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Comment

Can someone make F, v, and B in the math part look like bold and italic. And also make the HTML F, v, and B bold and italic. Thanks. dave 00:41 24 Jul 2003 (UTC)

Just noting that this seems to have been done. JesseW 08:54, 11 Jun 2005 (UTC)

The Origins of the Lorentz Force

Q. When was the name 'Lorentz Force' first used?

I'm asking because Maxwell has a similar expression in his treatise, whereas Hendrik Lorentz (Lorentz transformation) was not active at Maxwell's time. Ludwig Valentine Lorenz (Lorenz gauge) published some papers before Maxwell but then we don't have a 't' in his name.

If we could track down the first use of the name then we could get this clarified. --Equanimous2 20:49, 16 July 2006 (UTC)

A. The Lorentz force appeared as equation (77) in Maxwell's 1861 paper On Physical Lines of Force, and the vXB term also appeared as a Coriolis Force at equation (5) in the same paper. The Lorentz Force also appeared as equation (D) in his 1864 paper A Dynamical Theory of the Electromagnetic Field. Equation (D) is one of the original eight Maxwell's equations.

The Maxwell/Heaviside equations of 1884 do not include the Lorentz Force because they are written in partial time derivative notation, whereas the vXB term is a convective term.

The Lorentz Force predates Lorentz. It is credited to Lorentz because he independently discovered it in about 1894 in connection with the motion of an electron in a magnetic field. (203.115.188.254 07:41, 18 February 2007 (UTC))

Question? Is The Lorentz Magnetic Force correct?

The force on a charged bodie in a magnetic field is F= q(v.B + vxB). Lorentz has left out the parallel force component (v.B) when the angle between the field and the velocity of the charged particle is not perpendicular. The parallel force component produces a simple harmonic motion parallel to the magnetic field. This motion effectively 'traps' the particle in an orbit around the magnetic field direction. If there is no parallel velocity then the orbit is perpendicular to the magnetic field. If there is a parallel velocity (vcosa) then the orbit is inclined to the filed axis. If there is no perpendicular velocity (vsina) then the orbit collapses to a simple harmonic vibration along the the magnetic field axis. This conclusion should be easy to test. Conservation of energy is conserved in this formulation, e.g mv^2 = m((vcosa^2) + (vsina)^2)= mv^2(cosa^2 + sina^2).

By ignoring the parallel velocity Lorentz's formulation does not conserve energy when the velocity is not perpendicular.

The so-called mirror effect in the magnetosphere could be diposed of with realization that particles could be 'trapped' by the parallel simple harmonic motion along magnetic field.

An example of this result is given mathematically; let B=J and v=(I + J) then the force would be F= qvB= q(I + J)J = q(-1 + K) This force attracts (-1) omnidirectionally and pushes in the K-direction, resulting in F=q(-1 + K)J = q(-I -J) This force movers in the negative, v direction -(I + J).

This results in F= -q(I + J)J = q(1 - K) . The result of this force is F = q(1 - K)J = q(I + J) and the cycle repeats. You can see that the parallel force along J causes the simple harmonic motion along the J-axis and the perpendicular force I, causes the rotation around the J axis. These two actions cause an inclined orbit around J, not a spiral along J.

The mathematics that describes this action is quaternion. Vector mathematics (J^2=1) never lets the cycle get negative it is always J to 1 to J to 1.

Comments welcome.

Definition of Lorentz force is ambiguous

I would like to point out the the definition of the Lorentz force is ambiguous unless one specifies what the velocity v is referred to: since the current in a wire does not depend on the reference frame, it (and therefore the magnetic field) is uniquely determined by the relative velocity of the electrons and ions in the wire (which is unrelated to the velocity v in the Lorentz force). Also, the resultant electric field of the wire is obviously zero. So the definition of the Lorentz force is ambiguous unless one specifies what v is referred to. I would think that this should be the center of mass of current system producing the magnetic field, i.e. approximately the frame where the ions in the wire are at rest (see also my website http://www.physicsmyths.org.uk/#lorforce in this respect).--Thomas

• See the discussion at Talk:Magnetic_field#velocity with_respect to what ?. --Bob Mellish 18:47, 5 November 2005 (UTC)

asdasdasdasd

Should the Lorentz Force Include the Electric Field?

I noticed an inconsistency between this article and the one regarding the magnetic field. In the latter the definition of the Lorentz Force law does only contain the magnetic field term, whereas for this article it contains also the electric field. I think that inclusion of the electric force in the Lorentz force is counter-intuitive and misleading. The point is that for the electric field term there is already another name i.e. the 'Coulomb Force' and one should not combine this with an (unnamed) magnetic force into a resultant 'Lorentz Force'. Fact is that the magnetic force (or what is traditionally understood as 'Lorentz Force') exists separately from the Maxwell Equations. The latter would not be a complete description of electrodynamics without the additional magnetic force, so the term 'Lorentz Force' should only refer to the latter, as otherwise the phenomena would be mixed up.--Thomas

There are sound reasons why Lorentz Force means the total electromagnetic force. I can explain if you like; it has to do with the fact that electric and magnetic phenomena are all mixed up! But, in any case, that's how the term is used, as you can see for example here: . I have clarified the Magnetic Field article to reflect this. -- SCZenz 20:07, 10 November 2005 (UTC)

Quoting sources where the same didactical error with regard to the use of the term 'Lorentz force' is being made (in my opinion anyway) doesn't really answer the points I made above. Mixing up things is unlikely to clarify the understanding in any branch of science. If you want to emphasize a unified view of electromagnetic phenomena, this should be done separately under a different header, or better even in a different article altogether. --Thomas

To disagree with the unanimous opinion of reputable sources on electromagnetism would violate the policy Misplaced Pages:No original research. -- SCZenz 19:20, 11 November 2005 (UTC)

The point is that it is not unanimous. Many physics textbooks use the term 'Lorentz Force' merely for the magnetic force F=qvxb . The American Heritage Dictionary defines it as 'The orthogonal force on a charged particle traveling in a magnetic field', and (what could be more reputable) on the web page of the Lorentz-Institute ( http://ilorentz.org/history/lorentz/lorentz.html ) it says 'A magnetic field exerts a force on these particles, now called the "Lorentz force" '(this is also how I learned it and how it is correct I think following my arguments given above).

It is therefore not about 'original research' here, but about presenting theoretical issues in a conceptually and didactically structured and unambiguous way. After, all this article is not for yourself, but for people who are ignorant about 'Magnetic Field' or 'Lorentz Force' or 'Coulomb Force' and want to have a basic understanding of it. Any inconsistencies in the usage of these terms will therefore only be confusing. --Thomas

If the language is really inconsistent in reputable sources—and I don't think the American Heritage dictionary is intended to be an accurate source for details on physics—then we should note both. But it is unquestionably original research for us to choose which one (especially the one less common in physics textbooks) because an editor is of the opinion that one is better than the other.

Oh, and in case you're wondering, the reason to call q(vxB+E) the Lorentz force is that it is invariant under Lorentz transformations, while (as you've pointed out elsewhere) qvxB is not. Only the sum has any physical meaning, unless E happens to be 0.

That being said, if there's a textbook or published paper that clearly uses it for only the magnetic field (rather than mentioning it in passing), we will have to note both uses. -- SCZenz 18:14, 12 November 2005 (UTC)

It would be nice if the relationship of the Lorentz force to the Lorentz transformations and relativity were mentioned in the article. I'm not the one to write this though. Alison Chaiken 22:01, 28 December 2005 (UTC)

• Misplaced Pages should reflect actual usage, and its clear that usually the electric field is included. However, there's no harm pointing it out if it is sometimes defined differently (I think I recall seeing a distinction in one textbook between the "Lorentz force" which is purely magnetic, and the "Lorentz force law" which has both E and B.) In fact, if you'd care to dig out the original publication by Lorentz to see which he used, that would be a good addition to the article. I don't have a copy of Jackson here, but that may have the reference. --Bob Mellish 19:34, 12 November 2005 (UTC)

Spiral?

I don't think the description of "spiraling" is correct.

The E,B and v terms are all vectors and depending on their various relative orientations, many different paths may result. that I don't think I would characterize as "spirals"

For instance, if the E and B fields are perpendicular and the initial velocity is 0, then the particle will travel in a "Cycloid" (the weird looking path that a point on the rim of a bicycle takes).

If E=0 and V is perpendicular to the B field then it goes in a circle.

Cloud chamber tracks are spirals because the particle is loosing kinetic energy and velocity as it creates the trails.

If E!=0 and B=0 then the particle undergoes constant acceleration in the E direction. (Straight line or parabolic depending on initial velocity)

If E=0 and B!=0 then particle undergoes constant acceleration "perpendicular" to the B field and the velocity which can be motionless,circulular or a helix depending on the initial velocity.

Lorenz Equations

For some reason the phrase "Lorenz Equations" links here, and I guess it makes sense as Lorenz might be seen as a mispelling of Lorentz. However "Lorenz Equations" also refers to the equations governing the Lorenz Attractor and as such it would probably be better to redirect to there, unless there is some other reason the phrase ends up here that I'm missing.

