Is the Magnetic Force Really Doing No Work?

[cabraham]

Your argument doesn't seem to adress Studiot's main concern. For a magnet that is large in comparison to whatever it is lifting, the fringing fields are negligable when the object is far from the edges (i.e. more or less centered). Even for the car/crane example, a uniform verticle field is a decent rough approximation. More importantly, a purely vertical field can produce a net force of attraction that is vertical on an object containing many charges (but not on a single point chrge) due to the interactions between charges. This is born out by my previous calculation in which I assumed a vertical external field.

Are you quite sure this is what you meant?

That V x B always has a Z component because there is always a vertical component to the B field?

1) No, the lateral component of the B field is not negligible. It is not "fringing", it is a solenoidal field. All B fields are. As I stated there is a lateral & vertical component to the B field, even when the object is flush against the pole of the magnet. If the lateral part was negligible, why would the iron filings on the paper exhibit curvature? The solution to this problem was given to all of us in middle school. Since then we've extended it, & refined it, but the answer lies in the curvature of the flux lines.

2)What I meant & said is that v x B has a z component because there is always a lateral B component. The lateral B component crossed with the lateral velocity component results in a z force proportional to the sine of the angle between v & B. That is just elementary vector calculus. The iron filings discussed above demonstrate the curvature of the flux lines, revealing the lateral (x,y) & vertical (z) components. This issue is so well closed that debate is pointless.

All science is based upon observation & measurement. All I've presented is built upon observation & measurement, & I am not aware of my omission of pertainent details. If I have erred by omission or otherwise, please enlighten me. The x-y-z issue has been not only discussed, but proven w/ scientific findings dating to the 19th century, still valid today. What more do you want? Best regards to all.

Claude

 

[Studiot]

One thing I notice is that no one has asked for any proof/derivation of the formula I gave.

In fact it comes out very nicely using the theorems of virtual work.

Let the car be suspended in equilibrium under the magnet.

Now consider a virtual displacement, d, in the direction of the lifting force, P.

By the principle of virual work

External work done by lifting force = Internal work done by magnetic field = internal energy loss/gain

Pd = 1/2HB = 1/2x1/\muxB²xAxd

 

[Studiot]

The H (or B) field lines emerge from the electromagnet pole downward in the z direction, wrapping around horizontally, & then upward in the z direction into the opposite pole.

The first part of this statement appears to be at variance with your own later statements. It very clearly states that the flux emerges with only a vertical component, an infinitesimal distance below the surface of the magnet.

The second part is pure nonsense, which was carried on into later posts.

How can the flux curve upwards to the opposite pole, which lies below the magnet on the object being lifted?

The field is far from solenoidal.
Instead of insulting my schooldays I suggest you visit a manufacturer of electrical machinery and study the shape of the flux field in the gaps between the poles.

Why do you act as though you have the only answers, when even your links do not work?

 

[cabraham]

The first part of this statement appears to be at variance with your own later statements. It very clearly states that the flux emerges with only a vertical component, an infinitesimal distance below the surface of the magnet.

The second part is pure nonsense, which was carried on into later posts.

How can the flux curve upwards to the opposite pole, which lies below the magnet on the object being lifted?

The field is far from solenoidal.
Instead of insulting my schooldays I suggest you visit a manufacturer of electrical machinery and study the shape of the flux field in the gaps between the poles.

Why do you act as though you have the only answers, when even your links do not work?

Boy that was rude! I never claimed to have the only answers, but rather that the scientific community has had the right answer all along. You're saying that the whole science world has been wrong for over 100 yrs. & you have it right. You, sir, are the one that claims to have a monopoly on wisdom. I am adhering to the body of work of many others over the span of 2 centuries. Let's now examine the "infinitessimal distance below the pole" & the curvature of flux lines.

There is curvature right at the pole face & even in the interior of the bar magnet. It is universally known that a magnet is a collection of a great many tiny magnets called *domains*. Each domain has a N & S pole of its own with solenoidal (wrap-around) flux lines. At the pole face, each domain at the pole-air boundary has wrap-around flux lines. So the lateral component at the pole face is quite substantial.

This is the only view that agrees with observation. Considering the wrap-around nature of flux lines for each tiny domain, the center of the bar magnet exhibits the smallest lateral flux line component. That is likely why a magnet is weakest at its center.

Of course placing 2 bar magnets together, N against S poles results in a new magnet. The center is now the junction of the N & S poles of the individual magnets, & is the weakest in terms of force. The flux lines at this new center have much less wrap around when the magnets are joined due to the geometry than they had as individual separated magnets.

