned the simple digram contradict the idea of magnetic force/field not doing work on a loop... And this formula is like the main one to look at.

Unfortunately for my lack of experience with maxwell's equations I can't product a good argument based on what Dale + Van are saying... Thanks to Claude his showing the other side of things.

Again this is going more deeper and more interesting!

 

[cabraham]

You have 'answered' my questions but not completely satisfactorily...sorry.
'Most electrons are already in the conduction band and need no work done on them'...that is what I thought. How does this affect your presentation?
A lot of confusion regarding power factor !...you have 'heard it defined' as pi/4... definitions are not communicated by hearsay... where is it published as pi/4
I did not realize that AC motors were implied in what you have produced...sorry.
Also, I am not certain what is meant by this phrase: ' & energy maxes out when the poles are 90 degrees apart'...is this a recognised technical term?

The pi/4 value of power factor was conveyed in an IEEE seminar I attended in the 1980's. I would have to compute the integral to verify it. When I have time I can do that & post. For any circuit driven from a smooth dc voltage source w/ no ripple, the current can be a pulse type of waveform if the load is switched, such a a power converter.

The average power is the dc input supply voltage times the average (dc) value of current. There is also an ac component to the current consisting of a fundamental & harmonics. These when multiplied by input voltage result in reactive or apparent power. A 50% duty factor square wave has an average value of 2/pi times the height of the square pulse. The frequency distribution is 1 for the 1st harmonic, 1/3 for the 3rd, 1/5 for the 5th, etc.

The rms value is sqrt(I₁² + I₃² + I₃² + ---). Off the top of my head the total including dc value plus ac computed to PF value of pi/4. The sqrt computes to pi²/8, so multiplying bu 2/pi gives pi/4.

As far as torque, energy, as a function of phase goes, "maxes out" is a shop talk term we EE's use, but in the reference texts, the torque is given as force times the normal component of the distance wrt the radius. At 90 degrees the torque is maximum. At 0 degrees, the poles are aligned & torque is zero. The moment of the force is zero because the force is acting towards the center. Imagine a bicycle upside down. To spin the wheel you apply a force tangential for maximum torque. If you push on the wheel directly towards the center, radially, you get minimum torque. I hope this helps.

Claude

 

[harrylin]

[..] if B does the work then the energy that B used to do the work must come from somewhere, so where did it come from?

I explained that in post #170 - based on, funny enough, your explanation in post #82

 

[vanhees71]

The original question enquired as to whether a magnetic field or force can work on a current carrying wire and the answer is yes it can.

No it cannot! It has been clearly shown in cabrahams note with the the attached scanned pdf, but I give up now. Obviously it is not possible to make you accept the simple conclusion from Maxwell's equations about the work done on charge and magnetization distributions, known as "Poynting's Theorem".

BTW: Poynting's Theorem has been found in the process to solve very practical problems concerning the energy bilance of sea cables by "the Maxwellians", of which Heaviside was the most important in this respect, but the energy bilance equation for fields and charges is indeed due to Poynting. The great success of Maxwell theory in electrical engineering is one very convincing proof of the correctness of this very theory. If it doesn't convince you, I can't help. :-(

 

[Dadface]

No it cannot! It has been clearly shown in cabrahams note with the the attached scanned pdf, but I give up now. Obviously it is not possible to make you accept the simple conclusion from Maxwell's equations about the work done on charge and magnetization distributions, known as "Poynting's Theorem".

BTW: Poynting's Theorem has been found in the process to solve very practical problems concerning the energy bilance of sea cables by "the Maxwellians", of which Heaviside was the most important in this respect, but the energy bilance equation for fields and charges is indeed due to Poynting. The great success of Maxwell theory in electrical engineering is one very convincing proof of the correctness of this very theory. If it doesn't convince you, I can't help. :-(

As others,including myself,have pointed out the energy input to the motor is from the power supply.But,of course there are intermediate energy changes.

The following is from "hyperphysics"

"Elecric motors involve rotating coils of wire which are driven by the magnetic force exerted by a magnetic field on an electric current."

