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

[Khashishi]

A sailboat is in a lake with the wind parallel to the sail. It doesn't accelerate. Now a person pulls the sail at an angle to the wind. This causes the sail to deflect the wind and the boat starts to move. In this case, the wind does work on the boat. The person requires force to move the sail, but he isn't doing any work to move the boat.

A wire in a magnetic field is like the boat. The electric current acts like the wind. But the electrons move parallel to the wire so there's no work on the wire. Applying the magnetic field deflects the electrons into the side of the wire, causing the wire to move. It is the motion of the electrons which does work on the wire, not the magnetic field. The electrons slow down when they ricochet off the side of the wire and push the wire. The magnetic field is exerting a force on the electrons, but not doing work.

 

[pgardn]

A sailboat is in a lake with the wind parallel to the sail. It doesn't accelerate. Now a person pulls the sail at an angle to the wind. This causes the sail to deflect the wind and the boat starts to move. In this case, the wind does work on the boat. The person requires force to move the sail, but he isn't doing any work to move the boat.

A wire in a magnetic field is like the boat. The electric current acts like the wind. But the electrons move parallel to the wire so there's no work on the wire. Applying the magnetic field deflects the electrons into the side of the wire, causing the wire to move. It is the motion of the electrons which does work on the wire, not the magnetic field. The electrons slow down when they ricochet off the side of the wire and push the wire. The magnetic field is exerting a force on the electrons, but not doing work.

What do the electrons ricochet off of?

What do they touch?

 

[Miyz]

A sailboat is in a lake with the wind parallel to the sail. It doesn't accelerate. Now a person pulls the sail at an angle to the wind. This causes the sail to deflect the wind and the boat starts to move. In this case, the wind does work on the boat. The person requires force to move the sail, but he isn't doing any work to move the boat.

A wire in a magnetic field is like the boat. The electric current acts like the wind. But the electrons move parallel to the wire so there's no work on the wire. Applying the magnetic field deflects the electrons into the side of the wire, causing the wire to move. It is the motion of the electrons which does work on the wire, not the magnetic field. The electrons slow down when they ricochet off the side of the wire and push the wire. The magnetic field is exerting a force on the electrons, but not doing work.

The B field and the electric current are both proportional to one another. If you'd think about it... When electric current creates a magnetic fields that will interact with other magnetic field of a magnet.

Magnetic forces does the work and the electric current to is doing work both forces would add up to do work in a sense as I said before they add um as total work done on an object. I don't really agree that one is doing work while the other is not.
They both are.

 

[Miyz]

+

Based on the motor effect: Electricity flow to the wire as a "force" then another "force" is acted upon it that result in ANOTHER FORCE.

Electricity & magnetism and related to on another and are each forces acted upon each other in that causes of a "loop" were electricity flows through it, magnetic force is applied and torque is generated as a consequence to the interaction of both forces together. If you'd like to understand let's break each step into forces? The flow of electrons within the wire is caused due to EMF, due to that force the charges will be in motion through the conductor. Due to that motion of charge a magnetic field is created throughout the whole loop. Once a magnet is introduced to the system. Its magnetic field will interact with the loop and would attract it or repel it in a sense electricity(force) flowing through that loop will be a temporary"based on the flow of charge" dipole. Thus there will be a magnetic force applied on the loop and motion + torque are created.

Now if a freely moving charge moved through a magnetic field as Claude said: "e- (electron) has a velocity & a mag field is present, then a Lorentz force acts on the e- in a direction normal to its present velocity, & normal to B. Thus a mag field can change an e- momentum value, but not its kinetic energy value. Hence a mag field does no work on a charge." That is true.

But in cause of the motor effect! Where both charges & magnetic field's are present in a different orientation work is done and the value of kinetic energy will change. Because the charges are moving throughout a conductor and due to their motion a magnetic field is created and the magnet's field would interact with it. That interaction would be a force! The e- to move and due to its strong nuclear force it moves the p+ and n0 again Claude perfectly clarified that:"Now we have a current loop, 2 of them in fact. Mag field 1, or B1, exerts a force on the electrons in loop 2, normal to their velocity. In accordance with the above, B does not alter the e- energy value, only its momentum value, by changing the e- direction. But as these e- move in a new direction, the remaining lattice protons get yanked along due to E force tethering. But did the E actually do the work? The stationary lattice was moved acquiring non-zero KE (kinetic energy) when it started at zero KE.

Likewise, the neutrons got yanked along by strong nuclear force, which tethers the n0 (neutron) to the p+ (proton). A mag force in a direction normal to the loop deflects e- in a radial direction, resulting in p+ & n0 getting yanked radially. The force due to B accounts for all motion & work. But B cannot act on p+ as they are stationary, nor on n0 since the are charge-less. Did E do the work? E cannot act on n0 since they are charge-less. Did SNF do the work? SNF does not act on e-.

The work done by E appears to me a near zero. E exerts force no doubt, but when integrated with distance I compute zero. The E force between e- & p+ does move the p+, but the e-/p+ system energy is not changing. If an E force changed the distance between e- & p+, then E did work. Likewise for SN force."

Still they say electrical force does the work? Not really... Magnetic field then? Not really... Strong nuclear forces? Nope. Then what?! The total net force of all three interacting with one another.

As I said this before and I will say it again.

Magnetic field's can do work under certain circumstances.ONLY in the presence of both Electrical forces + Nuclear forces can then magnetic fields do work.

Now again: Electricity & magnetsim are related forces. Interacting together would cause this effect.

As Me & Claude finally agree that Magnetic force/field DOES work in this system. There all proportional to each other without the presence of E forces + SN forces the mag field/force can't do anything.

Miyz,

(Please give me you're opinion or you're contradiction to this idea because so far nothing is against it.)