Cutting a single magnet in 2 results in 2 magnets. The original center of the 1st magnet was weak, but becomes quite strong after the cut. Why is that so? The answer lies in the wrap-around nature of flux lines emanating from the poles.

As far the the shape of the rotating machinery flux field in the gap between the poles is concerned, remember that we are dealing with 2 different magnets. The rotor has flux lines emerging from its magnetic pole as does the stator. In the rotor-stator air gap, we see a flux field formed by 2 discrete magnets. The electromagnet lifting a car is the topic under discussion. A single magnet has wrap around flux lines. If you don't know that, you should not be disputing anybody. Two magnets in proximity have a flux distribution in the gap as you mentioned, but each individual magnet has its own solenoidal field. All machinery texts will point that out. Your analogy is not an apple-apple comparison.

No other view fully agrees with observation. I do not claim a monopoly on wisdom, or access to inside info, or anything like that. Minds far greater than mine have already examined this issue & published the results for all to benefit from. Until better equipment can take measurements down to a finer level, what we currently have will have to do. Cheers.

Claude

 

[gabbagabbahey]

1) No, the lateral component of the B field is not negligible. It is not "fringing", it is a solenoidal field. All B fields are. As I stated there is a lateral & vertical component to the B field, even when the object is flush against the pole of the magnet. If the lateral part was negligible, why would the iron filings on the paper exhibit curvature? The solution to this problem was given to all of us in middle school. Since then we've extended it, & refined it, but the answer lies in the curvature of the flux lines.

My point is that even a purely vertical B-field can lift a magnetizable object upwards. The vertical component of the field is actually the primary contributor to the net upward force on the car when it is lifted by the crane's magnet. The easiest way to show that is to look at the force on a single dipole, \textbf{F}=\mathbf{\nabla}(\textbf{m}\cdot\textbf{B}), the dot product indicates that the component of the field that is parallel to the dipole moment is responsible for the net force on it.

 

[gabbagabbahey]

The field is far from solenoidal.

Solenoidal, in this context, means that the divergence of the field is zero, which is in agreement with one of Maxwell's equations.

 

[Studiot]

Solenoidal, in this context, means that the divergence of the field is zero, which is in agreement with one of Maxwell's equations.

I stand corrected.

 

[cabraham]

My point is that even a purely vertical B-field can lift a magnetizable object upwards. The vertical component of the field is actually the primary contributor to the net upward force on the car when it is lifted by the crane's magnet. The easiest way to show that is to look at the force on a single dipole, \textbf{F}=\mathbf{\nabla}(\textbf{m}\cdot\textbf{B}), the dot product indicates that the component of the field that is parallel to the dipole moment is responsible for the net force on it.

I realize that, but the argument that B fields can "do no work" is based on the force exerted on a single electron. That is where v x B comes into play. The force on a dipole is different. No dispute there. Hopefully you will concur that an e- being yanked upward towards the magnet is being acted on by a lateral component of B, not vertical.

A dipole will indeed be attracted to the magnet in accordance with the vertical (z) component of B. This is best described by the "A" vector, which is vector magnetic potential, & B = curl A. By definition, A is the vector corresponding to the magnitude & direction that a dipole is displaced when placed in the B field.

The question involved single charged particles. But if the magnetic forces involved are dipoles, such as the rotor & stator of a rotating machine, then the dipole approach is used. I believe that we are in agreement, so why argue? Cheers.

Claude

 

[gabbagabbahey]

I realize that, but the argument that B fields can "do no work" is based on the force exerted on a single electron. That is where v x B comes into play. The force on a dipole is different. No dispute there. Hopefully you will concur that an e- being yanked upward towards the magnet is being acted on by a lateral component of B, not vertical.[/color]

A dipole will indeed be attracted to the magnet in accordance with the vertical (z) component of B. This is best described by the "A" vector, which is vector magnetic potential, & B = curl A. By definition, A is the vector corresponding to the magnitude & direction that a dipole is displaced when placed in the B field.

The question involved single charged particles. But if the magnetic forces involved are dipoles, such as the rotor & stator of a rotating machine, then the dipole approach is used. I believe that we are in agreement, so why argue? Cheers.