Care must be taken when using Poynting:

1.There is an unjustified assumption that the medium is dispersionless and with zero resistance.*

2.It is likely to be applicable in a microscopic description of particles moving in a vacuum but not so useful in macroscopic media etc*

So does Poynting work in the macroscopic domain of current carrying conductors of structures such that they prevent the resultant movement being perpendicular to the force?Overall I need to look at this in more detail but at present feel that the applicability of Poynting to the situation being discussed here may be tenuous.


*From Poynting Theorem,Work and Energy www.phy.duke.edu

 

[vanhees71]

I can't find anything about Poynting's theorem on the Duke Physics home page. Poynting's theorem is derived from macroscopic electrodynamics and thus valid within the validity range of this (linear-response) approximation to the full (quantum) many-body-field problem. An electric motor is for sure within this valicity realm of classical macroscopic electromagnetics!

 

[truesearch]

I see a problem regarding communication and language in this long thread !
"The pi/4 value of power factor was conveyed in an IEEE seminar in the 1980's"
"max's out is a shop talk term we EEs use"... some sort of exclusive club!
This, together with a mistaken understanding of valence bands and conduction bands in metals, casts doubt for me on the quality of contributions from such a source.
The rules of these forums state clearly that clear reference to current textbooks should be available to back up contributions.

 

[Dadface]

I can't find anything about Poynting's theorem on the Duke Physics home page. Poynting's theorem is derived from macroscopic electrodynamics and thus valid within the validity range of this (linear-response) approximation to the full (quantum) many-body-field problem. An electric motor is for sure within this valicity realm of classical macroscopic electromagnetics!

Try googling "poynting's theorem work and energy"

 

[harrylin]

[..] Poynting's theorem is derived from macroscopic electrodynamics and thus valid within the validity range of this (linear-response) approximation to the full (quantum) many-body-field problem. An electric motor is for sure within this valicity realm of classical macroscopic electromagnetics!

I also thought so, but strangely enough I read in Wikipedia:

https://en.wikipedia.org/wiki/Poynting's_theorem :
"Poynting theorem is not valid in electrostatics or magnetostatics"

https://en.wikipedia.org/wiki/Magnetostatics :
"Magnetostatics is even a good approximation when the currents are not static — as long as the currents do not alternate rapidly."

That can be wrong of course, and I did not find a reliable source. Any comments?

Also useful may be Pointing's paper, as his discussion is indeed related to the discussion here:
https://en.wikisource.org/wiki/On_the_Transfer_of_Energy_in_the_Electromagnetic_Field

" if we accept Maxwell's theory of energy residing in the medium, we must no longer consider a current as something conveying energy along the conductor. A current in a conductor is rather to be regarded as consisting essentially of a convergence of electric and magnetic energy from the medium upon the conductor and its transformation there into other forms. "

 

[cabraham]

I see a problem regarding communication and language in this long thread !
"The pi/4 value of power factor was conveyed in an IEEE seminar in the 1980's"
"max's out is a shop talk term we EEs use"... some sort of exclusive club!
This, together with a mistaken understanding of valence bands and conduction bands in metals, casts doubt for me on the quality of contributions from such a source.
The rules of these forums state clearly that clear reference to current textbooks should be available to back up contributions.

Let's take the square wave power factor & pi/4 to another thread as it does not pertain to motors. The OP asked about torque on wire loops. The fact that I used "maxes out" in the shop does not invalidate what I have stated. I could have used the formal math term "attains its maxima at an angle of pi/2 radians". If I state it like that, consistent w/ reference texts, would you doubt me then?

"Mistaken understanding of valence & conduction bands"? Do they not overlap in good conductors? Do we not need an E field to obtain current (unless the winding is super-conductive, which I assumed it was not, just plain Cu)? What is mistaken in my treatise? Regardless of what I post, you dismiss it w/o any scientific evidence whatsoever, then declare me the loser. This is not the scientific method at all.

My diagrams clearly show that B exerts the force on the loop that results in spin, not E. It also shows E as what moves e- around the loop. If my diagram needs corrected, then please do so. I was already corrected on polarity which I accepted. Also, my last sketch was ambiguous, the loops should be oblique, but they can appear as co-planar.

Anyway, please offer proof for whatever conclusion you feel should be drawn. BR.

