Do Magnetic Fields Do Nonzero Work on Moving Objects?

[burashka]

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

Unfortunately, it won't. The mathematical expression for the Lorenz force has explicitly a charge or a charge density in it (if we use the expression for the force density). Expressions which contain currents, say J, are based on the assumption that J=rho*v, where rho is the charge density. See, for example, Landau, v.VIII.

Typically, people extrapolate and assume that the force which is applied, sticktly speaking, only to moving charged particles, is the same as the force which is acting on the whole electrically neutral system (the wire in this case). This is a mistake.

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

From Wikipedia:

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

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

The only assurances which are worth something are those of the Federal Reserve.

In pair-wise particle interactions, the Newton's third law is, of course, obeyed, unless retardation is taken into account. BTW, retardation is the major cause of the third law breaking. The motor engineers (or the people why contribute to Wikipedia) do not know about that because they have never seen a retarded Green's function.

But the reason for the third law breaking in our case is somewhat different. It is the presence of an external constraint to the motion.

Consider a bunch of electrons flying along the axis of a positively charged holow cylinder. All electrons are on axis and the system is electrically neutral, on average. Now apply an external magnetic field perpendicularly to the cylinder axis. The magnetic part of the Lorenz force will act on the moving electrons but not on the stationary positively-charged cylinder. The magnetic field would force the electrons to deviate from the straight-line trajectory and to curve either to the right or to the left and eventually bump into the cylinder wall. When such collision occurs, the momentum is conserved and the third law is satisfied. The cylinder gets a little momentum, say, to the right, and the electron recoils backwards, say, to the left. But the magnetic field would continue to bend the electron's motion and to change its momentum direction until the electron again bumps into the wall.

The net effect of all these bumps is the following: the positive cylinder acquires some momentum pointed to the right, but the electrons don't acquire equal momentum, pointing to the left. This is because the magnetic field can not change energy but can change momentum.

Thus, when averaged over many collisions, one would observe that the electrons push the cylinder to the right. The third law breaks.

Constrained motion is a difficult concept and it is often left out of the undergraduate classical mechanics courses. Even in Landau v.1, the chapter on parametric resonance (which is somewhat similar conceptually) is listed as "optional" in a course of theoretical physics. May be this fact can explain the misunderstandings. But lack of education is not a good explanation for the blatant and arrogant rudeness that the previous poster has demonstrated. Stupidity, however, is.

 

[SystemTheory]

My understanding is that in the modern view Conservation of Momentum can be used to derive Newton's Third Law for an isolated system. Momentum p = mv is conserved, then the terms F = dp/dt in a time-derivative of conserved momentum should include action reaction pairs.

I haven't studied the theory extensively, but in a direct current brush motor the moving electrons collide with the wall of the wire to generate torque in the air gap, and the motor casing, which holds the permanent magnets, transfers a torque to the system to which it is attached.

This suggests to me that the magnets and current conducting wire have a coupled tendency to change momentum (force) and Newton's Third Law holds true. I am not aware of how or why this law would not hold for a closed system (one that incorporates the source of magnetic flux in the system boundary).

 

[burashka]

Yes, exactly, the third law follows from conservation of momentum. Momentum is conserved in every pair-wise collision. However, the magnetic field does change the momentum of freely moving charged particles 9the conductivity electrons) inbetween the collisions. This is why, I think, the third law can breaks here when we average over many collisions.

 

[SystemTheory]

The simple case of the charge changing velocity (accelerating) without colliding with anything is then that of an electron (or proton) moving in a constant circle in a magnetic field at constant velocity vC.

It seems to me the conservation of momentum and Newton's Third Law would hold upon proper analysis of the source of centripital force, regardless of its cause (gravity, magnetism, etc) in that case. However it is also recognized that a centripital force accelerates the body without changing it's kinetic energy, and does zero work. This comment was just made on another thread about the change in kinetic energy in different frames of reference.

 

[burashka]

The simple case of the charge changing velocity (accelerating) without colliding with anything is then that of an electron (or proton) moving in a constant circle in a magnetic field at constant velocity vC.