Merge

I add notice box about merging with electromagnetic force since the two definitions talk about the same thing. Only that they are seen from different angle (electromagnetic/relativity view here and quantum/field theory there); of course, unless the definition here (or there) changes (e.g. we exclude electric component here). Tttrung 09:55, 14 October 2006 (UTC)

I am against a merge. The Lorentz force ought to be contained in a seperate article. Lorentz Force is a commonly used term and it does warrant a seperate article to discuss the history of the term and the law.Millueradfa 03:50, 16 December 2006 (UTC)

I am against a merge as well. This is a no-brainer. The Lorentz force is a subset of Maxwell's field equations. I will remove the merge tags. --Sadi Carnot 16:16, 13 January 2007 (UTC)

Alternative form ??

To my opinion, the part of the article about the Lorentz force, called "Alternative form", should be removed as misleading. It is correct and reasonable to write the Lorentz force for a point particle with the charge q. Writing the Lorentz force in the form of an integral over some volume (presumably, the volume of a body) causes many questions. Consider for example a real situation when one places a body (metallic, or dielectric, or whatever) in an external electric field. The external field polarizes the body, so that the electric field inside the body turns out to be substantially different from the external field (in a metal it is zero, for instance). In the discussed formula the integral is presumably taken over the volume of the body, hence E there is the total internal fields, i.e. the sum of the external field and the field induced by the redistribution of charges in the body. This total field is a complicated function of the external field, the shape of the body, and its dielectric properties and is actually unknown. In addition, the body of a complicated shape in external electric and magnetic fields will in most cases experience not only just a force, but also the moment of force. So the physical meaning of the discussed formula is fully unclear.

Template:Electromagnetism vs Template:Electromagnetism2

I have thought for a while that the electromagnetism template is too long. I feel it gives a better overview of the subject if all of the main topics can be seen together. I created a new template and gave an explanation on the old (i.e. current) template talk page, however I don't think many people are watching that page.

I have modified this article to demonstrate the new template and I would appreciate people's thoughts on it: constructive criticism, arguments for or against the change, suggestions for different layouts, etc.

To see an example of a similar template style, check out Template:Thermodynamic_equations. This example expands the sublist associated with the main topic article currently being viewed, then has a separate template for each main topic once you are viewing articles within that topic. My personal preference (at least for electromagnetism) would be to remain with just one template and expand the main topic sublist for all articles associated with that topic.--DJIndica 22:09, 6 November 2007 (UTC)

Faraday's law vs Lorentz force

I don't think that it's correct to say that the Lorentz force "is the solution to the differential form of Faraday's Law" or that they "both express the same physics", as added by 61.7.150.6 last April. They are different laws, expressing different physics, and are related only by special relativity.

Say you drop a loop of wire through a fixed, inhomogeneous magnetic field. A current will be generated, to be sure, but the electric field will be zero everywhere. In Faraday's law, an electric field is created by a changing magnetic field, but here the magnetic field is constant, and the electric field is zero. This is called motional EMF, and it's a direct consequence of the Lorentz force (qv x B), and has nothing to do with Faraday's law (which is responsible for something different, induced EMF).

If, on the other hand, you hold the loop of wire steady while moving the device that generates the inhomogeneous magnetic field, then the Lorentz force (qv x B) does nothing (since the charges aren't initially moving), but Faraday's law says that the changing magnetic field creates an electric field, which in turn pushes the electrons around the loop.

"Motional EMF" and "Induced EMF" are different physics, applicable in different situations, as explained in any good textbook. The reason people get them confused is: (1) Inertial transformations can turn one into the other (a fact which Einstein used in the introduction to his paper on special relativity), and (2) Some physics teachers will teach the so-called "Faraday's law" in a particular form (namely, in terms of "flux through a loop of wire") which encompasses both induced EMF (when the wire is fixed) and motional EMF (when the wire is moving). I don't think this is standard, though, and the most standard ways in which Faraday's law is written (its "differential form" and "integral form") do not include motional EMF.

If no one objects, I plan to edit the article accordingly.--Steve (talk) 00:45, 21 February 2008 (UTC)

Sounds good - go for it. PhySusie (talk) 01:16, 21 February 2008 (UTC)

There are two aspects to electromagnetic induction. There is the induced electric field that is generated when a stationary wire is exposed to a changing magnetic field. There is also the electric field generated when a wire moves in a magnetic field. Both of these aspects are covered by Faraday's law and by the Lorentz force. If we take the curl of the Lorentz force, we get Faraday's law.

The former aspect is given by E = -(partial)dA/dt and the latter aspect is given by E = vXB. If we take the curl of the combination, we get the differential form of Faraday's law in full with total time derivatives. The former aspect alone just gives the partial time derivative version of Faraday's law as is used to derive the EM wave equation. But the E =vXB term leads to the (v.grad)B term that enables Faraday's law to be written with a total time derivative and include all aspects of EM induction. 203.99.236.10 (talk) 06:51, 28 February 2008 (UTC)

When a loop of electric current rotates in a magnetic field as in the case of an AC generator, this simultaneously involves Faraday's law and the F = qvXB force. The rate of change of magnetic flux by virtue of the enclosed area of the loop rotating leads to Faraday's law. The induced EMF in the wire is given by E = vXB. Is somebody seriously trying to argue that Faraday's law and the Lorentz force are expressing different physical effects.

The arguments of Sbyrnes321 above explain one of the aspects of EM induction using Faraday's law, and the other aspect using the Lorentz force. In fact both aspects can be explained by both laws. 122.52.185.53 (talk) 09:52, 28 February 2008 (UTC)

The Full Expression

I notice that Sbyrnes321 keeps reverting the full expression for the Lorentz force to the masked version and claiming that the masked version is more transparent. The E term is given by the sum of -(partial)dA/dt, where A is the magnetic vector potential, and the Coulomb force. Sbyrnes321 wants to conceal this fact claiming that the mere expression E tells us more. How can that be? How can a symbol for a vector field function tell us more than the contents of a that function?

It's not surprising that he should think like this bearing in mind his total confusion about the relationship between Faraday's law and the Lorentz force. He wants to mask out all the material that clarifies that relationship. If we take the Lorentz force in the form that Sbyrnes321 disaproves of, and differentiate it, we get Faraday's law. It seems that Sbyrnes321 wants to mask the full expression because it exposes his own lack of understanding of the link between Faraday's law and the Lorentz force. 122.52.185.53 (talk) 10:01, 28 February 2008 (UTC)

Hello! I'll start with the first point. The question is, which of the following expressions is better:

${\displaystyle \mathbf {F} =q\cdot (-\nabla \Phi -{\frac {\partial \mathbf {A} }{\partial t}}+\mathbf {v} \times \mathbf {B} ),}$

${\displaystyle \mathbf {F} =q\cdot (\mathbf {E} +\mathbf {v} \times \mathbf {B} ),}$

To start with, they're manifestly equivalent, and contain exactly the same information. So the only question is, which form is most helpful, and gives the most insight to a typical reader? I feel strongly that it's the second one, with E. One reason is that E is a physical, measureable field, whereas the scalar and vector potentials are not (since they are only defined up to gauge transformations). At least in classical electromagnetism, the measureable quantities E and B are the more fundamental starting points, and the potentials are defined in terms of them, as convenient mathematical tools for their manipulation (this is how it's presented in every electromagnetism textbook I've seen; I'd be happy to provide examples). Another reason is that it's relatively well-known that an electric field produces a force qE on a charged particle, whereas the potentials (A in particular) are much less familiar to typical readers. I believe that a reader with only a basic knowledge of electromagnetism will be able to get more insight and understanding out of the second form than the first. Finally, if you look at wikipedia, journal articles, books, and textbooks, the electric field E is discussed all the time--No one is advocating that authors go through their books, and cross out every mention of E, replacing it with ${\displaystyle -\nabla \Phi -\partial \mathbf {A} /\partial t}$. To me, that's good evidence of a consensus in the physics and engineering communities that E is a useful, substantial concept in its own right, and not uniformly inferior to its expression in terms of the scalar and vector potentials (which is what you seem to be implying above). What do you, and other people, think?

As for the second point, I think part of the problem is that the following law:

${\displaystyle {\mathcal {E}}=-N{{d\Phi _{B}} \over dt},}$

where ${\displaystyle \Phi _{B}}$ is the flux through each of N turns of a wire, is often called "Faraday's Law". The following two are also called Faraday's law:

${\displaystyle \oint _{C}\mathbf {E} \cdot d\mathbf {l} =-\ {d \over dt}\int _{S}\mathbf {B} \cdot d\mathbf {A} }$

${\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}}$

which are equivalent to each other, but not to the first, because the first also includes motional EMF, when the wire is in motion. I'm fairly confident that Faraday's law (in the latter forms) cannot be proven by differentiating the Lorentz force (at least, without also assuming special relativity): For example, when light is propegating through a vacuum, the changing electric field creates a magnetic field, but it has nothing to do with the Lorentz force, since there are no charged particle around to experience a force. I cited a reliable source backing up what I said about the relation between Faraday's law and the Lorentz force. Do you have a reliable source for what you're saying? I'd be very interested in seeing that, so please post it here if possible.