Claude

 

[Miyz]

I also thought so, but strangely enough I read in Wikipedia:

https://en.wikipedia.org/wiki/Poynting's_theorem :
"Poynting theorem is not valid in electrostatics or magnetostatics"

https://en.wikipedia.org/wiki/Magnetostatics :
"Magnetostatics is even a good approximation when the currents are not static — as long as the currents do not alternate rapidly."

That can be wrong of course, and I did not find a reliable source. Any comments?

Also useful may be Pointing's paper, as his discussion is indeed related to the discussion here:
https://en.wikisource.org/wiki/On_the_Transfer_of_Energy_in_the_Electromagnetic_Field" if we accept Maxwell's theory of energy residing in the medium, we must no longer consider a current as something conveying energy along the conductor. A current in a conductor is rather to be regarded as consisting essentially of a convergence of electric and magnetic energy from the medium upon the conductor and its transformation there into other forms. "

Does that mean Poynting's Theorem is irrelevant to our discussion? It does not apply?

Out of what I read it looks irrelevant to my question...

 

[vanhees71]

Poynting's theorem is generally valid. It's not trivial when it comes to macroscopic electromagnetics in media, but it's nothing else than the conservation of energy and momentum of a system consisting of charges (with magnetic moments) and the electromagnetic field. This conservation law is valid as long as special relativity is applicable, and this is a very wide range of validity. For sure it holds for all electric and electronic gadgets in everyday use, including electric motors as we discuss here.

It also holds under stationary circumstances. As an exercise calculate the energy flow in a coaxial cable with a DC current, i.e., get the full solution for the electromagnetic field and calculate the energy density, the Poynting vector, and the dissipative work through the finite conductivity. It's a very nice exercise and very illuminating concerning the issue of "energy transport" from the battery at one end of the cable to the resistance at the other end (simulating a passive electric device like a light bulb or something thelike).

The solution can be found in Sommerfeld's Lectures on Theoretical Physics, Vol. III. I recommend to read this book, which is one of the best ever written on electromagnetics, although it's a bit old-fashioned. The same holds true for Becker/Sauter, but the latter book is even better in the relativistic treatment of electromagnetics of moving bodies.

 

[cabraham]

Poynting's theorem is generally valid. It's not trivial when it comes to macroscopic electromagnetics in media, but it's nothing else than the conservation of energy and momentum of a system consisting of charges (with magnetic moments) and the electromagnetic field. This conservation law is valid as long as special relativity is applicable, and this is a very wide range of validity. For sure it holds for all electric and electronic gadgets in everyday use, including electric motors as we discuss here.

It also holds under stationary circumstances. As an exercise calculate the energy flow in a coaxial cable with a DC current, i.e., get the full solution for the electromagnetic field and calculate the energy density, the Poynting vector, and the dissipative work through the finite conductivity. It's a very nice exercise and very illuminating concerning the issue of "energy transport" from the battery at one end of the cable to the resistance at the other end (simulating a passive electric device like a light bulb or something thelike).

The solution can be found in Sommerfeld's Lectures on Theoretical Physics, Vol. III. I recommend to read this book, which is one of the best ever written on electromagnetics, although it's a bit old-fashioned. The same holds true for Becker/Sauter, but the latter book is even better in the relativistic treatment of electromagnetics of moving bodies.

Your info is generally correct but I hope you don't get mad at me when I say that it has little to do with the OP question re forces/work on current loops. I believe that the OP question has been answered. If those of us whom you differ with have erred, please offer feedback. Thanks.

Claude

 

[Miyz]

Your info is generally correct but I hope you don't get mad at me when I say that it has little to do with the OP question re forces/work on current loops. I believe that the OP question has been answered. If those of us whom you differ with have erred, please offer feedback. Thanks.

Claude

Why should he be mad? I mean this is a place of learning we share our ideas and opinions. If someone does not agree they should use theories to support their claims...
I do agree with the fact that the OP has been answered quite fairly.

Thanks to all you're efforts!

 

[Dale]

cabraham, it looks like you missed my post 186 about our disagreement on the facts. Can you please comment? I haven't worked out the problem, but would be willing to attempt it if we can confirm that is the source of disagreement.

