# Can a magnet's magnetic field perform work on another magnet?

Miyz
Hallo everyone,

Can a magnet do work on another magnet? (I believe it can. Just wanted to make sure.)

What formula's do you use to support you're answer?
Finally,
I know that magnetic field can not do ANY work on a free charge based on Lorentz force so no need to reference that.
Regards,

Miyz.

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Miyz

Page 8-12.

Miyz,

Mentor
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Here is my previous response, with two minor edits:
Well, I think that I am ready to post some final conclusions on my part:

1) a [STRIKE]motor[/STRIKE] magnet is governed by classical electromagnetism. I.e. It follows Maxwells equations and the Lorentz force law, the "EM laws".

2) from the EM laws the power density transferred from the fields to matter (the work on matter) is E.j

3) therefore, the B field does not directly do work under any situation governed by the EM laws, including [STRIKE]motors[/STRIKE] magnets.

4) however, the B field does store energy and Faradays law relates E to B and Amperes law relates j to B and E, so the B field does do work indirectly, through its impact on E and j.

5) tethering and other related concepts are irrelevant because they are internal forces and internal forces cannot do work on a system

Darwin123

Hallo everyone,

Can a magnet do work on another magnet? (I believe it can. Just wanted to make sure.)

What formula's do you use to support you're answer?
Finally,
I know that magnetic field can not do ANY work on a free charge based on Lorentz force so no need to reference that.
Regards,

Miyz.
The magnetic field is not doing any work on the electric charge carriers. It is doing work on the matrix of nuclei that keep the electrons in the magnet.
A magnetic is not composed of electric currents alone. It contains the atoms which supplied the electrons that created the electric current. The work done on the magnets includes the work done on the atoms from which the electrons were supplied.
Even when the magnetic field of one magnet does work on the other magnetic, it does not do work on the current. The electric currents can be pictures as d-orbital electrons jumping from nucleus to nucleus. However, the nucleus and the jumping electrons are oppositely charged. There is an electric field from the nucleus that attracts the jumping electrons.
The result is that when the electric current changes direction, the jumping electrons change direction. The jumping electrons then pull the nuclei by its electric field. It is the electric field that does work on the nuclei.
The thing to remember is that "the magnet" is a system. It isn't just electric currents. If there weren't nonmagnetic forces holding the magnet together, the electrons would not stay in the magnet.
Work done on any component of a system is not necessarily the work done on the system. The electric currents are a component of the magnet, not the magnet itself.
A magnetic field can't do work on a current. However, a magnetic field can do work on a system that includes a current.

Q-reeus
If the almost consensus position in https://www.physicsforums.com/showthread.php?t=621018, from which this follow-on obviously derives were true (dW = E.j dv for any EM system), then uniformly magnetized permanent magnets should interact as though they were perfectly conducting surface current inductors. That is, the so-called surface magnetizing currents Im owing to bulk cancellation of the combo of orbital and spin electronic contributions to magnetization, should perfectly obey Lenz's law and the consequences of the classical Faraday's law curl E = -dB/dt from which Lenz's law derives. So a long straight magnetized rod enclosed within a similarly shaped solenoid should completely demagnetize when the solenoid generates a B field Bs equal in magnitude and of the same sign as that of the magnet's initial B field Bm. [Edit: not quite perfectly, as there is a finite but relatively tiny 'angular KE' contribution owing to the electronic gyromagnetic ratio μ/S ~e/me] This manifestly does not happen. The actual magnetic response is known to be quite complex and material dependent - particularly in the demagnetizing regime when Bs opposes Bm. Assuming the rod is fully magnetized, when Bs has the same sign as Bm, typically there is very little change in the latter regardless of how great Bs is made.

In short, permanent magnets do not obey classical EM in this important respect, and it cannot be maintained that dW = E.j dv covers the situation. I therefore disagree with #3, while #4's picture of magnetization as "d-orbital electrons jumping from nucleus to nucleus" is at best only partially true (orbital contributions are an important contribution in ferrites but not otherwise) and imo misses the real point here. QM 'exchange interactions' stemming from Pauli exclusion principle are intimately tied up with any detailed energy exchanges (includes magnetic domain growth and reorientation), an observation I admit to not being at all qualified to expand upon in any detail. Beside that, there is the electron's intrinsic magnetic moment which clearly cannot be modeled as a tiny classical loop current. If it could, then particularly when Bs has the same sign as Bm, Lenz's law would continue to hold as for a classical perfectly conducting solenoid but does not. I followed only a tiny fraction of the postings in the above linked thread, so pardon please if I am repeating other's arguments already made there.

