Do Magnetic Fields Do Nonzero Work on Moving Objects?

[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 energy increase. Regards.