It seems to me the conservation of momentum and Newton's Third Law would hold upon proper analysis of the source of centripital force, regardless of its cause (gravity, magnetism, etc) in that case. However it is also recognized that a centripital force accelerates the body without changing it's kinetic energy, and does zero work. This comment was just made on another thread about the change in kinetic energy in different frames of reference.

I am a little confused. There is no centripetal force in the lab frame; only the Lorentz force. The really-really total momentum is, of course, always conserved, but to see that you need to account for the momentum of the cyclotron radiation. As for the mechanical system only, its momentum does not need to be conserved in this problem.

So the simple mathematical statement is correct: a constant magnetic field can change the momentum of a charged particle moving in it. Of course, the field is never truly constant.

 

[Longstreet]

You have the two conservations, in vector form:

Energy:

<br /> \nabla \cdot S + J \cdot E + \frac{\partial u}{\partial t}= 0<br />

Momentum:

<br /> [\frac{\partial S}{\partial t} + \rho E + J\times B]_i - \frac{\partial T_{ij}}{\partial x_j} = 0<br />

S = poynting vector (viewed as energy flux density, and/or momentum flux density)
u = EM energy density
T = EM stress tensor

So it can be seen that energy is exchanged with matter solely through the electric field, while momentum is exchanged through both electric and magnetic fields. But of course it is a two way street. You would view this as Newtons third law for EM. Viewing it this way Newton's third law is not violated, just reinterpreted. All momentum exchange total zero.

 

[Per Oni]

The mathematical expression for the Lorenz force has explicitly a charge ...in it

Just like I said.

Consider a bunch of electrons flying along the axis of a positively charged holow cylinder. All electrons are on axis and the system is electrically neutral, on average.

I know what you are getting at as long as you are aware that those electrons would immediately start to accelerate towards the +ve cylinder even without a magnetic field. (or even without a +ve charge) And secondly those electrons have already a kinetic energy.

Now apply an external magnetic field perpendicularly to the cylinder axis. The magnetic part of the Lorenz force will act on the moving electrons

And in turn the electrons will act on the magnetic field. Force and counter force.
No real need to go any further. But I’ll do anyway.

but not on the stationary positively-charged cylinder. The magnetic field would force the electrons to deviate from the straight-line trajectory and to curve either to the right or to the left and eventually bump into the cylinder wall. When such collision occurs, the momentum is conserved and the third law is satisfied. The cylinder gets a little momentum, say, to the right, and the electron recoils backwards, say, to the left. But the magnetic field would continue to bend the electron's motion and to change its momentum direction until the electron again bumps into the wall.

The net effect of all these bumps is the following: the positive cylinder acquires some momentum pointed to the right, but the electrons don't acquire equal momentum, pointing to the left. This is because the magnetic field can not change energy but can change momentum.

Thus, when averaged over many collisions, one would observe that the electrons push the cylinder to the right. The third law breaks.

There’s no real need for many collisions. Just let the electrons curve into the cylinder wall and have an inelastic collision. Then they loose their KE and momentum in one go. The cylinder gets a push to the right but at no time was the third law violated. Even if you want many bounces nothing changes.

 

[SystemTheory]

I regard a field as a mathematical model to predict changes in momentum (force) over distance specified with or without a time delay. These momentum interactions can be of course microscopic or macroscopic and through such interactions we infer the existence of a field and build a model consistent with what is observed. The term "force field" is not used by experts yet it is faithful to the science when used in popular culture.

On the issue of which force-fields do work if a source and sink interact, the electrical or magntetic force-field, I have not thought hard about the topic. In DYNAST shell multi-domain simulator there is a domain for magnetic circuits including magnetic capacitors and lossy conductors/resistors, but no element for a magnetic inductor. This suggests to me that magnetic energy and power transfer are at least defined in a domain separate from the more common domain of electric circuit theory. It seems to me there is a domain where EM power interactions are better characterized as purely magnetic in character.

The potential in the magnetic domain is measured in the SI unit of ampere. I confess difficulty grasping the concept of magnetic circuits, although I've seen diagrams for, say, the magneto to produce spark in a combustion engine.