I consider myself knowledgeable on this topic, but heck, I've been wrong before. I'm interested in hearing what you and anyone else have to say, and especially interested in any references you might provide. Also, I hope that in the future you can try a bit harder to be follow the spirit of WP:AGF. --Steve (talk) 22:10, 28 February 2008 (UTC)

Steve, the mistake you are making is this. The equation that you quote,

${\displaystyle {\mathcal {E}}=-N{{d\Phi _{B}} \over dt},}$

is indeed Faraday's law in full and it does, as you say, contain the motional dependent term vXB. This is because we are using total time derivatives.

The other term that you listed,

${\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}}$

only contains partial time derivatives and just as you say, it doesn't involve the vXB effect. This latter term is one of Heaviside's group of Maxwell's equations. Maxwell had already shown that the vXB effect was not needed for the derivation of the EM wave equation, and so presumably this is one of the reasons why Heaviside only used partial time derivatives.

As you know, total time derivatives are related to partial time derivatives through the expression d/dt = (partial)d/dt + v.grad

The v.grad term is known as the convective term and in the case of Faraday's law, the convective term is (v.grad)B . This can be shown by taking the curl of vXB. It expands into four parts and only one of those parts, (v.grad)B remains because div B is zero and also because v is not a vector field and so the differential terms vanish.

Hence, since curl A = B and since the curl of the Coulomb force is zero, then if we take the curl of the full version of the Lorentz force, it is clear how we end up with the total time derivative version of Faraday's equation,

${\displaystyle \nabla \times \mathbf {E} =-{{d\mathbf {B} } \over dt},}$

This linkage is not so transparent if we simply use the vector E to cater for the combination of the Coulomb force and the case of electromagnetic induction that occurs when a magnetic field varies.

The Lorentz force in full contains three distinct effects. There is an E field yielded by the Coulomb force, there is an E field yielded by the ${\displaystyle -{\frac {\partial \mathbf {A} }{\partial t}}}$, and there is an E field yielded by vXB. 203.99.236.12 (talk) 03:41, 29 February 2008 (UTC)

Hi again, thanks for responding.

I understand your proof, but I believe that the key step is a nontrivial application of special relativity. As I said, I fully understand and accept that the Lorentz force and Faraday's law are linked by special relativity---and in fact I put that in the article before you deleted it.

Say you have a particular particle, with some charge q, velocity v, and position r, and you want to take the curl of the Lorentz force law. You can't, since both sides of the equation are vectors, not vector fields. So what you do instead is define F(x) to be the force that would be experienced by a particle with the same charge q and velocity v, but at an arbitrary position x. OK, so far so good.

Now, when you do the manipulations you mentioned, you get

${\displaystyle \nabla \times \mathbf {F} =-q(d/dt)(\mathbf {B} )}$

i.e., the total derivative, or the time-rate of change of the B-field experienced by the particle. But this is only about F, not E. That necessitates the last step, which is to Lorentz-transform to a frame moving at velocity v relative to the original one. (This requires substantial effort, since the Lorentz-transformation affects curls, time-derivatives, forces, and magnetic fields.) In the new frame, the Lorentz-force law says that the (transformed) F is q times the (transformed) E, since v is zero. Finally, you transform back (which again, requires knowing the exact transformation laws for E, etc.), all the factors with gamma cancel out, and you have Faraday's law.

But if you don't use the additional assumption that Maxwell's equations are relativistically invariant (including assuming the exact form of the transformation laws for E and B), you cannot derive Faraday's law from the Lorentz Force. In a given, fixed, frame of reference, they are different physical effects.

I agree with you that writing the equation in terms of the scalar and vector potentials helps illuminate the connection with Faraday's law. But the connection with Faraday's law is not the only aspect of the equation, which describes an important phenomenon in its own right. And by writing the law itself with E, and not the potentials, we're expressing the phenomenon of the Lorentz force in the form which is both the most common, and the most easily-comprehensible. How about if I change it to E at the top, but also put in a section on the connection between Faraday's law and the Lorentz Force, which would include the equation in your preferred form, and also this derivation?

Another thing is that the following paragraph was deleted:

"The Lorentz force, along with Maxwell's equations, form the basis of the theory of classical electromagnetism. While Maxwell's equations describe how electrically charged particles and objects give rise to electric and magnetic fields, the Lorentz force law completes that picture by describing the effect of these fields on other electrically charged particles and objects."

I'm willing to change "Maxwell's equations" in the first sentence to "the four Maxwell's equations", to clarify that I don't mean his original set, but rather the four equations that are today universally known as Maxwell's equations. If I do that, would you agree with me putting it back in? Here's the quote, from a reliable source, which backs it up:

"In the last section we put the finishing touches on Maxwell's equations: . Together with the force law, F=q(E + v x B), they summarize the entire theoretical content of classical electrodynamics (save for some special properties of matter...) --Griffiths E&M, 3rd ed., p326.

What do you (and anyone else) think? --Steve (talk) 05:34, 29 February 2008 (UTC)

Oh, and here's the quote from Griffiths E&M 3rd ed., page 300-303, supporting my contention that the motional-EMF and inductive-EMF are different:

"In 1831 Michael Faraday : EXP 1: He pulled a loop of wire to the right through a magnetic field. A current flowed in the loop. EXP 2: He moved the magnet to the left, holding the loop still. Again, a current flowed in the loop...I don't think it will surprise you to learn that exactly the same emf arises in ...There are really two totally different mechanisms underlying . In Faraday's first experiment it's the Lorentz force law at work; the emf is magnetic. But in the it's an electric field (induced by the changing magnetic field) that does the job. Viewed in this light, it is quite astonishing that processes yield the same formula for the emf. In fact, it was precisely this 'coincidence' that led Einstein to --he sought a deeper understanding of what is, in classical electrodynamics, a peculiar accident..."

--Steve (talk) 05:43, 29 February 2008 (UTC)

Steve, nobody has been disputing that there are two distinct electromagnetic induction effects. There is the motion of a charged particle (or conductor) in a magnetic field vXB and there is the changing magnetic field effect on a stationary particle (or conductor) ${\displaystyle -{\frac {\partial \mathbf {A} }{\partial t}}}$. Maxwell goes into detail on the different mechanisms of each of these two effects. The two effects combine together to give both the Lorentz force and Faraday's law. Take the curl of the Lorentz force and we get Faraday's law.

What effect are you suggesting is covered by the Lorentz force that is not covered by Faraday's law, and vica-versa? Both laws cover both effects, accept that the Heaviside version of Faraday's law only covers the time varying effect. All this was sorted out long before relativity came on the stage. All relativity does is adds a correction factor which becomes pronounced at high speeds, but we don't need relativity to unite electricity and magnetism. Maxwell already did that.

If you want to mention that the Lorentz force is additional to the four Maxwell's equations which were produced by Heaviside and Gibbs in 1884 then at least you should also mention that the vXB force was actually removed from Faraday's law by Heaviside because it wasn't needed for the derivation of the EM wave equation. But it seems strange to use a partial differential form of Faraday's law which only contains one aspect of EM induction and then claim the second aspect for Lorentz when in fact it was well known already to Faraday and Maxwell and it appeared in Maxwell's original papers.

Think about it for a while before making any alterations because I can assure you that as it stands right now, it is thoroughly correct. The way it was before merely reflected a total misunderstanding of the where exactly the two aspects of EM induction fit into both Faraday's law and the Lorentz force.125.212.19.212 (talk) 13:31, 29 February 2008 (UTC)

Oops! Never mind what I said before, I think your proof of Faraday's law from taking the curl of the Lorentz force is wrong. Two reasons: (1) You have provided no reference. Original research is not allowed on wikipedia. (2) When you write E = -dA/dt - grad Phi, you're already assuming Faraday's law! (Take the curl of both sides). It's hardly surprising that you're able to derive Faraday's law when you already use it as an assumption. Try deriving Faraday's law from F=q(E+vXB) without replacing E by its expression in terms of scalar and vector potentials (an expression which is only possible because of, and equivalent to, Faraday's law).

I have a reliable reference (Griffiths) that states clearly that when you move a magnet near a stationary wire, it's Faraday's law and not the Lorentz force that produces the current. (The whole discussion is three pages, and this point is made very clear.) Likewise, when the wire moves and the magnet is stationary, the textbook says explicitly that it's motional EMF, caused by the Lorentz force, but not by "Faraday's Law" (i.e. the modern differential form of Faraday's law), but yes by the form of "Faraday's Law" in terms of flux through a wire. Therefore, the onus is on you to find an even more reliable source or sources for your claim. (19th-century papers are, as a rule, less reliable than modern textbooks or articles, so please look for the latter.) Sorry to be taking up your time, and thanks for working so hard on this article! --Steve (talk) 15:11, 29 February 2008 (UTC)

Steve, your first few sentences are absolutely correct but they totally undermine the overall point that you are making. The expression E = -dA/dt - grad Phi does indeed assume Faraday's law. But that expression is absolutely correct. Hence the conclusion is that the E term of the Lorentz force is the inductive aspect of Faraday's law. The inter relationship goes back at least as far as Maxwell's 1861 paper.