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permanent magnets do not obey classical EM in this important respect,
Please provide a mainstream reference supporting this or a rigorous derivation from Maxwells equations which supports your point.

Classical EM does not explain how a material is magnetized, but given that it is magnetized, it correctly describes the forces and energy.

Q-reeus
Please provide a mainstream reference supporting this or a rigorous derivation from Maxwells equations which supports your point.
The rigorous derivation you require of me and no one else here has been adequately summarized by use of my example in #5 imo. Instead of a terse challenge, how about furnishing your own 'rigorous', or just rational, reconciliation of your viewpoint in #3 with the long-magnetized-rod-in-solenoid scenario I have furnished.
Classical EM does not explain how a material is magnetized, but given that it is magnetized, it correctly describes the forces and energy.
Easy to just say. Then provide your own explanation of just where the total conventionally calculated magnetic energy density comes from when, say, Bs = 100*Bm (hint here: (a+b)2 = a2+b2+2ab, and, even allowing for non-linearity in getting to the b2 bit (non-linear magnetization), it's that 2ab bit that could be a bit worrying for your viewpoint - imho). [Forgot to explicitly add that we assume magnetic saturation early on here, say when Bm = 0.01 Bs (final)] That is, how do you equate net solenoid input energy with the notional net stored energy using only ME's? No problem computing solenoid input energy via integrating over a non-linear rod magnetic susceptibility. But how to explain how those tiny magnetic dipoles somehow resist Lenz's law to give that ~ 2ab part. Moral - don't try putting me on the back-foot pal! Looks like our relationship is back to the usual situation. :tongue:

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I don't know, how often I posted this trivial thing now, but you can describe permanent magnets within usual classical Maxwell electrodynamics by using the effective magnetization current in the Ampere-Maxwell Law, $\vec{j}_{\text{mag}}=c \vec{\nabla} \times \vec{M}$, where $\vec{M}$ is the magnetization density of the magnet, in addition to the usual convection currents of moving charges, $\vec{j}_{\text{convection}}=\rho \vec{v}$. The conduction current is usually described in linear-response approximation to the electric field by Ohm's law, $\vec{j}_{\text{cond}}=\sigma \vec{E}.$ These are the usual simplified equations assuming bodies at rest and the velocity of all charges much smaller than $c$, i.e., the non-relativistic approximation for the description of matter. Note that this approximation can be misleading. E.g., the description of the homopolor generator always needs a fully relativistic treatment. It's one of the most prolific direct application of relativistic effects in engineering :-).

I do not know of any example where Maxwell electromagnetics is proven wrong within the range of applicability of the classical approximation to full quantum electrodynamics, which is of course the most comprehensive theory we have about electromagnetics. This holds for both, "vacuum QED", where one considers scattering events of a few particles (usually two particles) mediated by the electromagnetic interaction, and "in-medium QED" like plasma physics and condensed-matter physics.

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Instead of a terse challenge, how about furnishing your own 'rigorous', or just rational, reconciliation of your viewpoint in #3 with the long-magnetized-rod-in-solenoid scenario I have furnished.
Fair enough. See here for a rigorous proof based on established mainstream science demonstrating that the power density delivered by an EM field is given by E.j in all cases: http://farside.ph.utexas.edu/teaching/em/lectures/node89.html

You are the one attempting to overthrow established mainstream science with nothing more than a handwaving assertion of some problem with no evidence to support it, either theoretical or experimental. It isn't up to me to prove you wrong, it is up to you to prove yourself right.

Moral - don't try putting me on the back-foot pal! Looks like our relationship is back to the usual situation. :tongue:
I don't know what you mean by "the back-foot", but if you cannot justify your assertion here then there is nothing left to do, the default position (particularly on PF) is that the mainstream scientific theory stands in the absence of compelling evidence to the contrary (which you certainly have not provided).