 

[kcdodd]

I don't think magnetic circuits have anything to do with anything other then the magnetic field itself. Maxwells equations are nearly symmetric except for a minus sign and the absence of magnetic charge/current, so you can use things we have to solve electric fields to solve magnetic fields as well. If there was such a thing as a magnetic charge then everything would automatically apply from what we know about electrical circuits. The lorentz force would have some extra terms, and where the electric field cannot do any work on magnetic charges from the J_m\times E term (J_m = magnetic current), just like the J_e\times B term for electric current.

 

[burashka]

There you go again.

Forces do the work, not fields.
Never any field does any work.

I thought we've discussed this. This is purely a matter of terminology. I have explained that when physicists say, for example, "electric filed does work" they imply the more precise statement that the force qE does work. When they say that MF does no work, they imply that the force (q/c)vxB does no work. That's just the widely used terminology; I have explained it to you and went on with the physical arguments. I am sure that you understand perfectly what is meant. Why then making so much fuss about nothing?

Incorrect. Lorenz force does not need net charge, that is an EFFECT of superposition where positive electric charge neutralize negative, mathematically by vector addition, but the CAUSE and the direction for Lorentz force comes from the velocity vector of those charges, regardless of the presence of protons or neutrons. This interaction is very well defined by magnetic force, both Lorentz and/or Ampere's force. Do you disagree with Wikipedia?

Would you please write an expression for the Lorenz force which does not contain charge or charge density? If you use current J, then define this quantity from first principles.

By the way, you correctly write that "...the CAUSE and the direction for Lorentz force comes from the velocity vector of those charges [that move], regardless of the presence of... [other charges]". Equally correct is the statement that the Lorenz force is only applied to those charges that move, not to the stationary charges or the system as a whole.

http://en.wikipedia.org/wiki/Lorentz_force
http://en.wikipedia.org/wiki/Ampère's_force_law

Promise to me never to look in wikipedia again.

"...when they deviate"?

Electrons deviate from their trajectories because of...?

Because of the force (q/c)vxB or because, as I would say, of the external magnetic field.

Would that explain Z-pinch as well? http://en.wikipedia.org/wiki/Z-pinch
"The Z-pinch is an application of the Lorentz force, in which a current-carrying conductor in a magnetic field experiences a force. One example of the Lorentz force is that, if two parallel wires are carrying current in the same direction, the wires will be pulled toward each other. The Z-pinch uses this effect: the entire plasma can be thought of as many current-carrying wires, all carrying current in the same direction, and they are all pulled toward each other by the Lorentz force, thus the plasma contracts."
[/QOUTE]

Of course, it would explain any experimental observation. Maxwell equations + Lorenz force explain the vast majority of macroscopic EM phenomena.

There you go again.

FORCES do the work, not fields.
Never any FIELD does any work.

And you...

Are you calling me stupid for your inability to distinguish between FIELDS and FORCES, which I tried to help you with by capitalizing letters, is that what you're talking about? Stupidity is a good explanation for rudeness, eh?

Actually, I referred to someone else, not you. That poster was really rude. And yes, the cause of that rudeness was stupidity. Any moderately smart person would understand that being rude is not going to advance his argument at all.

Yes, and yes. Again, it is known as "Ampère's force law".
http://en.wikipedia.org/wiki/Ampère's_force_law

If you believe that you can predict some experimental observation which is not anticipated in the traditional theory, you should be able to publish your findings. In other words, if your ideas are in any way novel and correct, they are publishable. There are two journals which consider somewhat contaversial or of-mainstream articles: Foundations of Physics and Old and New Concepts in Physics... You might try to send your ideas there if you feel serious about them.

 

[burashka]

Just like I said.

I know what you are getting at as long as you are aware that those electrons would immediately start to accelerate towards the +ve cylinder even without a magnetic field. (or even without a +ve charge) And secondly those electrons have already a kinetic energy.

Yes, they would. But add also friction (resistance) and they would, on average, attain a constant drift velocity.

And in turn the electrons will act on the magnetic field. Force and counter force.
No real need to go any further. But I’ll do anyway.

Yes, the total momentum of matter+field is always conserved. But you need to consider radiation to see how this works. Perhaps that was what you meant by "acting on magnetic field". Accelerating charges radiate and the radiative photons balance the momentum.

