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

[Miyz]

The concept of thermodynamic work (the definition I cited) is a generalization of the concept of mechanical work (the definition you cited). The thermodynamic definition is the one that is typically used for fields, since it can be applied in situations where the mechanical definition is hard or impossible to use.

http://en.wikipedia.org/wiki/Work_(thermodynamics)
http://www.lightandmatter.com/html_books/lm/ch13/ch13.html#Section13.1
http://zonalandeducation.com/mstm/physics/mechanics/energy/work/work.html

Fair enough. However, isn't it more fit for our situation to use the mechanical model? Since were dealing with a lot of forces?

 

[Miyz]

I've already refuted that argument. E dot J is the dot product of 2 vectors acting tangential to a current loop. No torque is incurred on the rotor. I'll draw a diagram & post it later. Without a diagram showing the forces, it's hard to visualize.

Claude

Looking forward for that diagram!

 

[Miyz]

@DaleSpam

What happened to you're conclusion?

 

[Dale]

Fair enough. However, isn't it more fit for our situation to use the mechanical model? Since were dealing with a lot of forces?

I think that it is pretty clear with the confused descriptions of tethering and internal forces and redirections and other such irrelevancies that the participants on this thread are not capable of coming to a clear conclusion that way. Also, it is always safe to use a more general definition instead of a less general definition. When a more general definition is also easier to apply, then it makes little sense to use the less general and more difficult definition.

 

[Dale]

What happened to you're conclusion?

Maxwell's equations clearly oppose the idea that magnetic fields can do work on matter, as do all of the other examples I can think of, but I still haven't been able to figure out what happens with permanent magnets. Clearly an external magnetic field can increase the KE of a permanent magnet, and I cannot think of any internal form of energy which is decreased to compensate. So it would seem that permanent magnets are an exception, but exceptions make me uncomfortable and make me suspicious that I am just not smart enough to figure it out.

So I still don't want to make a general conclusion that magnetic fields cannot do work in any circumstance, but I will make a specific conclusion that it now seems clear to me that magnetic fields do not do work in a motor. I think that the reasoning I presented in the last paragraph of post 146 is compelling and justifies this specific conclusion.

 

[Miyz]

Maxwell's equations clearly oppose the idea that magnetic fields can do work on matter, as do all of the other examples I can think of, but I still haven't been able to figure out what happens with permanent magnets. Clearly an external magnetic field can increase the KE of a permanent magnet, and I cannot think of any internal form of energy which is decreased to compensate. So it would seem that permanent magnets are an exception, but exceptions make me uncomfortable and make me suspicious that I am just not smart enough to figure it out.

"but exceptions make me uncomfortable and make me suspicious that I am just not smart enough to figure it out." haha! Thats how I've been feeling for weeks now! And that sensation of scratching you're head thinking about it all day!

I feel Maxwell equation is based on a general way? Not as complicated and controlled like the motor effect.

So I still don't want to make a general conclusion that magnetic fields cannot do work in any circumstance, but I will make a specific conclusion that it now seems clear to me that magnetic fields do not do work in a motor. I think that the reasoning I presented in the last paragraph of post 146 is compelling and justifies this specific conclusion.

I'm sorry but I do disagree in that point.However, I personally have no response now but I will develop one soon and come back.

Magnetic fields certainly can do work in other circumstances other then the motor effect Dale. You know there is potential energy when you take to bar magnets apart and put them back... You know they can do work in certain configurations. Again! Don't confuse yourself with the charged particle! Keep it out of the picture.

I'll study and come back with a better answer to support my opinion.

Miyz,

 

[Dale]

I feel Maxwell equation is based on a general way? Not as complicated and controlled like the motor effect.

Are you saying that you believe that motors violate Maxwells equations? If that is your claim then I suggest you find some very strong peer reviewed references to support that claim before asserting it here. Otherwise you will probably get yourself banned.

I hope I am misunderstanding your point, in which case I apologize in advance.