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Q-reeus
Flux quantization in superconducting circuits, as experimentally verified in 1961 by Fairbanks & Dever, Doll & Nabauer, means that a closed circuit supercurrent can only respond to a time-changing flux - and thus an E = -dA/dt, in discrete jumps. In between, no change occurs and in that interval Lenz's law fails totally, and holds only as an average over a periodic interval. An electron can in a way be thought of as the ultimate in supercurrent miniaturization - with the added restriction there are no flux jumps at all. Hard then to see how any time-changing E fields involving relative motion of fully magnetized magnets can be made to 'do work' on each other - save for the usual resistive eddy currents which are not the main concern here. As we are merely talking about a redistribution of energy within a system, seems a whole lot more sensible to me to treat the situation in terms of magnetic energy only, at least for slow motions in the frame of interest.

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Q-reeus
Fair enough. See here for a rigorous proof based on established mainstream science demonstrating that the power density delivered by an EM field is given by E.j in all cases: http://farside.ph.utexas.edu/teachin...es/node89.html [Broken]
I will give it a look over. [Edit: Now had a look; this is just a pretty standard derivation of Poynting's theorem. Not at all in conflict with #5 and #10 imo.]

As far as this bit goes:
You are the one attempting to overthrow established mainstream science with nothing more than a handwaving assertion of some problem with no evidence to support it, either theoretical or experimental. It isn't up to me to prove you wrong, it is up to you to prove yourself right.
Overthrowing mainstream science? Putting things a little dramatically there. Well as I say, why not just give your own explanation. Still, if it comes down to a case of quoting esteemed authority figures, I just managed to find the following, which might give pause for thought: http://physics.stackexchange.com/qu...field-do-work-on-an-intrinsic-magnetic-dipole A range of opinions, but I side with Lubos Motl there.

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Gold Member
To a non-physicist, it seems intuitively obvious that a magnet does work, as when picking up a paperclip. I was easily able to find the following link to confirm that is true.

Question

Since magnetic forces can do no work, what force IS doing the work when a bar magnet causes a paper clip to jump off a table and stick to the magnet?

The original assumption that a magnetic field can do no work is incorrect. A magnetic field has an energy density that is equal to the magnetic induction (B) squared divided by twice the permeability (mu sub zero). If you were to sum (integrate) this energy of the magnet over all of its field before it picked up the paper clip and compared it to the same sum after you picked up the paper clip, you would discover that there was a loss of field energy. The paper clip has in effect 'shorted out some lines of magnetic flux'.

How much energy was lost? If you took hold of the paper clip and pulled it out to such a distance that the magnetic pull was insignificant, the work you did in this process would exactly equal the amount of energy lost when the clip was on the face of the magnet. When you picked up the clip with the magnet the clip was accelerated toward the magnet acquiring kinetic energy. This kinetic energy will equal, ignoring air drag, the loss of magnetic energy in the field. This kinetic energy will be dissipated in the form of heat on impact of the clip with the magnet.

For further understanding of the energy in a magnetic field, you may want to study magnetic fields in solenoids. See the Reference below.

Physics, Volume 2 by Halliday and Resnick

Answered by: Robert Gardner, M.S., Retired Physicist

Respectfully submitted,
Steve

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Overthrowing mainstream science? Putting things a little dramatically there.
You are specifically claiming that Maxwell's equations predict that putting a bar magnet in a current carrying solenoid will demagnetize it, are you not?

That is clearly contrary to experiment, so if Maxwell's equations actually made such a prediction then they would be overthrown. Indeed, that was your point in suggesting that they make such a prediction. So I think the description is accurate, not dramatic.

However, your claim is also unsubstantiated (either via reference or derivation) and it appears that you have no plans to substantiate it, so it can be safely dismissed.

I just managed to find the following, which might give pause for thought: http://physics.stackexchange.com/qu...field-do-work-on-an-intrinsic-magnetic-dipole A range of opinions, but I side with Lubos Motl there.
As I said in in my point 4 both E and j depend on B, so B does work indirectly. In particular, Lubos is talking about the magnetization which is directly linked to j via the equation that vanhees71 posted above.

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To a non-physicist, it seems intuitively obvious that a magnet does work, as when picking up a paperclip.
The work is entirely accounted for by E.j so the B field only does work via its influence on E and j. See the reference I posted above for a derivation.

Gold Member
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Dotini, there is no contradiction between the quote you give and the fact that magnetic fields don't do work. Of course, if you compare the final state (paper clip attached to the magnet) with the initial state (paper clip separated from the magnet), you of course find that the change in magnetic-field energy is given by the work necessary to pick up the paper clip, attaching it to magnet.