There’s no real need for many collisions. Just let the electrons curve into the cylinder wall and have an inelastic collision. Then they loose their KE and momentum in one go. The cylinder gets a push to the right but at no time was the third law violated. Even if you want many bounces nothing changes.

In fact, inelastic collisions conserve momentum. Check an elementary book on classical mechanics. It is exclusevly and specifically the magnetic field that causes the momentum to be not conserved.

(Again, we account here only for the momentum of particles. The momentum carried by radiation is not included. We all do understand that the total momentum of a closed system is conserved.)

 

[sweet springs]

Dear Members.
I enjoy reading your comments and I almost understand the case of electric circuits.
Mystery Remains in permanent magnets. Unlike battery to wires, there seem no supply of energy from outside to magnets, but two magnets start to move and accelerate thus do work mutually. What are the differences of the cases of electric circuit and permanent magnet?

Permanent magnet consist of charged and uncharged particles. Magnetic field do no work to each of these particles. Why and How magnet as total of these particles can get work from magnetic field?

Your explanation or suggestion of references are appreciated.
Regards.

 

[Born2bwire]

Dear Members.
I enjoy reading your comments and I almost understand the case of electric circuits.
Mystery Remains in permanent magnets. Unlike battery to wires, there seem no supply of energy from outside to magnets, but two magnets start to move and accelerate thus do work mutually. What are the differences of the cases of electric circuit and permanent magnet?

Permanent magnet consist of charged and uncharged particles. Magnetic field do no work to each of these particles. Why and How magnet as total of these particles can get work from magnetic field?

Your explanation or suggestion of references are appreciated.
Regards.

Because the magnets are moving, you also get electric fields since the magnetic fields are now changing in time. In a material, we explain that the magnetization of the material is due to the net alignment of magnetic dipoles. These dipoles are produced by the orbits of the electrons in the material. The magnetic fields create macroscopic bound currents, these are the macroscopic result of the atomic loop currents that are induced. These bound currents experience a force from the electric field contribution to the Lorentz force and it is this contribution that does work. Griffiths even notes this explicitly in his textbook when he discusses magnetization, magnetic fields do no work, however, a time-varying magnetic field will have a time-varying electric field and it is this electric field that does the work.

 

[Born2bwire]

Allow me to attach a scan from Griffiths' textbook.

 

[sweet springs]

Thank you for your comment. Let me clarify your point.

Because the magnets are moving, you also get electric fields since the magnetic fields are now changing in time. .

The magnets are pinched still. there's no electric field. Then at time zero they are released and start to move. In such a case, zero electric field at time zero could be the driving force?
Thanks again in advance.

 

[Born2bwire]

Thank you for your comment. Let me clarify your point.



The magnets are pinched still. there's no electric field. Then at time zero they are released and start to move. In such a case, zero electric field at time zero could be the driving force?
Thanks again in advance.

At t=0, the only force is the magnetic forces, yes. But these forces operate on the magnetic dipole currents that give rise to the magnet's field. This causes the currents to be displaced and now we have started our mechanism to create a time-varying situation. As soon as these currents are displaced, the magnetic field that they are creating changes in time and there is now an electric field.

Magnetic fields can apply forces on charges and cause them to be displaced, however, it is only done in a manner that no work is done on the charges. Instead the momentum of the charges are changed, not their energy. But since how these charges are moving in space give rise to our magnetic fields, even moving them in a way that does not change their energy creates a secondary effect, a change in their produced magnetic fields. Since energy is not taken out of the magnetic field, the initial energy in both our new time varying magnetic and electric fields will be the same as the original magnetic fields at t=0. But as the new electric fields do work, they expend the energy stored in their fields. When we bring the system to rest and have (effectively) a static magnetic field system, the magnetic field will now have a different amount of energy stored in it. The change in energy in the field was mediated by the electric field when it did work as the system was in a dynamic state.

 

[Per Oni]

Yes, they would. But add also friction (resistance) and they would, on average, attain a constant drift velocity.

So you take an charged cylinder inject some electrons down the middle, add some friction/resistance, add a magnetic field and here we have the logic which will explain the violation of Newtons 3rd law. Oh, I see we also got to add some acceleration.
And this from the person who claims:

The motor engineers (or the people why contribute to Wikipedia) do not know about that because they have never seen a retarded Green's function.