Any modern textbook that explores what the E in the Lorentz force is will conclude that it is E = -dA/dt - grad Phi.

At what point did textbooks begin to put a greater emphasis on covering up the underlying Faraday relationship E = -dA/dt - grad Phi by writing it simply as E?

E is electric field. It means simply 'force per unit charge'. It doesn't specify the source of this force. We do however know that it can arise from either/or Coulomb's law or Faraday's law.

Your textbook reference that says that an induced EMF arising from a changing magnetic field is Faraday's law is correct. It is indeed Faraday's law. It is also the E term in the Lorentz force.

I am not arguing with the textbooks. There is however a minor problem with terminology due to the fact that some textbooks use the term "Lorentz force" to cater for both the E and the vXB terms, whereas other textbooks use the term "Lorentz force" specifically to cater for the vXB term. There is a certain rationale to the latter usage in that the vXB term is the term that is additional to the Heaviside version of Maxwell's equations and that it can be made to appear as a result of Lorentz transformations (as it indeed can from any linear transformation).

So your textbook, that claimed that the EMF that is induced by moving the conductor in the magnetic field is the Lorentz force, was applying the term Lorentz force strictly to the vXB term.

This article however, applies the term Lorentz force to the total sum of E + vXB which in full is E = -dA/dt - grad Phi + vXB.

In actual fact, there is only a limited rationale behind classifying the first two terms as E field and the vXB term as magnetic force. In reality, all three are E field mathematically. But for EM wave purposes, we only consider the E field at stationary pints in space and so we ignore the vXB term. For the purposes of Faraday's law however E also equals vXB. It is a force per unit charge that applies at the location of the moving charge. The curl of this expression is unequivocally (v.grad)B which is the convective component of Faraday's law which brings the limited Heaviside version of Faraday's law (with partial time derivatives) into the full total time derivative form as is taught in high schools in relation to rate of change of flux.

A loop rotating in a magnetic field invokes the convective (v.grad)B aspect of Faraday's law and a magnetic field rotating about a stationary loop invokes the inductive aspect -(partial)dB/dt. Combined, these come to -(total)dB/dt which is the anti-curl of -dA/dt - grad Phi + vXB.

That final expression does not under any account constitute original research. It is found in any university textbook on EM. I first learned it in my standard university EM textbook. Off-hand I can't even remember it's name. It was either Leonhard Eyges of MIT, or Grant and Phillips. At any rate, the expression goes back to Maxwell and maybe even further back still. 203.99.236.11 (talk) 04:04, 1 March 2008 (UTC)

The presentation in the modern textbook I cited takes the view that E is a physical field, which is defined in terms of forces on stationary test charges. Likewise, B is a physical field defined in terms of forces on dipoles, or on moving test charges. Then Faraday's Law and Gauss's law for magnetism are written out. And only then can the scalar and vector potentials be defined, by invoking Helmholtz decomposition. That's the approach of Griffiths, and also of Jackson (p239). When you say, "Any modern textbook that explores what the E in the Lorentz force is will conclude that it is E = -dA/dt - grad Phi", that misstates the relation between the E and B on the one hand, and the potentials on the other: The potentials do not "lie behind" E and B, rather E and B are more fundamental, and due to certain empirical laws that they happen to follow (namely, Gauss's Law for magnetism and Faraday's Law), it turns out that scalar and vector potentials can be defined in terms of them. According to these reliable sources, the Lorentz Force is F=q(E+vXB), and a consequence of Faraday's Law is that the Lorentz Force can also be rewritten in terms of A and Phi. Maybe there are other presentations, but you need a reliable source for them.

Again, I showed a reliable source that clearly stated that Faraday's law and the Lorentz force describe different physical phenomena. For example, it said explicitly that when a moving magnet induces a current in a stationary loop of wire, the Lorentz Force cannot explain this phenomenon. If this is not true, you need to find an even more reliable source.

I'm sure you're busy, but I've read three standard university EM textbooks, and none of them say that Faraday's law can be derived from the Lorentz force (at least, without invoking special relativity and the specific Lorentz-transformation rules), and one of them strongly implies that it cannot. I know you may be busy, and maybe don't have all your old textbooks, but please try to find a reliable reference that backs up everything you're saying. Otherwise it cannot be put in the article.

I do appreciate that you're engaging me in this interesting exchange, though, and I'm glad you care so much about this article being accurate! Best, Steve (talk) 05:44, 1 March 2008 (UTC)

Steve, you say that "it (Griffiths) said explicitly that when a moving magnet induces a current in a stationary loop of wire, the Lorentz Force cannot explain this phenomenon."

The effect unequivocally comes from the E term in the Lorentz force. What is the exact page number and paragraph number in Griffiths, and what is the full quote?

The E term in the Lorentz force is the one that caters for E fields that are induced by time varying B fields, which is the case in question. The -(partial)dA/dt term is the particular component of the E field in question. If you think that I am wrong, then what do you think the E term in the Lorentz force caters for? 122.3.219.93 (talk) 11:12, 1 March 2008 (UTC)

Page 302, first paragraph. At this point in the book, the Lorentz Force equation (F=q(E+vxB)) has been introduced, but Faraday's Law has not. See the other excerpt above for context.

I don't think it will surprise you to learn that exactly the same emf arises in Experiment 2...if the loop moves, it's a magnetic force that sets up the emf, but if the loop is stationary, the force cannot be magnetic--stationary charges experience no magnetic forces. In that case, what is responsible? What sort of field exerts a force on charges at rest? Well, electric fields do, of course, but in this case there doesn't seem to be any electric field in sight. Faraday had an ingeneous inspiration: A changing magnetic field induces an electric field...

I think this quote makes it clear that Faraday's "inspiration" (that changing magnetic fields induce electric fields) is a phenomenon that is distinct from the Lorentz Force. Yes, the Lorentz Force says that stationary electrons respond to electric fields, but the Lorentz Force cannot explain where the electric field came from.

Equation bank

Since I'm tired of us talking past each other, here's an equation bank, so that we can be more on the same page. Feel free to add to it.

E1 F=q(E + v x B)

E2 ${\displaystyle \nabla \times \mathbf {E} =-\partial \mathbf {B} /\partial t}$

E3 EMF = -dPhi/dt for any loop of wire (stationary or in motion) and any magnetic field (constant or changing)

E4-1 ${\displaystyle \mathbf {F} =q\cdot (-\nabla \Phi -{\frac {\partial \mathbf {A} }{\partial t}}+\mathbf {v} \times \mathbf {B} )}$

E4-2 ${\displaystyle \mathbf {E} =-\nabla \Phi -{\frac {\partial \mathbf {A} }{\partial t}}}$

E4-3 ${\displaystyle \mathbf {B} =\nabla \times \mathbf {A} }$

The equation E1 is what all modern references call the "Lorentz Force". Many references actually use it to define E and B. The equation E2 is what all modern references call either "Faraday's Law" or "The differential version of Faraday's Law". Equations E1 and E2 contain different information, and neither can be derived from the other, since E2 gives no information about forces, and E1 contains no information about how E and B vary between different spacetime points.

Equation E3 is also called "Faraday's Law" in all modern references (a usage that Griffiths calls "confusing", since E2 is also called by this name). It contains the information of both E1 and E2. When the loop is stationary, it's exactly the same as E2. When the magnetic field is constant, it reduces to E1.

Equations E4 also contain the information of both E1 and E2. The information of E2 comes directly from taking the curl of both sides of E4-2. It has nothing to do with E4-1 (how do you simplify the curl of the force anyway?), so it's misleading in any case to say that you're "proving E2 from the 'Lorentz Force Law'". You're "proving" E2 from the definition of the scalar and vector potentials, and has nothing to do with any physical force.

So equations E1 and E4 contain different information. Which one of these two different laws should be called the "Lorentz Force" in the definition given in an encyclopedia article? Certainly the one that's used in every modern textbook, namely E1. Maybe some historical argument says that E4 is more appropriate, but that argument belongs in a "History" section, not the opening paragraph.