This is precisely the content of Poynting's theorem, nicely explained at DaleSpam's link. This epxlains the the work is done by induced currents and electric fields during the transient (i.e., time-dependent!) situation when picking up the paper clip!

Gold Member
I can create a charged object by rubbing a balloon on my hair. And then do work with it by rolling an aluminum can around on the floor. No magnet is required in this instance, as the work is done by an electric field.

Is this agreeable? Or is the work done by me moving the balloon?

Respectfully,
Steve

Gold Member
The original assumption that a magnetic field can do no work is incorrect.
Answered by: Robert Gardner, M.S., Retired Physicist

magnetic fields don't do work.

Shocking and disconcerting that physicists and perhaps even textbooks are in disagreement!

Respectfully,
Steve

Q-reeus
You are specifically claiming that Maxwell's equations predict that putting a bar magnet in a current carrying solenoid will demagnetize it, are you not?
Go back and read what I actually said and argued in #5, and then try and not twist it out of shape, as you proceed to do below.
That is clearly contrary to experiment, so if Maxwell's equations actually made such a prediction then they would be overthrown. Indeed, that was your point in suggesting that they make such a prediction. So I think the description is accurate, not dramatic.
Nonsense. The aim was to show that Faraday's law applied to a permanent magnet modeled as a classical charge/current distribution would indeed necessarily 'discharge' as claimed there. Do you dispute that simple observation? That this is not the case points to the radically different response of a real magnet - owing to QM. Stop twisting what I have been saying!
However, your claim is also unsubstantiated (either via reference or derivation) and it appears that you have no plans to substantiate it, so it can be safely dismissed.
Is this how the real DaleSpam defends his own position?
Q-reeus: "I just managed to find the following, which might give pause for thought: http://physics.stackexchange.com/que...agnetic-dipole" [Broken]
The derivation there is for force density, not power density. If you go through the next step then you get E.j. As I said in in my point 4 both E and j depend on B, so it does work indirectly.
Huh? As I said, there are a range of views expressed there, and I back those of Lubos, which is *not* just about force density! Try reading at least all of his entries there.
As Lubos rightly imo points out in that link I gave, electrons cannot be successfully modeled as the limit of a classical loop current. Electrical interactions of the E.j type simply do not and cannot apply in that wholly QM regime. And it carries over to a permanent magnet as a QM glued ensemble of such. You can dismiss this yet again as 'hand-waiving', but I notice you still haven't supplied any kind of coherent rebuttal to either #5 or #10. Just hope I don't get stuck in a useless circular dialogue with you here. Please, be prepared to shift position, however painful it seems at the time. Must go. :zzz:

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I can create a charged object by rubbing a balloon on my hair. And then do work with it by rolling an aluminum can around on the floor. No magnet is required in this instance, as the work is done by an electric field.

Is this agreeable? Or is the work done by me moving the balloon?
I don't think that classical EM (Maxwell's equations and the Lorentz force law) accurately describes the work on the can. Classical EM does accurately describe the work on the paperclip. The two situations are not analogous.

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Go back and read what I actually said and argued in #5, and then try and not twist it out of shape, as you proceed to do below.
Tell me how I am twisting this out of shape:
So a long straight magnetized rod enclosed within a similarly shaped solenoid should completely demagnetize when the solenoid generates a B field Bs equal in magnitude and of the same sign as that of the magnet's initial B field Bm. ... This manifestly does not happen.

Huh? As I said, there are a range of views expressed there, and I back those of Lubos, which is *not* just about force density!
You must have started responding before my edit.

Gold Member
I don't think that classical EM (Maxwell's equations and the Lorentz force law) accurately describes the work on the can. Classical EM does accurately describe the work on the paperclip. The two situations are not analogous.

Franklin and Faraday may have begun the study of electricity and magnetism, but I must assume that Maxwell and Lorentz did not end it.

Respectfully,
Steve

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Electrical interactions of the E.j type simply do not and cannot apply in that wholly QM regime.
I agree.

And it carries over to a permanent magnet as a QM glued ensemble of such.
I do not agree. If this were correct then classical mechanics would never be valid as every classical object is a "QM glued ensemble". As long as the energies and masses in your system are all much larger than the Planck scale then you are in the classical limit of QM and classical physics applies.