Bye for now, It’s been a real pleasure.

 

[sweet springs]

Hi. Born2bwire.
Start up issue was cleared by your teaching. Thanks.

At t=0, the only force is the magnetic forces, yes. But these forces operate on the magnetic dipole currents that give rise to the magnet's field. This causes the currents to be displaced and now we have started our mechanism to create a time-varying situation. As soon as these currents are displaced, the magnetic field that they are creating changes in time and there is now an electric field.

Energy of electric current is converted to kinetic energy of electrons and cores, i.e. the whole body, thus electric current dissipates. In order to keep the body accelerated under magnetic field, in case of wire we connect buttery to supply energy to maintain current.
In case of permanent magnet why we do not have to supply energy to maintain magnetic dipole currents to keep the magnet accelerated?

Maybe you already answered but I cannot find it. Thanks for further advice in advance.

 

[Born2bwire]

Hi. Born2bwire.
Start up issue was cleared by your teaching. Thanks.



Energy of electric current is converted to kinetic energy of electrons and cores, i.e. the whole body, thus electric current dissipates. In order to keep the body accelerated under magnetic field, in case of wire we connect buttery to supply energy to maintain current.
In case of permanent magnet why we do not have to supply energy to maintain magnetic dipole currents to keep the magnet accelerated?

Maybe you already answered but I cannot find it. Thanks for further advice in advance.

On an atomic level, an atom can have its own magnetic dipole moment. This moment is created by the electrons orbiting the nucleus. There is also an additional contribution from the intrinsic moment of the electrons and protons themselves but we are ignoring that for the most part in our macroscopic analysis. In a very rough, and non-quantum way, think of the electron in a circular orbit about the proton. This causes a loop current which creates a magnetic dipole. The total magnetic dipole of an atom or molecule is going to be dependent upon the orbitals so not every atom exhibits a significant dipole moment. In addition, in most materials, the moments of the atoms are aligned randomly, thus giving rise to no net magnetic field. However, in permanent magnets, we find that in certain materials, large areas of the material will have most of their magnetic moments aligned. These areas of net alignment are called domains. If we apply a process to make all of these domains line up too, then we can create a strong magnet. One way to think of these microscopic atomic-level currents is as a net macroscopic loop bound current.

For example, let us think of a rectangle that has loop currents on its surface. If you look at the left-hand side of the attached picture, you will notice that on the interior, the currents of the top half of a loop will be canceled out by the currents in the bottom half of a loop above it. That is, the adjacent parts of neighboring current loops "cancel" each other out. What we are left then is a net current loop that runs along the outside edge of the rectangle. This can be shown to be true mathematically and is the conceptual idea of how all these atomic loop currents can add up to a large loop current. This large loop current can be treated as a magnetic field source and it can react to the Lorentz force from other magnets. This can be found under a discussion of magnetization in a textbook.

So that is how all these little loop currents can add up to a significant magnetic field. The main point is that we have to align a large number of them along the same direction to get them to work together. This can be done by applying a large magnetic field to our material (like how you can run a magnet along an iron nail and temporarily magnetize it). Heating and physical shock can undo this alignment, randomize the domains, and destroy the magnet. Since these currents are from the atomic orbitals, there is no need to keep supplying energy because the orbitals are stable themselves. On a very basic level, if we have an electron orbiting in a circle, we do not need to expend any energy to keep it orbiting, only a constant force. However, when we ourselves physically move the magnets around a magnetic field, we are inputting and taking out energy from these orbitals. That is, if I pull two magnets apart, I impart work that gets injected back into the magnetic fields. This would correspond to adding energy into the electron orbits. Likewise, if I release the magnets and they pull themselves together, they would release the energy I gave them. It is a conservative system, like gravity.

 

[sophiecentaur]

"In case of permanent magnet why we do not have to supply energy to maintain magnetic dipole currents to keep the magnet accelerated?
"
In a permanent magnet, these 'circulating currents' are not interacting with anything which could dissipate the energy.
The same happens in a superconducting magnet, in which the resistance is effectively zero and the current does not transfer any energy.

 

[sweet springs]

Born2bwire, Thanks for your quick and detailed answer. also to you, sophiecentaur.
Let me confirm my understanding of what you say.