& Appreciate all you're efforts to this very very strong thread! almost 4,000 views!

NOTE: "Hope whom ever reads this post could say I agree or disagree backing up their claims with proper illustration of the motor effect and any formula's that my support their claims"

 

[vanhees71]

Again I must stress, I don't understand your insistance on a statement which contradicts very basic calculations within the system of Maxwell's equations. You find this in any serious textbook of classical electromagnetics under the name "Poynting's Theorem".

I can only repeat that this no-brainer gives the clear answer that the electric components of the electromagnetic field do the work on any distribution of matter
$$P=\int \mathrm{d}^3 \vec{x} \vec{E} \cdot \vec{j}.$$
The current density $\vec{j}$ has to be understood as containing both the flowing charges $\vec{j}_{\text{charges}}=\rho \vec{v}$ and the equivalent current for any kind of magnetization (through ring currents or through generic magnetic moments of elementary particles associated with their spin, which is a semiclassical picture of a quantum phenomenon), $\vec{j}_{\text{mag}}=c \vec{\nabla} \times \vec{M}.$
As in all my postings I use Heaviside-Lorentz units (rationalized Gaussian units).

 

[Dale]

The e- to move and due to its strong nuclear force it moves the p+ and n0 ... the remaining lattice protons get yanked along due to E force tethering. ...

Likewise, the neutrons got yanked along by strong nuclear force, which tethers the n0 (neutron) to the p+ (proton).

Definition of work: a transfer of energy other than through heat.

None of the "tethering" stuff is relevant. Those are internal forces, and internal forces cannot do work on a system. Internal forces can only change a system's configuration, not its energy.

I am not yet convinced that the magnetic field cannot do work in the case of permanent magnets, but I am convinced that the magnetic field does not do work in a motor.

In a motor the integral of E.j that vanhees71 has posted fully accounts for the energy transfer in all situations. The B field is not relevant. If you double E.j then you double the work done on the motor regardless of B. If you double B then you do not change the work done on the motor. If you have E.j=0 then no work is done on the motor, regardless of B, but even if you have B=0 the work done on the motor is still given by E.j which then goes rapidly to thermal energy.

 

[cabraham]

Again I must stress, I don't understand your insistance on a statement which contradicts very basic calculations within the system of Maxwell's equations. You find this in any serious textbook of classical electromagnetics under the name "Poynting's Theorem".

I can only repeat that this no-brainer gives the clear answer that the electric components of the electromagnetic field do the work on any distribution of matter
$$P=\int \mathrm{d}^3 \vec{x} \vec{E} \cdot \vec{j}.$$
The current density $\vec{j}$ has to be understood as containing both the flowing charges $\vec{j}_{\text{charges}}=\rho \vec{v}$ and the equivalent current for any kind of magnetization (through ring currents or through generic magnetic moments of elementary particles associated with their spin, which is a semiclassical picture of a quantum phenomenon), $\vec{j}_{\text{mag}}=c \vec{\nabla} \times \vec{M}.$
As in all my postings I use Heaviside-Lorentz units (rationalized Gaussian units).

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

 

[Miyz]

Definition of work: a transfer of energy other than through heat.

"In physics, mechanical work is a scalar quantity that can be described as the product of a force and the distance through which it acts in the direction of the force.""If a constant force of magnitude F acts on a point that moves a distance d in the direction of the force, then the work W done by this force is calculated as: W= Fd"

http://en.wikipedia.org/wiki/Work_(physics)I do know that work is the transfer of energy. However, in our case what would you like to envision? Forces, not energy.(I personally don't and can't imagine the kinds of energy I just break it down to work then the forces involved in the system to have a better idea of what's going on.)

Eventually we know energy has been transferred from point A to B, or conserved as heat.

 

[Darwin123]

"In physics, mechanical work is a scalar quantity that can be described as the product of a force and the distance through which it acts in the direction of the force."


"If a constant force of magnitude F acts on a point that moves a distance d in the direction of the force, then the work W done by this force is calculated as: W= Fd"

http://en.wikipedia.org/wiki/Work_(physics)


I do know that work is the transfer of energy. However, in our case what would you like to envision? Forces, not energy.(I personally don't and can't imagine the kinds of energy I just break it down to work then the forces involved in the system to have a better idea of what's going on.)

Eventually we know energy has been transferred from point A to B, or conserved as heat.

Unfortunately, there is a lot of ambiguity in the jargon of physics. Units alone do not completely specify the important units alone. For instance, "potential difference" and "electromotive force" are completely different concepts, even though both have units of volts. Sometimes, "heat" means "energy" and sometime "heat" means entropy. Although these two definitions of "heat" have different units, they sometimes flow together. Sometimes they don't flow together.
That last sentence of yours can cause a lot of confusion if the physical concepts aren't specified, either explicitly or by the context. Students just starting can be thrown by the least bit of confusion.
There is a book that helps me a great deal with ambiguous physics concepts. It is:
"The Teaching of Physics" by J. W. Warren.
I have an edition published by Butterworth's in 1965.
Unfortunately, I don't know where or even if the book is still published anyplace. I don't know if there is a link to the book somewhere on-line. I certainly hope so.
It is a small book but it clears up a lot of basic questions students ask about physics. It discusses ambiguities in the jargon of electrodynamics, thermodynamics, calorimetry, classical mechanics and atomic physics.
This book emphasizes deficiencies in the way physics was taught in 1965. Judging by the questions people are still asking, I don't think the situation has improved since then. Most of the concepts clarified in this book are still taught the same way. Badly!

 

[Dale]

"In physics, mechanical work is a scalar quantity that can be described as the product of a force and the distance through which it acts in the direction of the force."

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

 

[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.