Does this help clarify what I'm saying? Thanks! --Steve (talk) 17:56, 1 March 2008 (UTC)

Steve, I see clearly where you are going wrong. You say, "The information of E2 comes directly from taking the curl of both sides of E4-2. It has nothing to do with E4-1"

Equation E4-1 is the same as equation E4-2 but with the extra vXB term added on. The curl of this extra vXB term will add the convective (v.grad)B term to the partial time derivative Farady's law at E2 and the result will be the total time derivative Faraday's law at E3.122.3.109.133 (talk) 19:36, 1 March 2008 (UTC)

Equation E4-1 is a formula for force. Equation E4-2 contains no information about the force on any particle. These two equations are qualitatively different, since F is not the same as E. When you add a term vXB to E4-2, you still have an equation that gives no information about force. Moreover, adding a term vXB to E4-2 doesn't make sense, since every point has some specific value of E, which is independent of the velocity of the test charge that you put at that point. For the force F, on the other hand, it makes perfect sense for it to be velocity-dependent, since F is defined to be the force on a specific particle, and that ought to depend on the velocity of that particle. You can't have different values of E for two particles at the same point but with different velocities. The equation

E5 ${\displaystyle \mathbf {E} =-\nabla \Phi -{\frac {\partial \mathbf {A} }{\partial t}}+\mathbf {v} \times \mathbf {B} }$

is an equation which I've never seen in any reference, and I don't see any way that it could be interpreted in a way that makes physical sense.--Steve (talk) 20:19, 1 March 2008 (UTC)

You seem to be having a big problem with the fact the E represents force per unit charge. And you want to use the term E to mask the source of the forces involved. You seem to think that E can't have two different values at a point where there exists two particles with different velocities. Why not? More importantly, can we have two particles at the same point anyway? 202.69.174.93 (talk) 07:53, 2 March 2008 (UTC)

I do have a big problem with the assertion that E is force per unit charge. In fact, E is force per unit stationary test charge. I think what you're saying is that E and F/q are always synonymous. If this were true, then plug into the Lorentz Force equation to get Eq = q(E+vXB), and therefore vXB=0 always---a manifestly false conclusion.

The electric field, in classical physics, is a single-valued function of space. Each point in space and time has a certain, specific, value of E, whether or not you put a test charge at that point. Likewise with B. This is clearly stated in any textbook.

Again, you won't find E5 in any modern reference book or article, for the good reason that it's not true and doesn't make sense.

There's nothing in classical electrodynamics that stops two charged blobs from passing through each other, if their charge is small enough that they don't repel each other away. But it's not an essential point anyway.

In both the references I have on-hand (Jackson and Griffiths), E and B are defined via the Lorentz Force equation. In this approach, the Lorentz Force equation, as an empirical statement about reality, contains a very limited amount of information:

The electromagnetic force on a test charge at a given point and time is a certain function of its charge and velocity, which can be parameterized by exactly two vectors E and B, in the functional form F=q(E+vXB).

As you keep saying, you want to put more information into the equation, namely the "source" of E. That's a fine thing to do, but then the Lorentz Force Law becomes a different, more specific, empirical statement about reality. According to all the references, the Lorentz Force Law does not contain this extra information, and the equation you favor would best be described as a "formulation of the Lorentz Force Law which also incorporates other aspects of electromagnetism". You have not provided any reference to the contrary, so what you're claiming cannot go into the article.--Steve (talk) 18:34, 2 March 2008 (UTC)

The Griffiths Reference

Steve, the quote from Griffiths does not mean that the Lorentz force cannot account for the EMF on a stationary charge. The quote from Griffiths simply states Faraday's law. It is Faraday's law that contributes part of the E term to the Lorentz force (The other part being from the Coulomb force). And the Lorentz force will indeed explain this in full if we write it out in full. However if we mask the two E field terms under the symbol E, as you wish to do, then the Lorentz force will not expose its origins in both Faraday's law and Coulomb's law.

You are the one who was so keen to write the Lorentz force in the manner that will mask the origins of the E field. I am the one that has been wanting to write out the full expression in order to clearly expose the origins of all the elements of the Lorentz force.

If you change the article and write F = qE + qvXB it will be technically correct, but it will be a dummied down article. Why bother to do that? Why not leave it as it is? It is written transparently and exactly as it appeared in equation (D) of Maxwell's original eight equations in 1864.

The way it is right now leaves nobody in any doubt about the origins of the three terms of the Lorentz force, and that if we take the curl of these three terms we will have Faraday's law in full and not just the limited partial time derivative version of Faraday's law that appears in Heaviside's version of Maxwell's equations. 122.3.109.133 (talk) 19:25, 1 March 2008 (UTC)

The quote from Griffiths states that "there doesn't seem to be any electric field in sight". Remember, that this is long after the discussion of the Lorentz Force. If the Lorentz Force included the phenomenon whereby changing magnetic fields create electric fields, that quote wouldn't make any sense.

Given that equations E1 and E4 contain different information, and that E1 is the one that today is universally used when reliable references define the "Lorentz Force Equation", we have to use E1. It would be incorrect to use E4. Again, we can include a history section where you can discuss in full detail what Maxwell did or did not write, and we can also include a section on "Formulations of the Lorentz Force Equation which also include other electromagnetic phenomena", and put E3 and E4 into it. I fully support putting in such sections. But the definition in the article has to conform with modern usage, as set out by reliable sources. --Steve (talk) 20:37, 1 March 2008 (UTC)

Steve, can you give me a single electromagnetic effect that is not catered for by the full Lorentz force expression? The case discussed in Griffiths was of a changing magnetic field acting on a stationary charge. That is catered for in the Lorentz force equation by -(partial)dA/dt. That expression unequivocally represents a changing magnetic field. When we take its curl, we end up with the limited partial time derivative case of Faraday's law curl E = -(partial)dB/dt. The fact that div B = 0 means that there exists a more fundamental magnetic vector A such that curl A = B. The vector A is every bit as much a magnetic field vector as is the vector B.

Are you trying to tell me that if we were to use the expression E in the Lorentz force, hence masking the underlying -(partial)dA/dt term, that this E wouldn't include any effects of Faraday's law? Of course it would. The E in the Lorentz force has always referred to -grad(phi) - (partial)dA/dt going right back at least to equation (77) in Maxwell's 1861 paper where he derived it from Faraday's law at equation (54).

There is no way that I am going to interpret Griffiths as having meant that the E in the Lorentz force doesn't include an EM induction effect. That was a very long shot on your part. Griffiths was simply saying that the E field on a stationary charged particle comes from the changing magnetic field, which we now know to be -(partial)dA/dt from Faraday's law. That E has always been included in the Lorentz force.

Likewise, the full Faraday's law involving total time derivatives that is taught in high schools includes all the effects in the Lorentz force. You have been basing your arguments on a limited partial time derivative version of Faraday's law that appears in Heaviside's versions of Maxwell's equations.

I am personally of the opinion that you began to edit this article before you were fully aware of the current state of knowledge. You thought that you had noticed things that hadn't been noticed before. You then began to list your observations before you had seen the completed pattern. Now you are rejecting that completed pattern merely to save face, since you made some erroneous deductions based on your incomplete knowledge.

Your initial point that E is more transparent that -grad(phi) - (partial)dA/dt was the thing that set the alarm bells ringing that we were dealing with somebody who wasn't really clear about what they were talking about, but yet presumed to be in a leadership role as regards the article.

The current expression is found in many textbooks and it is the most transparent expression. It goes back to Maxwell. If you change it, you are merely dummying down the article by replacing a transparent term with an opague term purely to back up your own misinformed viewpoint that E doesn't tell us anything about EM induction. 202.69.174.93 (talk) 08:15, 2 March 2008 (UTC)

You asked, "can you give me a single electromagnetic effect that is not catered for by the full Lorentz force expression?" I don't dispute that equations E4 can fully account for both the moving wire and the moving magnet. I am disputing that E4 is the "Lorentz Force Law". I would say that E4 is an "equation that incorporates both the Lorentz Force Law and other electromagnetic effects." And I am also disputing that E1 can (by itself) account for the moving magnet. What I am saying is consistent with textbook presentations, whereas you are making certain claims--in particular (1) your assertion that E5 is a correct and meaningful equation, (2) your claim that "The Lorentz Force Law implies Faraday's Law"--that are not in any modern textbook or reference that I've seen.

More evidence against the claim (2): see , which opens with "Many elementary texts on electricity and magnetism demonstrate for a simple example that the Lorentz force law implies Faraday's law of induction when partial B/partial t=0" (a fact which I stated above). It goes on to give a one-page general proof. But it is very much implied by this sentence and this article that E1 does not imply E3 when partial B/partial t does not equal zero, which is, again, exactly what I said above. Can you please find a reference that says that "The Lorentz Force Law" implies E2 or E3 in full generality? --Steve (talk) 18:57, 2 March 2008 (UTC)

Force per unit Charge

Steve, I've amended the article to reflect your preferred format. I have replaced two of the terms of the Lorentz force with the umbrella term E. The key below will be able to inform readers as to what the E refers to.

Your argument that E = E + vXB, therefore implying that vXB must always be zero was a totally specious argument. It was specious because the two E's are not the same. The equation is more accurately E(total) = E (electrostatic + EM induction for stationary charges) + vXB.

But in time, I believe that you will realize that you raised alot of complaints that have stemmed entirely from your own limited knowledge on the subject. The E in the Lorentz force was never restricted to the electrostatic Coulomb force. I'm not even going to bother looking for references because this is such a fundamental fact in EM theory that we shouldn't be having to debate it.

You began all this because you noticed that in the limited case of the partial time derivative version of Faraday's law that we find in modern Maxwell's equations, that this equation didn't cater for the vXB effect. Correct.