Since these currents are from the atomic orbitals, there is no need to keep supplying energy because the orbitals are stable themselves. On a very basic level, if we have an electron orbiting in a circle, we do not need to expend any energy to keep it orbiting, only a constant force. However, when we ourselves physically move the magnets around a magnetic field, we are inputting and taking out energy from these orbitals. That is, if I pull two magnets apart, I impart work that gets injected back into the magnetic fields. This would correspond to adding energy into the electron orbits.

----------------------------
Do the two types of the equivalent large loop currents, i.e.
A adding up of atomic loop currents of a magnet
B net loop current in a superconducting ( or zero resistance ) circuit
behave differently under a magnetic field, i.e.
A keep accelerated
B stop accelerated after all the current kinetic energy are transferred to the whole body kinetic energy
?
----------------------------
Regards.

 

[sweet springs]

Hi. No reply means agreement, I guess and go on.

【Question】At t=0 in no gravitational vacuum space, The same type of two magnets are placed still counter.
Figure 　　０------｜------０
One of the magnets should be replaced by one of the followings of the same shape and the mass.
A-1 A closed loop net current, equivalent to adding up of atomic loop current, in the wire of resistance R.
A-2 A closed loop net current, equivalent to adding up of atomic loop current, in the wire of resistance 0.
B-1 A loop net current, equivalent to adding up of atomic loop current, conditioned constant during the process by the designed electric circuit and battery inside the body, in the wire of resistance R.
B-2 A loop net current, equivalent to adding up of atomic loop current, conditioned constant during the process by the designed electric circuit and battery inside the body, in the wire of resistance 0.
C Arranged molecules composed of S monopole, the distance bar and N monopole, equivalent to adding up of atomic loop current

Q1. Which ones move the same way as the magnet?
Q2. As for them where do kinetic energy come from?

【Answer】
A1. B-1,B-2 and C. B-1 generates heat Q also.
A2. The kinetic energy of the body is
Magnet: -∫ｄVmagnet　M・ΔH　 where ΔH =（▽H・v + ∂H/∂t）Δt , change of magnetic intensity.
B-1: -Δ(energy in battery)
B-2: -Δ(energy in battery) - Q
C : -Δ（stress energy stored in the bar)　　　

Does this QA make sense?
My remaining interest in this issue is, How M・ΔH≠0 and q(vXB)・v=0 harmonize?

Magnetic fields do NOT work on particles with 0 spin, but DO work on particles with charge and spin, don't they ?

Regards.

 

[cesiumfrog]

ah, magnetic fields, the invisible inclined slopes..

The magnets are pinched still. there's no electric field. Then at time zero they are released and start to move. In such a case, zero electric field at time zero could be the driving force?

(Haven't read the whole thread but) I see your point that some initial work appears to be done by a field that is purely magnetic. The fact is that the rule "magnetic fields do no work" was never really intended to apply to intrinsic magnetic dipoles (just as it would not apply to free magnetic monopoles). Nonetheless, in the case of the atoms of your magnet, even the intrinsic magnetic dipole can to a reasonable extent be attributed to rotation in the electron cloud/orbital (and could be modeled like a tiny electric current loop with zero resistance), and from the rest frame of any point in this rotating charge distribution (unlike the rest frame of the whole atom or apparatus) there actually is an external electric field (due to relativistic effects which naturally explain magnetic force) acting even at time zero.

 

[kcdodd]

You have to make a distinction between a magnetic dipole formed by "spinning electric charge", and that which would be formed by two magnetic charges (a pure dipole). Spinning charge has some internal energy associated with the rotation, and so any work done comes from this and not the magnetic field. I do not know for sure which type quantum spin is.

 

[sweet springs]

Dear kcdodd. Thanks for your comment.

Let me classify circulation of current in the following three.
A net current in artificail loop circuit
B quantum motion of electrons around the core in atom
C quantum spin of charged particle

On case A, I agree you

Spinning charge has some internal energy associated with the rotation, and so any work done comes from this and not the magnetic field.

But as for quantum cases B and C, I am not sure if such motions can tenure energy in the system and sometimes pour it our for kinetic enrgy increase. Regards.