 

[Miyz]

Are you saying that you believe that motors violate Maxwells equations? If that is your claim then I suggest you find some very strong peer reviewed references to support that claim before asserting it here. Otherwise you will probably get yourself banned.

I hope I am misunderstanding your point, in which case I apologize in advance.

Relaaaaax Dale,

No I'm not saying that it violates Maxwell's law. I apologize for putting it in that way. What I really wanted to say is maybe things are DIFFERENT in the MOTOR effect.

You used to say magnetic field do indeed do work? Now you changed you're mind based on Maxwell's equations. I'm not saying that Maxwell's equations are wrong. I believe in them and certainly agree with it.However, What explains the "motor effect" then? Maybe Maxwell's equation is applied only on a solo charged particle? Not a loop of wire where things certainly are different?

In a motor effect's case I think things certainly differ.

check out this thread.

Could possibly help out with you're conclusion.

 

[Miyz]

Ow yea, another point.

Yesterday I was thinking of this matter and brought some old motors of same size & specs. Broke one up to examine the parts and used the other to examine work,motion,etc... When more "Watts" are introduced to a motor its increase its spread.

Now one would say its because more input of electricity was added. True.But! What really happens? As more current flows to the wire it creates a "stronger" magnetic field doesn't it? Ok, then what happens? Well that "Stronger" magnetic field generated by the more input added to the loop would be attracted easier and repeled greater by the permanent magnet within it. (Logically)

In a general way when we break the system up we only find 2 main components doing work and its obvious.

1 - Magnetic field of the permanent magnet.(Permanent Dipole)
2 - Controller and temporary magnetic field of a loop.(Current's flow would create that magnetic field more input = greater field.)

In they end its like bringing a permanent magnet and another permanent magnet(in this cause a loop that constantly changing it poles AC current applied) and just repelling and attracting each other until the battery runs out.

Now that just a simple point that clarifies magnetic fields can do work? Doesn't it? Add to that magnetic potential to that system as well...
Its really something interesting and really wonderful process!

 

[vanhees71]

I still fail to understand, where your problem is. First of all Maxwell's equations hold within the realm of classical electrodynamics, and this for sure includes motors and permanent magnets, at least as long as you don't ask about the underlying microscopic workings of ferromagnetism, which is clearly a quantum effect, because (a) it is related with the spin of the electron which is a quantum phenomenon (point particle with inner angular momentum) and (b) with the socalled exchange forces related with the indistinguishability of particles, here electrons, which are fermions.

From a macroscopic point of view a permanent magnet is well described as a body with a magnetization density \vec{M}, which in turn is effectively equivalent to a contribution to the current density, \vec{j}_{\text{mag}}=c \vec{\nabla} \times \vec{j}.

As has been nicely demonstrated in the paper, I've cited earlier,

PHYSICAL REVIEW E 77, 036609 (2008)
Dipole in a magnetic field, work, and quantum spin
Robert J. Deissler
DOI:10.1103/PhysRevE.77.036609

The motion of a magnetic body, be it one where the magnetic field is created by a current in the proper sense, i.e., moving charges or a permanent magnet, where the electromagnetic field is due to ferromagnet in the sense detailed above. In the following I call both types simply "magnet". The accelerated motion of the magnet induces an electric field (Faraday's Law of induction, which is another Maxwell equation, \vec{\nabla} \times \vec{E}=-\frac{\partial}{c \partial t} \vec{B}. This induced electric field is responsible for an induced current opposing the current causing the motion in an applied magnetic field. All together energy is conserved, and the power transferred from the em. field to the body is due to the electric field according to Poynting's Law.

There is no contradiction between the fundamental laws of the electromagnetic field and its interaction with matter known today! Also the very fact that electric motors, generators, and other machines in everyday life, involving the electromagnetics of moving bodies, work as they do shows that the application of Maxwell's laws in electrical engineering is very successful.