But you then wrongly assumed that the E term in the Lorentz force didn't cater for the EM induction effect associated with the EMF induced on a stationary charge in a changing magnetic field. And you then further resisted all attempts to write the Lorentz force in a manner that would clearly reveal the EM induction effect -(partial)dA/dt. You effectively argued that if we write the Lorentz force in the way that it is now presented, then the E term doesn't reveal its source and hence we cannot know that it comes partly from EM induction, even though we know it fine well.

You then noted that high school Faraday's law involving total time derivatives includes both of the EM induction effects. But you couldn't see the pattern, yet you openly declared yourself to be quite an authority on the whole matter.

I would say that in time, when you think about it more, you may even want to change it back again to the form that exposes the three terms of the Lorentz force. But meanwhile, I'm happy enough to leave it as it is because the readers can still see the meaning of E in the key below. 202.69.178.230 (talk) 07:06, 3 March 2008 (UTC)

First, about E and F. E is a function of space. At every time t and point r there is a unique, well-defined vector called E, which is a function of r and t. There aren't "two E's which are not the same", and there's no ambiguity in the term E. A particle at r and t experiences an electric field equal to exactly E(r,t), regardless of whatever velocity and charge that particle happens to have. If two blobs pass through each other, that doesn't mean that there are two simultaneous values of E for that point in spacetime: there's always one and only one E(r,t). Perhaps you've been confused by the fact that E(r,t) is often abbreviated E. Anyway, if you dispute this fact, and continue to assert that E5 and E4-2 are not mutually contradictory, then please, please re-read the first chapter of your electromagnetism textbook. Or email your old physics professor and ask. Or continue to look through textbooks and articles for equation E5, until you eventually convince yourself that no modern reliable source has ever written that equation down. (While you're at it, you can also search for the clam that "Faraday's Law is a consequence of the Lorentz Force Law".)

The other point that you keep trying to make is that if F=q(E+vXB), and if E and B contain all the information in electromagnetism, then all the information in electromagnetism is part of the "Lorentz Force Law". This is exactly like arguing that Newton's second law, F=ma, contains all the information in Hooke's Law, Newton's Law of Gravity, the friction law, etc., because that's all part of the "meaning of F". Do you see what I mean? Have you ever heard someone say that "Hooke's Law is a consequence of Newton's second law"? When a physicist is trying to demonstrate a new force law, would you say that that she is "doing research into Newton's second law"? Would it be appropriate for the wikipedia article on Newton's second law to put in a "key", saying "F=ma, where F is the sum of the spring force, the friction force, the gravity force, the normal force, the buoyancy force, ..."? Certainly not. But there it is, F is definitely in the equation of Newton's second law, and the buoyancy force is definitely part of the "full expression of F". Does this help clarify where I'm coming from? --Steve (talk) 22:12, 3 March 2008 (UTC)

Hello other editors!?

Since both this anonymous editor and myself are convinced that the other has some very fundamental misunderstandings about electromagnetism, could any other editors offer any comments? In case you haven't been following, here's an equation bank:

E1 F=q(E + v x B)

E2 ${\displaystyle \nabla \times \mathbf {E} =-\partial \mathbf {B} /\partial t}$

E3 EMF = -dPhi/dt for any loop of wire (stationary or in motion) and any magnetic field (constant or changing)

E4-1 ${\displaystyle \mathbf {F} =q\cdot (-\nabla \Phi -{\frac {\partial \mathbf {A} }{\partial t}}+\mathbf {v} \times \mathbf {B} )}$

E4-2 ${\displaystyle \mathbf {E} =-\nabla \Phi -{\frac {\partial \mathbf {A} }{\partial t}}}$

E4-3 ${\displaystyle \mathbf {B} =\nabla \times \mathbf {A} }$

Here are a list of points which I believe are true, which I'd like to put into the article, and which are under dispute. (Well, I can say for sure that 1,2,4,6 are under dispute; if any of the others are not under dispute, so much the better.)

1 Faraday's law is not a consequence of the Lorentz Force Law (at least, not without assuming special relativity).

2 E1 is the Lorentz Force Law. The equations E4 are a "formulation of the Lorentz Force Law that also incorporates other electromagnetic effects" (namely, Faraday's Law and Gauss's Law for magnetism, which are automatically built into the definitions of the scalar and vector potentials...take the curl of E4-2 or the divergence of E4-3). Therefore, E1 should be at the top of the article as the "Lorentz Force Law", and it would be incorrect (not merely confusing, but incorrect) to put E4 at the top of the article instead.

3 E3 (one version of "Faraday's Law"), like E4, can be described as a "formulation of the Lorentz Force Law that also incorporates other electromagnetic effects"---when B is constant in time, it reduces to E1, and when B is not constant in time, it contains different information. It would be appropriate to put E3 and E4 into a section entitled something like "Formulations of the Lorentz Force Law that also incorporate other electromagnetic effects".

4 The following equation is incorrect and doesn't even make sense:

E5 ${\displaystyle \mathbf {E} =-\nabla \Phi -{\frac {\partial \mathbf {A} }{\partial t}}+\mathbf {v} \times \mathbf {B} }$

where E is electric field and v is the velocity of, I guess, a particle at that point. An editor who would state and repeatedly defend this equation is not an editor who should be giving me a strongly-worded lecture about what E means.

5 When a loop of wire rotates in a fixed magnetic field, the EMF generated is "motional EMF" which can be entirely explained by the Lorentz Force Law, and has nothing to do with E2. When a magnetic field rotates around a fixed current loop, the EMF is generated by Faraday's Law E2, along with the first term of E1, F=qE. The equation E3, which is also called "Faraday's Law", explains both of these situations.

6 E is a more fundamental quantity than the scalar and vector potentials. It's misleading to imply that E is defined by E4-2. Rather, the scalar and vector potentials are defined by E4-2 and E4-3. In particular, when an equation involving E is introduced, it would be inappropriate to say afterwards, "...where E=-grad Phi-partial A/partial t".

7 Many modern treatments take the Lorentz Force Law to be the definition of E and B. When this approach is taken, then the Lorentz Force Law is not vacuously true by definition, rather it contains exactly the following empirical information, and no more:

The electromagnetic force on a test charge at a given point and time is a certain function of its charge and velocity, which can be parameterized by exactly two vectors E and B, in the functional form F=q(E+vXB).

So! What do other people think? Which if any of my above assertions is correct? Am I way off-base, or is the other editor? Should I be making the appropriate changes to the article, or should I be writing letters of apology to the students who had me as a TA for E&M last semester? :-) --Steve (talk) 18:19, 3 March 2008 (UTC)

Well, let's see. I'd call E1 the Lorentz force law, and Faraday's law obviously doesn't follow from that alone. E5 is obviously wrong. E4-1 is correct but very strange; you can write the force law in terms of E and B or in terms of Φ and A, but mixing them like that makes no sense. The only point I'm not sure I agree with is number 6; Aharonov-Bohm shows that E and B don't quite tell the whole story. -- BenRG (talk) 00:40, 4 March 2008 (UTC)

Thanks for responding! Fair enough regarding 6, I made the point a little stronger and broader than I needed to. Let me be more specific:

6': If we put E1 at the head of the article, we can follow that up with either "...where E is the electric field", or we can say "...where E is the electric field, which satisfies ". Of these, I'm asserting that the first one is better. The first one is not dumbed down, and not deceptive--it's exactly the appropriate description. --Steve (talk) 05:47, 4 March 2008 (UTC)

Steve, perhaps you haven't noticed that I already changed the head of the article back to E1 yesterday. E1 is correct, but it doesn't yield the source of the E term. However, the key below does that.

On point number 6, Maxwell showed that A is more fundamental than E and he concluded that A is what Faraday termed the 'electrotonic state'. Dirac is on record as having said that A is a velocity. Maxwell saw it as a momentum. Anybody who has ever studied this subject in depth will realize that A is more fundamental than either E or B. 202.69.178.230 (talk) 05:55, 4 March 2008 (UTC)

BenRG, you say that Faraday's law can't be derived from E1 alone. All you need to do is take the curl of E1 and you have Faraday's law. What effects did you think are catered for by Faraday's law that are not catered for by E1? Maxwell derived E1 from Faraday's law between equations (54) and (77) of his 1861 paper.

I notice that you also say that E5 is obviously wrong. E5 is in fact Maxwell's fourth equation as found in his 1865 paper. It is equation (D) of the original set of eight equations. See page 6 of the pdf file in this web link

http://www.zpenergy.com/downloads/Maxwell_1864_3.pdf

E4-1 which you say is correct but very strange follows directly from Maxwell's fourth equation (E5) which you deny.202.69.178.230 (talk) 05:59, 4 March 2008 (UTC)

In the special case v=0 (stationary charges in the loop) the curl of E1 is ${\displaystyle \nabla \times \mathbf {F} =q(\nabla \times E)}$. There's no way you can get Faraday's law from this (in the case v=0 and therefore in general) because it doesn't mention B anywhere. Honestly I'm not sure exactly what Faraday's law says; the article Faraday's law of induction seems to give formulations equivalent to E2 and E3 that are not the same. But at a bare minimum you need a time derivative of the magnetic field in there somewhere, and there's no way to get that from E1 alone.