 

[Dale]

If someone does not agree they should use theories to support their claims

He did. In fact, the theory is quite clearly in agreement with him. And even cabraham's analysis seems to support his claim that the B field provides torque and the E field provides work. That cabraham interpreted his results differently seems to stem from a disagreement on fact, but we are still hashing that out.

 

[cabraham]

cabraham, it looks like you missed my post 186 about our disagreement on the facts. Can you please comment? I haven't worked out the problem, but would be willing to attempt it if we can confirm that is the source of disagreement.

E.J is all important. But you must recall the dot product. It is zero when E & J are normal. Only the component of E in the same direction of J provides the work. My sketch shows this in detail. E does work by providing energy to the e- so as to restore that lost in lattice collisions, & move some e- from valence into conduction.

B is normal to E & exerts force on the loop. When the loop dipole aligns with the other loop dipole, there is no torque since the force acts over zero moment. In a motor when the poles are exactly aligned, the torque is zero. At 90 electrical degrees the torque is maximum.

The references quoted by my critics are valid, but they deal with work done on charges, providing conduction current, heating, & providing magnetic dipoles due to conduction current. But the work done spinning the loop is mechanical, not electrical. Of course at a small enough scale there ceases to be a difference between mech & elec. Cheers.

Claude

 

[Miyz]

He did. In fact, the theory is quite clearly in agreement with him. And even cabraham's analysis seems to support his claim that the B field provides torque and the E field provides work. That cabraham interpreted his results differently seems to stem from a disagreement on fact, but we are still hashing that out.

"Someone else" Dale, Not Van.

So far when I read about his theory it does not bring the proper answer to me personally, I'll study this over and over and see where it goes. But so far not relevant to my OP...

 

[Dale]

E.J is all important. But you must recall the dot product. It is zero when E & J are normal. Only the component of E in the same direction of J provides the work. My sketch shows this in detail. E does work by providing energy to the e- so as to restore that lost in lattice collisions, & move some e- from valence into conduction.

B is normal to E & exerts force on the loop. When the loop dipole aligns with the other loop dipole, there is no torque since the force acts over zero moment. In a motor when the poles are exactly aligned, the torque is zero. At 90 electrical degrees the torque is maximum.

The references quoted by my critics are valid, but they deal with work done on charges, providing conduction current, heating, & providing magnetic dipoles due to conduction current. But the work done spinning the loop is mechanical, not electrical. Of course at a small enough scale there ceases to be a difference between mech & elec.

Hi cabraham, from your previous post I could not discern the answer to my question. Can you please answer clearly:

It looks like we have a disagreement of fact. I believe that E.j is greater than the Ohmic losses, you believe it is equal.

If you are correct on that fact, then I agree with your reasoning.

If I am correct on that fact, do you agree with my reasoning?

Basically, I think that your logic is sound but your premise is counter factual. I want to know if you also think that my logic is sound but my premise is counter factual, or if you believe that my logic is flawed as well.

 

[cabraham]

Hi cabraham, from your previous post I could not discern the answer to my question. Can you please answer clearly:
Basically, I think that your logic is sound but your premise is counter factual. I want to know if you also think that my logic is sound but my premise is counter factual, or if you believe that my logic is flawed as well.

You claim that E.J > conduction loss, but rather it is conduction loss plus mechanical energy spinning the loop. Yet a dot product is involved. If E spins the loop as well as provide loop current, here is the flaw in such logic. The work done setting up loop current is done tangent to the loop. J is tangent as is velocity u, so that E imparts energy to e- in the loop. E.J is correct since only the tangential component of E contributes to this work.

But the torque on the loop is due to force acting radial to the loop, see my sketch. This force is normal to J & u. Whjich means that if this were an E force (as opposed to a B force), then the work must be non-zero. But if said work is included as a part of E.J, we have E & J at right angles, & the work is the dot product. But a right angles, the dot product is zero!

E.J cannot be the work done spinning the loop, in whole nor in part. Also, per Ampere & Faraday laws, B is normal to the plane of the current loop, or a component of B depending on present position of rotor, see sketch. Induced loop current is normal to B. B force acts radially & cannot impart energy to e- to move it around the loop. But E is tangenetial doing just that.