I notice you still haven't supplied any kind of coherent rebuttal to either #5 or #10.
Correct, and I will not until you provide some solid supporting evidence. The burden of proof is on you, not me; I will not accept it simply because you cannot be bothered to support your own claims. I have supported mine.

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Franklin and Faraday may have begun the study of electricity and magnetism, but I must assume that Maxwell and Lorentz did not end it.
Agreed. So what? Do you think that means that classical EM does, in fact, accurately describe the work done on the aluminum can?

Gold Member
Agreed. So what? Do you think that means that classical EM does, in fact, accurately describe the work done on the aluminum can?

What else could it be? I'm only a retiree/hobbyist, reading only basic textbooks on electricity and magnetism at this time, so I really have no idea of what else it could be.

Respectfully yours,
Steve

Homework Helper
Gold Member

Page 8-12.

Miyz,

MIT is certainly a respectable organization, but that does not mean that every detail of everything published by them is rigorous and accurate. First, it looks as though these are course notes for an introductory level course on electricity and magnetism, and so it is not unreasonable to expect that some important details may be glossed over in the interest of not making the course material too complex for a 1st or 2nd year student. Second, any author, whether they work for MIT or not, is capable of both making mistakes, and having fundamental misunderstandings.

That said, I would argue two things that are in disagreement with that article:

(1) The net force on a magnetic dipole placed in a magnetic field $\mathbf{F}=\mathbf{ \mu } \cdot \mathbf{ B }$ is not truly a magnetic force,. It is the net result of the magnetic force on the current elements in the loop and whatever (nonmagnetic!) agent/force is responsible for maintaining the current in the loop (there are of course other forces at play which make the loop go where the current elements go, by keeping the current confined to the loop, but these are irrelevant to this discussion, and incapable of doing work on the loop/dipole as they are internal forces).

(2) Since the magnetic force on each current element is always perpendicular to the motion of the current element, the work is not done by the magnetic field, but rather by whatever agent maintains the current in the loop/dipole.

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If the almost consensus position in https://www.physicsforums.com/showthread.php?t=621018, from which this follow-on obviously derives were true (dW = E.j dv for any EM system), then uniformly magnetized permanent magnets should interact as though they were perfectly conducting surface current inductors. That is, the so-called surface magnetizing currents Im owing to bulk cancellation of the combo of orbital and spin electronic contributions to magnetization, should perfectly obey Lenz's law and the consequences of the classical Faraday's law curl E = -dB/dt from which Lenz's law derives. So a long straight magnetized rod enclosed within a similarly shaped solenoid should completely demagnetize when the solenoid generates a B field Bs equal in magnitude and of the same sign as that of the magnet's initial B field Bm. [Edit: not quite perfectly, as there is a finite but relatively tiny 'angular KE' contribution owing to the electronic gyromagnetic ratio μ/S ~e/me] This manifestly does not happen. The actual magnetic response is known to be quite complex and material dependent - particularly in the demagnetizing regime when Bs opposes Bm. Assuming the rod is fully magnetized, when Bs has the same sign as Bm, typically there is very little change in the latter regardless of how great Bs is made.

In short, permanent magnets do not obey classical EM in this important respect, and it cannot be maintained that dW = E.j dv covers the situation. I therefore disagree with #3, while #4's picture of magnetization as "d-orbital electrons jumping from nucleus to nucleus" is at best only partially true (orbital contributions are an important contribution in ferrites but not otherwise) and imo misses the real point here. QM 'exchange interactions' stemming from Pauli exclusion principle are intimately tied up with any detailed energy exchanges (includes magnetic domain growth and reorientation), an observation I admit to not being at all qualified to expand upon in any detail. Beside that, there is the electron's intrinsic magnetic moment which clearly cannot be modeled as a tiny classical loop current. If it could, then particularly when Bs has the same sign as Bm, Lenz's law would continue to hold as for a classical perfectly conducting solenoid but does not. I followed only a tiny fraction of the postings in the above linked thread, so pardon please if I am repeating other's arguments already made there.

Classically, permanent dipoles are modeled as the limiting case of a current loop shrinking to zero size, but in a way that leaves its magnetic dipole moment constant.