Nobody uses Maxwell's original equations any more; the equations we call "Maxwell's equations" are really Heaviside's. I don't know anything about the original equations and I can't say whether E5 makes sense in that context, but it's wrong in modern notation. The article Electromotive force says "Maxwell's 1865 explication of what are now called Maxwell's equations used the term 'electromotive force' for what is now called the electric field strength," so perhaps this is the source of the disagreement. I'm not saying that there's necessarily no place for Maxwell's original approach in the article, but it should be in its own section; the main article should use the modern vocabulary. -- BenRG (talk) 09:46, 4 March 2008 (UTC)

BenRG, the only reason that Maxwell's original equations were mentioned is because you said that E5 was clearly wrong. It is in fact clearly right, and it is exactly Maxwell's fourth equation in his original set of eight. It embodies all the physics in both Faraday's law and the Lorentz force.

As regards your first sentence above, when v=0, if we take the curl of E in equation E1, we get -(partial)dB/dt. That is Faraday's law of induction in the limited partial time derivative format that appears in Heaviside's versions of Maxwell's equations. However, in the more general case when v does not equal zero, we get the full total time derivative version of Faraday's law.

Maxwell's original eight equations differ from Heaviside's four only by virtue of the extra vXB term in the original eight. Heaviside was working on the telegraphy equation and vXB was not required because the EM wave equation considers the E field at stationary points in space. The original eight Maxwell's equations also include Ohm's law, the electric displacement equation, and the equation of continuity.

The way that this article is currently presented accurately reflects the current state of knowledge, and this state of knowledge goes back at least to Maxwell's time. —Preceding unsigned comment added by 202.69.178.230 (talk) 13:34, 4 March 2008 (UTC)

If you take the curl of E in equation E1 you just get the curl of E. If you also assume E2 then that's equal to −dB/dt, but then you're not deriving Faraday's law from E1, you're deriving it from E1 and E2. I'm happy to accept that it can be derived from E1 and E2.

I finally noticed that E5 is in fact listed at Maxwell's_equations#Maxwell's original eight equations, and after staring at it for a few minutes I think I finally understand. Maxwell didn't think of the magnetic field as exerting a force directly; instead it made an extra contribution to the E field and the E field alone determined the force (which would explain why he called it the electromotive force). So Maxwell had

${\displaystyle \mathbf {F} =q\mathbf {E} }$

${\displaystyle \mathbf {E} =-\nabla \Phi -{\frac {\partial \mathbf {A} }{\partial t}}+\mathbf {v} \times \mathbf {B} }$

whereas we now say

${\displaystyle \mathbf {F} =q(\mathbf {E} +\mathbf {v} \times \mathbf {B} )}$

${\displaystyle \mathbf {E} =-\nabla \Phi -{\frac {\partial \mathbf {A} }{\partial t}}}$

All that's changed is the definition of E. But it has changed, and the article needs to reflect that. The E in E5 is not the same as the E of modern E&M. -- BenRG (talk) 16:25, 4 March 2008 (UTC)

BenRG, the original disagreement was never about E5, although I personally would have no objections to using E5. The original disagreement came about because Steve wanted to replace the more informative E4-1 with the less informative E1. I have now actually done that for him because either case is correct. The important thing is that we also make it clear that the E in E1 is the same E that satisfies E4-2 and hence E2.

The disagreement was rather strange because Steve wanted to put the less informative version at the head of the article and then argue that because the source of E was not explicit, then we had no basis upon which to link it to Faraday's law, when in actual fact anybody who has studied the topic knows that the E in E1 is the very same E that is in E2.

It was like as if I was saying, 'lets write out the full expression'. The full expression contains all the elements of Faraday's law. But Steve was saying, 'no let's substitute the two E4-2 terms for E and act as if we don't know what this E refers to'. 'Then if we don't know what it refers to, then we don't know that it comes from Faraday's law'. It was like as if Steve hadn't actually realized that it has been known since at least Maxwell's time that the E in E1 comes from Faraday's law and that Maxwell derived E1 from Faraday's law between equations (54) and (77) in his 1861 paper. It was almost as if Steve assumed that because he didn't know that the E in E1 came from Faraday's law that nobody could therefore know it. I'm wondering did Steve think that the E in E1 was just the Coulomb electrostatic term.

The bottom line is that E1, E4-1, E5, and E3 all contain exactly the same physics, and we have known about the inter-relationship of these equations since the time of Maxwell. E2 and E4-2 contain less information since they don't involve the vXB effect.202.69.174.166 (talk) 17:39, 4 March 2008 (UTC)

It's a big problem that you "would have no objections to using E5", since E5 is not correct according to the modern universally-accepted definition of E. By reading outdated sources and then trying to integrate their information, without understanding what's changed since then and what hasn't, you're putting the reliability of the article at risk. This discussion wasn't originally about E5, but I keep bringing it up because it's a very good demonstration that you do not have a proper understanding of the Lorentz Force Law, as it is understood in modern physics. I've now been backed up by another editor, who also agrees that it's "obviously wrong" according to modern definitions. Now that we've established that, perhaps you could be a little more humble about your knowledge on these matters.

As BenRG points out, the definitions and understandings of electromagnetism have changed since Maxwell. Please try to find modern sources for your understanding of electromagnetism. For example, in both of my two, modern, widely-respected textbooks on classical electromagnetism, E4-2 and E4-3 are unambiguously the definitions of Φ and A, not E and B. Whatever Maxwell or Dirac or Faraday wrote is a less reliable source than these, since they're completely outdated. This is a modern article, and we need to follow the modern understanding, except in the history section.

You assert that "E1 is correct, but it doesn't yield the source of the E term. However, the key below does that." Every term in this equation could have more things said about it. E is the electric field, which satisfies E4-2. B is the magnetic field which satisfies Ampere's Law. Φ is the electrostatic potential which, in the Coulomb gauge, is the solution to Poisson's equation. F is the force, which equals acceleration divided by mass. v is the velocity, which is the derivative of displacement.

The point of these "keys" is not to flush out the physical meaning of the equation, but merely to translate the ambiguous symbols into unambiguous words. And what is E? It's the electric field. That's exactly what we should say. What is the electric field? If you don't know, you click the hyperlink, or read on in the article, to see that E is determined by charges and currents, and makes many important phenomena happen, etc. --Steve (talk) 18:16, 4 March 2008 (UTC)

The New Edits

Steve, the new edits are basically fine because it is clear that you have learned from the debate. The original argument was never about terminologies. It was about the fact that you had been wrongly arguing that the E in the Lorentz force did not cater for the induced EMF that arises when a stationary charged particle sits in a changing magnetic field. We have known since the time of Faraday and Maxwell that it does.

You also made another argument based solely on the limited form of Faraday's law that appears in the modern Heaviside versions of Maxwell's equations. This limited partial time derivative version of Faraday's law does not cater for motional EMF.

Hence you made the grossly over simplistic conclusion that the Lorentz force caters for one aspect of electromagnetic induction whereas Faraday's law caters for the other aspect. You further exposed your confusion by noting that another version of Faraday's law catered for both aspects of electromagnetism.

I chose to put the full version of the Lorentz force at the top of the article to highlight the inclusion of both aspects of electromagnetic induction. You however seem to prefer the current version with the key to the E field, exposing its dual sources in Coulomb's law of electrostatics and Faraday's law of electromagnetic induction, further down the page.

I have given the article a superficial check over and it seems to be factually correct now. It acknowledges that all aspects of electromagnetic induction are catered for by both Faraday's law and the Lorentz force. This fact is totally independent of the theory of relativity, so I may delete that clause because relativity doesn't come into the issue. This is an article about the Lorentz Force that first appeared in Maxwell's 1861 paper. 202.69.178.230 (talk) 08:03, 5 March 2008 (UTC)

You say: "This is an article about the Lorentz Force that first appeared in Maxwell's 1861 paper". This article is (or at rate should be) about the modern law called the "Lorentz Force", as described in all modern textbooks and all modern papers, as taught in all modern courses and as understood by all modern physicists. If the "History" section isn't enough, you can start a new article Lorentz force (original historical form) where you can explain everything about that equation from Maxwell's 1861 paper.

I'm glad that you consider my edit "basically fine", and I haven't yet looked at your follow-up edits. --Steve (talk) 17:06, 5 March 2008 (UTC)

Steve, what I meant was that this article is about the Lorentz Force. I commented that the Lorentz force dates back to Maxwell's 1861 paper. The history section was fine. Your new lay out was fine. On the whole, it was factually correct and demonstrates that you now understand the situation. My fine tuning edits varied from coherence issues to correcting what you said regarding Maxwell and electric charge in the history section. 202.69.172.92 (talk) 21:15, 5 March 2008 (UTC)

Thanks. I reinserted some of the content you deleted in your "fine tuning edits", with many more citations to verify that the content is accurate. I also deleted or rephrased some things that you added, again with citations to confirm that the rephrasing was accurate.