 

[Dale]

No I'm not saying that it violates Maxwell's law. I apologize for putting it in that way. What I really wanted to say is maybe things are DIFFERENT in the MOTOR effect.

I am not sure what distinction you are trying to make here. If some phenomenon were different than what Maxwells equations predict then it would violate Maxwells equations. So it seems like a self contradiction to simultaneously claim that motors do not violate Maxwells equations but are different than them.

Anyway, the last paragraph of 196 seems pretty clear reasoning that a motor is not different than Maxwells equations wrt energy and work.

 

[Dale]

The accelerated motion of the magnet induces an electric field (Faraday's Law of induction, which is another Maxwell equation, \vec{\nabla} \times \vec{E}=-\frac{\partial}{c \partial t} \vec{B}. This induced electric field is responsible for an induced current opposing the current causing the motion in an applied magnetic field. All together energy is conserved, and the power transferred from the em. field to the body is due to the electric field according to Poynting's Law.

I don't buy this. Work is an energy transfer, so the magnet's own induced E-field cannot do work on the magnet because if it did then it is just a transfer from the magnet back to the magnet, which is not a transfer.

The only thing which can possibly do work on a system is external fields/forces. If the only external field is a purely magnetic field and if work is done then the magnetic field has done work. The paper you cited showed that work is not actually done in some cases where it seems that work is done, but rather different types of energy were exchanged internally.

 

[Dale]

As more current flows to the wire it creates a "stronger" magnetic field doesn't it? Ok, then what happens? Well that "Stronger" magnetic field generated by the more input added to the loop would be attracted easier and repeled greater by the permanent magnet within it. (Logically)

That is irrelevant for the same reason as I pointed out to vanhees71 above. The magnetic field of the rotor cannot do work on the rotor. It would be an energy transfer from the rotor to the rotor, which is not a transfer at all. The only things which can do work on the rotor are the external magnetic field of the stator (your permanent magnet above) and the external current and voltage.

 

[Dale]

You used to say magnetic field do indeed do work? Now you changed you're mind based on Maxwell's equations.

Yes. I thought that the limitation requiring that magnetic fields do no work was restricted to classical point particles. But as a result of this thread I looked in more detail at the covariant formulation of Maxwell's equations for continuous charge distributions and found:
f_{\mu}=F_{\mu\nu}J^{\nu}
and expanding out the timelike component in a standard inertial frame you get
f_{t}=E_x J_x + E_y J_y + E_z J_z

So even with a general distribution of charge and current you get power transfer equal only to E.j. This is primarily the reason why I am still trying to understand what other forms of internal energy could be reduced in a magnet. It seems that general charge distributions, not just point charges, follow the same law as for point charges wrt work by a magnetic field.

http://en.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism#Lorentz_force

 

[cabraham]

I scanned & uploaded a diagram detailing the relevant force fields. Comments welcome.

Claude

 

[Miyz]

I am not sure what distinction you are trying to make here. If some phenomenon were different than what Maxwells equations predict then it would violate Maxwells equations. So it seems like a self contradiction to simultaneously claim that motors do not violate Maxwells equations but are different than them.

Well, that's me being confused, looking for a way to explain my thoughts and pretty much FAILED at it.

 

[Miyz]

That is irrelevant for the same reason as I pointed out to vanhees71 above. The magnetic field of the rotor cannot do work on the rotor.

Wait what?! Since when did I say the rotor is doing all the work by it's own? Obviously an external forces is acted upon the rotor that's causing this to happen... If that was true then why the need for an external permanent magnet?

It would be an energy transfer from the rotor to the rotor, which is not a transfer at all. The only things which can do work on the rotor are the external magnetic field of the stator (your permanent magnet above)

Sorry Dale, but didn't understand what you ment there...

I think you mean the external forces of the permanent magnet and the magnetic field of the stator? Thats the only thing I could build up... Please do correct me If I'm wrong.

and the external current and voltage.

What external current & voltage? Do you mean the loops current & voltage?