As you point out, this model is not entirely accurate ( for one there must somehow be some mysterious energy source which keeps the magnetic dipole moment constant when subjected to external field, not to mention that elementary particles like electrons have a dipole moment associated with them that only comes in quantized values), but it does correctly predict the net force and torque on permanent dipoles without introducing an additional axiom to theory (one treating magnetic dipoles as fundamental and different from the other two types of fundamental sources, point charges and currents).

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Dotini, there is no contradiction between the quote you give and the fact that magnetic fields don't do work. Of course, if you compare the final state (paper clip attached to the magnet) with the initial state (paper clip separated from the magnet), you of course find that the change in magnetic-field energy is given by the work necessary to pick up the paper clip, attaching it to magnet.

This is precisely the content of Poynting's theorem, nicely explained at DaleSpam's link. This epxlains the the work is done by induced currents and electric fields during the transient (i.e., time-dependent!) situation when picking up the paper clip!

To expand on this view, which I agree with entirely (with the exception of the first sentence, as, obviously, the author's bold claim that "The original assumption that a magnetic field can do no work is incorrect." clearly contradicts the fact that magnetic fields don't do work), consider that the energy density associated with the magnetic field of a current loop is created when the current in the loop is first established. During the establishment of the current, some non-magnetic force (usually an electric force supplied by a battery or other power source) must do work against the back-EMF created by the changing magnetic field that exists as the current changes from zero to its final value. The net work done by that non-magnetic force is exactly equal to the energy that as attributed to the magnetic field once it is fully established.

Gold Member
I looked up Poynting's theorem; it seems to have some qualifications.

http://www.phy.duke.edu/~rgb/Class/Electrodynamics/Electrodynamics/node33.html

"It seems, then, that Poynting's theorem is likely to be applicable in a microscopic description of particles moving in a vacuum, where their individual energies can be tracked and tallied:

but not necessarily so useful in macroscopic media with dynamical dispersion that we do not yet understand."

Respectfully,
Steve

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What else could it be? I'm only a retiree/hobbyist, reading only basic textbooks on electricity and magnetism at this time, so I really have no idea of what else it could be.
The ideal gas law for the pressure inside the balloon, Hookes law for the tension in the balloon, and Newton's laws for the force on the can. Maxwell's equations don't figure in that kind of a scenario, at least not classically.

My position here is the same as it was in the earlier thread and I would say(with a slight reservation) that magnetic forces can do work.A good example of this was given by Dotini in post 12.

I would justify my position by describing that the force between the magnet and paper clip is best described as being a "magnetic force".It all boils down to accepted definitions and having done some searches,my impression is that there seems to be a majority who refer to such forces (and the force on a current carrying wire in a B field) as being magnetic.

My reservation stems from the fact that there are four fundamental forces named,in brief,as:

Weak
Strong
Electromagnetic
Gravitational

Forces,of course,are given other,more specialised names depending on the situation being considered.There's quite a long list of forces which includes,turning forces shear forces drag etc.
These other named forces may well be combinations of one or more of the four main forces but that is usually irrelevant.Suppose,for example,that an applied physicist or engineer was on a problem calculating work done against friction and then somebody came along and claimed "in actual fact the frictional force is electromagnetic in nature and blah blah blah".The physicist/engineer probably won't give a hoot and continue to refer to it as a frictional force.

Perhaps there would be agreement if the forces discussed in these threads were best described as electromagnetic forces.

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My position here is the same as it was in the earlier thread and I would say(with a slight reservation) that magnetic forces can do work.A good example of this was given by Dotini in post 12.
Do you believe that classical EM accurately describes the paperclip? If so, then the power density is E.j, and any work done by B is only through it's impact on E and j.

My post above refers to definitions,accepted nomenclatures.What word(s) would you use to name the force on the paperclip or the current carrying wire?The "magnetic" force seems to be a preferred description according to searches I have made so far.See,for example,the MIT lectures on the subject.
If we were not to call it the magnetic force then I have suggested that the electromagnetic force may be a better description,but is this being too fussy?.I imagine that most textbooks(at least up to A level standard)would still continue to refer to the "magnetic" force so as to distinguish it from the electric force between stationary charges.

I would have to look at how the E.j approach applies to paper clip/magnet type scenarios but I think I already agreed that it is relevant to current carrying wires.In the previous thread I suggested that E needs defining since there is the E.j due to the power supply which is the source of the energy and the E.j due to the back(counter emf) which illustrates the power output.