Claude

I disagree with the part highlighted in red. The upward force on an electron, due to its orbital motion, in an external magnetic field must come from the horizontal component of the field. However, electrons (and atoms) also have an intrinsic dipole moment, and an entirely vertical field can still produce an upward force on them as a result. Close to a large (in comparison to the object being lifted) magnet, the vertical component of the field is much larger than its horizontal components (when you are more or less centered below one of its poles). Moreover, the intrinsic magnetic moments of atoms are often much larger than the dipole moments due to the orbital motion of their electrons. When you lift iron filings, or a car, using a magnetic field, the vertical component of the field is usually the dominant factor.

We are really talking about dipoles for the crane/car example of Studiot's (Intrinsic dipole moments (spin) are the dominant source of Ferromagnetism)--- or when lifting iron filings with a fridge magnet. As far as I can tell, Studiot's main issue at this point is how, according to the Lorentz force law, the force on a dipole can be parallel to the applied magnetic field. This is the issue I think your earlier argument was failing to address. I think you were sidestepping the issue by claiming that the horizontal components of the field were responsible.

 

[Born2bwire]

One thing I notice is that no one has asked for any proof/derivation of the formula I gave.

In fact it comes out very nicely using the theorems of virtual work.

Let the car be suspended in equilibrium under the magnet.

Now consider a virtual displacement, d, in the direction of the lifting force, P.

By the principle of virual work

External work done by lifting force = Internal work done by magnetic field = internal energy loss/gain

Pd = 1/2HB = 1/2x1/\muxB²xAxd

Nobody has ever said that you cannot extract energy from the magnetic field. I have stated this multiple times previously. The caveat is that the direct mediator for transfering this force is always an electric field in respect to the frame of the charges. As such, it is perfectly consistent to be able to use a frame of reference where we only see magnetic fields to calculate the force from the energy since classical electromagnetics follows special relativity.

 

[cabraham]

I disagree with the part highlighted in red. The upward force on an electron, due to its orbital motion, in an external magnetic field must come from the horizontal component of the field. However, electrons (and atoms) also have an intrinsic dipole moment, and an entirely vertical field can still produce an upward force on them as a result. Close to a large (in comparison to the object being lifted) magnet, the vertical component of the field is much larger than its horizontal components (when you are more or less centered below one of its poles). Moreover, the intrinsic magnetic moments of atoms are often much larger than the dipole moments due to the orbital motion of their electrons. When you lift iron filings, or a car, using a magnetic field, the vertical component of the field is usually the dominant factor.

We are really talking about dipoles for the crane/car example of Studiot's (Intrinsic dipole moments (spin) are the dominant source of Ferromagnetism)--- or when lifting iron filings with a fridge magnet. As far as I can tell, Studiot's main issue at this point is how, according to the Lorentz force law, the force on a dipole can be parallel to the applied magnetic field. This is the issue I think your earlier argument was failing to address. I think you were sidestepping the issue by claiming that the horizontal components of the field were responsible.

I was not sidestepping any issue. Of course the dipole moments are important, I never denied that. The question I was addressing was how on Earth can a z-oriented B field lift an e- vertically. I was just pointing out that there is some component of B in the lateral x-y plane. The Lorentz force law involving v x B does not fail for individual e- as long as we account for thr lateral B component. That was my point.

I am well aware that orbiting e- & moving charges in general have an associated magnetic dipole moment. That has never been disputed. If you examine the moments involved you can ascertain the upward lift force. I was only demonstrating that the Lorentz law is still valid when viewing an individual e-. Some inferred that modern science cannot explain the upward lift, & that Lorentz' law was invalid, & I just addressed that issue to show that it is valid.

I don't have any beef w/ your magnetic moment discussion at all.

Claude

 

[gabbagabbahey]

The question I was addressing was how on Earth can a z-oriented B field lift an e- vertically. I was just pointing out that there is some component of B in the lateral x-y plane. The Lorentz force law involving v x B does not fail for individual e- as long as we account for thr lateral B component. That was my point.

And I feel this argument is misleading. In many cases, the horizontal components of the (external) field contributes very little to the lifting power of a magnet, and hence are often negligible (Like in the crane/car experiment). This doesn't mean that you can't apply the Lorentz force law and end up with a net vertical force from an entirely vertical field. The equation for the force on a dipole can be easily derived directly from the Lorentz force law. As can the equation for the force on a magnetizable material.

 

[UWStudent101]

Would anyone be able to give me an explanation of the magnetic forces regarding physically how they work? It is their physical property that I find fascinating rather than their equations and vector solutions. Any theories or explanations would be appreciated.

 

[quantum123]

Very interesting stuff. I happened to get an email notification and then start reading this thread. Thanks to you guys for the thought provoking discussion using various angles to look at this phenomenon, which is still rather mysterious to me.