 

[Miyz]

I scanned & uploaded a diagram detailing the relevant force fields. Comments welcome.

Claude

Thanks Claude!

And thank you all for you're efforts once again!

Time to study this matter deeply and come back with a thought! Still looking forward for you're replies + inputs.

 

[vanhees71]

I scanned & uploaded a diagram detailing the relevant force fields. Comments welcome.

Claude

Very nice! Now you yourself have shown that the work is done by the electric field, not the magnetic.

Of course, what you considered is the static case, i.e., the forces and torque at fixed loops, and that's why your electric field is only there to compensate for the loss due to resistance (producing heat through scatterings of the electrons providing the currents in the loops).

If you add the calculation in the paper, I've cited, for the dynamical case of the moving wires, you'll see that also the energy needed to set the loops in motion is provided by the electric field, and this shows that Maxwell's equations hold for this case as expected.

As the paper has also demonstrated, the same dynamics holds for the case when you substitute one of the loops by a permanent magnet, whose magnetism is due to the spins of the electrons and the quantum mechanical exchange force that directs the spins into macroscopic domains, which is the modern understanding of Weiss's model for ferromagnets.

 

[harrylin]

[..] Is the mag force doing "work"? Well, in the short term, YES, in the long term NO. The power source, battery, ac mains wall outlet, etc., is doing all of the long term work. [..]
Is the mag force doing work? Again, it stores energy then transfers it. [...]
Claude

I agreed with that summary and I supposed that everyone would have - obviously that did not happen! It may be useful to elaborate how I understood it, and why I still think that it is right in principle.

Take two springs, attach one spring to the wall and press with the other against the first one. Let loose. Now the springs release the contained energy by pushing each other away. Obviously the energy was provided by the person pushing, and by means of the other spring, but next both springs gave off that stored energy - and in that sense it may be said that "the spring on the wall did work".
And of course one can calculate how much work was done, ignoring the springs, by looking at how much energy was put into that system - that's besides the point.

I think that this corresponds to how Miyz meant that "the magnet can do work" (everything of course discussed from the "stationary" reference system).

The fields of two permanent magnets in repulsive orientation that are pushed together will store potential energy; this magnetic field energy is released when you let go, as they push each other away. Thus a permanent magnet that pushes an electromagnetic coil away does "do work" in that sense; and that simple consideration made me agree that magnetic fields/forces can do work on a current carrying wire, in that sense - IMHO, that answers in principle the question of this thread.

However, that is not all, we should also consider two perpendicular oriented magnets, as in post #1. In this case, the forces are such that they act to rotate each other; and again this must imply that magnetic field energy is released. However the situation is not symmetrical. Could it be that only magnetic field energy of the one magnet is released? For that "motor" case I'm not sure and the analysis is more difficult (perhaps the paper on Stern-Gerlach can be applied for that).

 

[cabraham]

Very nice! Now you yourself have shown that the work is done by the electric field, not the magnetic.

Of course, what you considered is the static case, i.e., the forces and torque at fixed loops, and that's why your electric field is only there to compensate for the loss due to resistance (producing heat through scatterings of the electrons providing the currents in the loops).

If you add the calculation in the paper, I've cited, for the dynamical case of the moving wires, you'll see that also the energy needed to set the loops in motion is provided by the electric field, and this shows that Maxwell's equations hold for this case as expected.

As the paper has also demonstrated, the same dynamics holds for the case when you substitute one of the loops by a permanent magnet, whose magnetism is due to the spins of the electrons and the quantum mechanical exchange force that directs the spins into macroscopic domains, which is the modern understanding of Weiss's model for ferromagnets.

Your cited paper calculation backs me up. It does not account for torque on the loop. That force is B, not E. You draw conclusions w/o any proof. Please draw a diagram & show the E force that spins the loop with torque. My diagram is consistent with the paper you cited & Maxwell's equations. How can E force spin the loop?