The work done by B is acting radially on the electrons. But the e- do not fly off the wire, rather they yank the lattice stationary protons as they are attached to the e- by E force. Likewisr neutrons are attached by SN force & get yanked along as well. The whole loop rotates as a result of B force acting on the e- in the radial direction. Any good machines text will have detail & illustrations. I recommend the following:

Electric Machinery, but Kingsley, Fitzgerald, & Umans (I had Dr. Umans spring 2010 for power class, he's very good)

Electrical & Electromechanical Machines, by Leander Matsch

Best regards :-)

Claude

 

[vanhees71]

Your info is generally correct but I hope you don't get mad at me when I say that it has little to do with the OP question re forces/work on current loops. I believe that the OP question has been answered. If those of us whom you differ with have erred, please offer feedback. Thanks.

Claude

I don't know, whether we agree or not. In your posting with your scanned calculations I had the impression we agree. To make it clear once more

I disagree with the claim magnetic fields do work on charges and magnetizations and I claim that Maxwell's theory and Poynting's theorem is generally valid on a fundamental level and within the validity range of applicability for the standard macroscopic theory.

There is the old controversy between the Minkowski and the Abraham definition of the energy flow (momentum density, Poynting vector) of the em. field in matter, but this also has been solved recently to the surprising result that both are correct but refer to different quantities (canonical vs. kinetic momentum), and the discrepancies concerning an experimental proof of the one or the other . This you can read in

S. M. Barnett, PRL 104, 070401 (2010)
http://dx.doi.org/10.1103/PhysRevLett.104.070401

 

[truesearch]

It also needs pointing out...again...that there is no energy gap between valence and conduction bands in a conductor.
It has no relevance in this post but it is an important physics concept that should be stated correctly.

 

[Dadface]

Please allow me to give some initial impressions of how some of the discussions here have been going on:
Firstly it has been pointed out that "it is the electric component of the field that does work on the charges".I think I sort of agree with that particularly when it was shown in post 75 that the power equation in post 74 is equivelent to P=VI(this equation being more familiar to me at the moment).
Let's consider this starting with the simplest relevant system I can think of,a battery connected to a wire by a switch the whole thing being reasonably well isolated from the surroundings.In terms of energy we can describe ,in broad outline,that when the current is steady,chemical energy is converted to electrical energy which is converted to heat energy in the wires(there are other changes but they are not relevant to the point I am making at present).We can write:

VI=I squared R

Now consider the moment at which the power is switched.When this is done energy is required to build the growing B field.A back emf is induced which falls exponentially with time approaching zero as the field establishes.In the situation described L and M may be "small" and the back emf small and transient(being most dominant at switch on and switch off) but nevertheless this changing B field features in even this most basic circuit.

The back emf (Eb) is a major factor in the analysis of the motor,and is present not only at switch on and off but also for all the time the motor is running.Also,the back emf can closely approach the applied voltage.It is most certainly not negligible but seems to have been largely overlooked and given scant regard in the discussions in this thread.

We can write VI=EbI+ I squared R+other losses (EbI=mechanical work done)

From this it might be reasonable to say that the work is done against the back emf (which orignates from the changing B field)

Finally,somethings that confuse me about some of these discussions.

1.There seems to be some agreement that the B field provides the torque.I go along with that but isn't it the torque that causes the rotation resulting in work being done?
(Work done =T theta)

2.Looking at it differently,for a straight wire at 90 degrees to the field f=BIl.The wire can move in the direcion of the force resulting in work being done.

These represent the simplest answers to the question I can think of so why are they being ignored?Is it me?Am I overlooking something?

 

[cabraham]

It also needs pointing out...again...that there is no energy gap between valence and conduction bands in a conductor.
It has no relevance in this post but it is an important physics concept that should be stated correctly.

But if the motor is a wound rotor induction type w/ external resistors, then we have an energy gap. For Cu they overlap meanint that many e- are already conductive needing no energy. Some do receive energy to transition from valence to conduction, that's what overlap means. Still, energy is needed to replenish that lost in collisions. You're making too much out of this narrow issue.

Claude