Paper you cited describes power density as "E dot J". Integrating over volume gives power. I've already affirmed that that is correct. To have current in the loop 2 types of work on the electrons are needed. We need to do work on the e- to transition it from valence to conduction band. Only E can do that. Second, when the e- loses energy due to lattice collisions, i.e. resistance, the E force restores this energy by doing work on the E.

If not for loop current, there would be no B force. So, E is all important & indispensable. Nobody is denying the important role played by E force. Without it, the motor does not operate. But the force spinning the loop is indeed B force, not E. Please show me the component of E in a direction radial to the loop. Which Maxwell equation applies here?

My diagram accounts for I, J, E, B, A, & velocity u. You keep citing that paper w/ the integral of E dot J. That integral proves that the work done by E is along the path of the current density J. But torque is normal to the current, where E dot J equals ZERO.

I recommend you draw a diagram for your own understanding. All you do is cite that integral, which clearly proves my case. BR.

Claude

 

[Dale]

I scanned & uploaded a diagram detailing the relevant force fields. Comments welcome.

It seems pretty well-done, and I only see 3 very minor mistakes, none of which substantially change the conclusions:

1) On page 1 you have the field B1 pointing in the wrong direction (or maybe the current I1 is in the wrong direction).
2) On page 2 it is not correct that E=-\frac{\partial}{\partial t} A. Because the curl of the divergence of any scalar function is 0 you can add the divergence of an arbitrary scalar to E and still satisfy \nabla \times E = -\frac{\partial}{\partial t}(\nabla \times A). However, by assuming that everything is uncharged, I suspect that you can use Gauss' law and the remaining gauge freedom to set the divergence of the scalar function to 0.
3) On pages 3 and 4 it seems that, since both loops are in-plane Fm squeezes the loop without producing any torque or spin. It is an equilibrium position, however it is an unstable equilibrium and any deviation from being in plane will provide a torque. So, it is not critical.

So, overall I agree with the conclusion. The E-field provides the work and the B-field provides the torque.

 

[Dale]

Since when did I say the rotor is doing all the work by it's own?

I think that is exactly what you were trying to say in post 159. In that post you seem to be trying to say that increasing the input power increases the work done on the rotor by the B field because it increases the B field of the rotor. This only makes sense if it is the B field of the rotor which is doing the work on the rotor.

If you weren't even trying to say that then the fact that increasing the current increases the rotor's magnetic field is even more irrelevant to the work done.

Per cabraham's analysis, increasing B increases the torque, but it is still E.j which does the work.

 

[cabraham]

It seems pretty well-done, and I only see 3 very minor mistakes, none of which substantially change the conclusions:

1) On page 1 you have the field B1 pointing in the wrong direction (or maybe the current I1 is in the wrong direction).
2) On page 2 it is not correct that E=-\frac{\partial}{\partial t} A. Because the curl of the divergence of any scalar function is 0 you can add the divergence of an arbitrary scalar to E and still satisfy \nabla \times E = -\frac{\partial}{\partial t}(\nabla \times A). However, by assuming that everything is uncharged, I suspect that you can use Gauss' law and the remaining gauge freedom to set the divergence of the scalar function to 0.
3) On pages 3 and 4 it seems that, since both loops are in-plane Fm squeezes the loop without producing any torque or spin. It is an equilibrium position, however it is an unstable equilibrium and any deviation from being in plane will provide a torque. So, it is not critical.

So, overall I agree with the conclusion. The E-field provides the work and the B-field provides the torque.

1) Yes, I need to remember my right hand rule from the left. That negative sign threw me. You are correct.
2) Yes, I am aware that there is not a 1 for 1 equivalence, that uncharged de-energized conditions have to be assumed for my equation to be absolutely valid.
3) I did not do a great job drawing the loops. They are supposed to be oblique, but my lousy drawing skills ended up making them look co-planar. Based on the co-planar appearance, you are right, there would be zero torque, & a little motion either way results in non-zero torque.

Thanks for your feedback, we are in agreement. One point needs to be clarified however. I agree that E does provide the work when it comes to producing loop current, since work is done elevating valence e- into conduction, & restoring energy lost due to lattice collisions, which is resistance. E does this exclusively. We agree that B produces torque. But remember that torque times angle equals work. B does rotational work equal to torque times radian angle measure. Torque, however, would be 0 if current were 0. But current is nonzero due to E. So B does rotate the loop, but its torque would not exist w/o J, which would not exist w/o E. BR.

Claude

 

[Miyz]

I think that is exactly what you were trying to say in post 159. In that post you seem to be trying to say that increasing the input power increases the work done on the rotor by the B field because it increases the B field of the rotor. This only makes sense if it is the B field of the rotor which is doing the work on the rotor.

If you weren't even trying to say that then the fact that increasing the current increases the rotor's magnetic field is even more irrelevant to the work done.

Per cabraham's analysis, increasing B increases the torque, but it is still E.j which does the work.

Umm, I think what lead you was my mistake of saying "within it" I apologize for that.I like were this is going. Work is done by E.j and torque is by the B field. Good conclusion + agreement.

 

[Miyz]

1) Yes, I need to remember my right hand rule from the left. That negative sign threw me. You are correct.
2) Yes, I am aware that there is not a 1 for 1 equivalence, that uncharged de-energized conditions have to be assumed for my equation to be absolutely valid.
3) I did not do a great job drawing the loops. They are supposed to be oblique, but my lousy drawing skills ended up making them look co-planar. Based on the co-planar appearance, you are right, there would be zero torque, & a little motion either way results in non-zero torque.

Thanks for your feedback, we are in agreement. One point needs to be clarified however. I agree that E does provide the work when it comes to producing loop current, since work is done elevating valence e- into conduction, & restoring energy lost due to lattice collisions, which is resistance. E does this exclusively. We agree that B produces torque. But remember that torque times angle equals work. B does rotational work equal to torque times radian angle measure. Torque, however, would be 0 if current were 0. But current is nonzero due to E. So B does rotate the loop, but its torque would not exist w/o J, which would not exist w/o E. BR.

Claude

Very nice point!

 

[Dale]

One point needs to be clarified however. I agree that E does provide the work when it comes to producing loop current, since work is done elevating valence e- into conduction, & restoring energy lost due to lattice collisions, which is resistance.

In a functioning motor E.j is greater than the energy dissipated by the resistance. It is equal to that plus the mechanical work.

We agree that B produces torque.

Yes.

But remember that torque times angle equals work. B does rotational work equal to torque times radian angle measure.

If that were true then energy would not be conserved. E.j is an amount of work done by E. That can be split into an amount of energy dissipated by the rotor's resistance plus some remaining amount. Now, you are saying that the B field does the mechanical work on the rotor, so what happens to the remaining amount of work done by E.j? It isn't increasing the thermal energy of the rotor, and according to you it is not doing mechanical work on the rotor, so where did it go? Also, 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?

 

[Dale]

Work is done by E.j and torque is by the B field. Good conclusion + agreement.

Excellent!

 

[cabraham]

In a functioning motor E.j is greater than the energy dissipated by the resistance. It is equal to that plus the mechanical work.

Yes.

If that were true then energy would not be conserved. E.j is an amount of work done by E. That can be split into an amount of energy dissipated by the rotor's resistance plus some remaining amount. Now, you are saying that the B field does the mechanical work on the rotor, so what happens to the remaining amount of work done by E.j? It isn't increasing the thermal energy of the rotor, and according to you it is not doing mechanical work on the rotor, so where did it go? Also, 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?

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

 

[Dadface]

We can write:
V-E=IR (v=supply voltage,E=back emf,I=current,R=resistance)
From this we can write:
VI=EI+I^2R

VI=power supplied,I^2R resistive heating power losses and EI=mechanical power output.

(A more detailed treatment would consider the other energy losses due to friction etc)

Sorry if this is irrelevant to the discussion.