I'm certainly convinced that you are knowledgeable about Maxwell's original presentation of electromagnetism, but I'm also more convinced than ever that are not knowledgeable about the modern understanding of electromagnetism. You've cited Maxwell plenty of times, but never in this whole exchange have you presented information from a single source written in the past 50 years. You don't even remember what textbook you originally learned electromagnetism from, to say nothing of being able to cite specific claims from it. And you continue to unapologetically make claims such as "Faraday's law is a consequence of the Lorentz force" or that you "would have no objections to using E5", which are contradicted by all modern textbooks and at least one other editor. Please: Find a modern textbook. Read it. Understand it. If it disagrees with things in the article, by all means make changes and add specific citations. But don't just draw on your outdated understanding to insult my intelligence, to delete or modify statements that are already backed up by references to reliable sources, and to confidently insist on your point of view without ever adding a single reliable citation to the article. I appreciate that you're working so hard on this, but you would be able to do a lot more good if you invested the time to learn (or refresh your knowledge) from a modern treatment of electromagnetism. Thanks a million, --Steve (talk) 00:19, 6 March 2008 (UTC)

Steve, I told you already that I learned EM from Grant and Philipps, and also from Leonard Eyges of MIT.

I learned none of this from Maxwell's papers. I only recently noticed that the full Lorentz force occurred in Maxwell's original papers,

I learned that E = -dA/dt from Grant and Philipps many years ago.

This entire problem has been due to the fact that you didn't realize how the three terms of the Lorentz force match up with Faraday's law.

The electrostatic part grad(phi) becomes curl = 0 in Faraday's Law. The -(partial)dA/dt term becomes curl = -(partial)dB/dt in Faraday's law. The vXB term becomes curl = -(v.grad)B in Faraday's law.

I am the one that has taught you all these things. You seem to now be taking the points on board while at the same time claiming that I am the one that is confused.

Faraday's law and the Lorentz force contain exactly the same physics.

Basically you went storming into this article with an incomplete knowledge of electromagnetic induction and you wanted to tabulate the incomplete picture as you saw it. You tried to deny that the qE term of the Lorentz force catered for electromagnetic induction in cases where the particle is stationary and where the magnetic field changes.

Now that you have realized the truth, you are still very uncomfortable with it and your edits clearly indicate that you want to play this truth down. You are much more comfortable when readers aren't made aware of the source terms for qE.

Reading between the lines, it seems that you have some ulterior motive. I think that you are trying to paint a picture of E fields and B fields being fundamental entities in their own right and you don't like attention being drawn to their origins in phi and A.

This argument was never about terminologies. It was motivated entirely by your discomfort surrounding the fact that qE has got magnetic origins as well as electrostatic origins.202.69.178.230 (talk) 09:43, 6 March 2008 (UTC)

This web link gives two legitimate ways of expressing the Lorentz force. So why has there been such a concerted effort to suppress the more informative second version that exposes the source of the E field and its roots in the scalar and vector potentials?

http://scienceworld.wolfram.com/physics/LorentzForce.html

Both versions should appear in the introduction.222.126.33.122 (talk) 12:24, 6 March 2008 (UTC)

Can you please find a source for your claim that "Faraday's law and the Lorentz force contain exactly the same physics"? A source, not an argument. If this claim is true, and I don't think it is, it would be very important and should certainly be in the article. So please try to find a source that says, unambiguously, that "Faraday's law" and the "Lorentz force" contain exactly the same physics. --Steve (talk) 16:53, 6 March 2008 (UTC)

There's a difference between "a way to express the Lorentz force" and "the definition of the Lorentz force". I agree that expressing F in terms of potentials is "a way to express the Lorentz force", but I disagree that it's "the definition of the Lorentz force". I can show you dozens or hundreds of books and articles that say F=q(E+vXB) is "the definition of the Lorentz force". Can you find any reliable sources (more reliable than "Eric Weisstein's World of Physics") that say that the expression in terms of potentials is "the definition of the Lorentz force"? Until you can find such a source, I think we have to go with the following compromise: List the expression F=q(E+vXB) at the top, and say "This is the Lorentz force law". Define the terms, and then below that, say "The Lorentz force can also be expressed as", and put in the expression in terms of Phi and A (and not B...as BenRG points out, it's highly unusual to use hybrid expressions with both potentials and fields). I'll give you a few days to find the appropriate sources, but unless you do, I will then go ahead and make that change, according to wikipedia verifiability requirements. --Steve (talk) 17:33, 6 March 2008 (UTC)

It seems to me that the important thing here is not which law is most useful or most general or equivalent to Faraday's law; the important thing is which law is actually called the "Lorentz force law" by practicing physicists. The only way to find that out is to look at papers and textbooks. Having just done a full-text search at the arXiv and a web search and looked at a couple of textbooks, I gather that there are two different laws called the Lorentz force law: some sources say that ${\displaystyle \mathbf {F} =q\mathbf {v} \times \mathbf {B} }$ is the Lorentz force and ${\displaystyle \mathbf {F} =q\mathbf {E} }$ is the Coulomb force, and others say that the combination is the Lorentz force. Among those in the latter category, most write ${\displaystyle \mathbf {F} =q(\mathbf {E} +\mathbf {v} \times \mathbf {B} )}$ and some use other notations like ${\displaystyle F^{\beta }=q_{\alpha }(\partial ^{\alpha }A^{\beta }-\partial ^{\beta }A^{\alpha })\,\!}$. I think all of this should be mentioned in the article. Though the details vary, the force is always expressed in terms of the field or in terms of the potential, never a combination like ${\displaystyle \mathbf {F} =q\left}$. If you want this combination to appear in the article, then you will have to find a source which refers to it specifically as the Lorentz force law.

Throughout this discussion you've been treating some equations as laws which need to be explicitly named and others as side conditions which can go unmentioned. Faraday's law can't be derived from ${\displaystyle \mathbf {F} =q(\mathbf {E} +\mathbf {v} \times \mathbf {B} )}$ alone, and it can't be derived from ${\displaystyle \mathbf {F} =q\left}$ alone. In the former case you need at least ${\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}}$ and in the latter case you need at least ${\displaystyle \mathbf {B} =\nabla \times \mathbf {A} }$. Do you consider these extra conditions to be a part of the Lorentz force law? Where do you draw the line between the Lorentz force law and the rest of electrodynamics?

As far as I can tell the equation ${\displaystyle \mathbf {F} =q\left}$ at ScienceWorld is wrong; I don't think there's any gauge condition that can make ${\displaystyle \nabla (\mathbf {A} \cdot \mathbf {v} )=\mathbf {v} \times (\nabla \times \mathbf {A} )}$. But even if it's correct, it doesn't match your preferred form without side conditions.

You say that you "only recently noticed that the full Lorentz force occurred in Maxwell's original papers." Your wording makes it sound as though you were surprised to learn this. I would have expected you to say that you only recently worked out where it occurred. It would be very strange for Maxwell to give a complete description of the magnetic field and then fail to mention how it acts on matter. You seem to think the implicit presence of the Lorentz force in Maxwell's work is an important revelation that needs to be told to the world, but it seems unsurprising and relatively uninteresting to me. -- BenRG (talk) 19:40, 6 March 2008 (UTC)

BenRG, what electromagnetic effect is catered for in Faraday's law that is not catered for in the Lorentz force? Can you describe any such scenario?

And what electromagnetic effect is catered for by the Lorentz force that is not catered for by Faraday's law? Can you describe any such scenario?

I think that you will find that the two laws cover exactly the same physics.

Consider the Lorentz force law and then take the curl.

The curl of the E term yields -(partial)dB/dt

The curl of the vXB term yields -(v.grad)B

Add them together and you get -dB/dt

That is Faraday's law.

Are you sure that you know exactly who was arguing what in this argument between myself and Steve? Steve Byrnes was trying to tell us all that the electromagnetic induction effect on a stationary particle in a changing magnetic field is not covered by the Lorentz force. He was trying to tell us all that Faraday's law expressed different physics than the Lorentz Force. He was basing this on a combination of his own misconception as stated above, and by comparing it with the limited partial time derivative version of Faraday's law that appears in the Heaviside versions of Maxwell's equations.

Steve also feels very uncomfortable about having the contents of the qE term exposed. The way the article is presented right now is absolutely fine. There can be absolutely no justification for removing the more informative version of the Lorentz force. All this talk about wanting to split it up and move it down the page is based exclusively on Steve's aversion to the relationship E = -(partial)dA/dt which reminds him of his earlier folly. He presumed to edit and radically alter this article without even knowing that that relationship was implicit in the Lorentz force.

Hence all the trivial and specious arguments about the difference between laws, equations and definitions. It's all a load of hokum to try and justify removing the single equation that best clarifies the meaning of all the terms in the Lorentz force. 202.69.172.152 (talk) 23:50, 6 March 2008 (UTC)

You already said all that. You blithely write "The curl of the E term yields -(partial)dB/dt", even though I explained my problem with this in my second paragraph above. Did you read it? You need to read what I wrote and respond to that, not ignore it and repeat yourself, otherwise I can't continue to talk to you. -- BenRG (talk) 10:12, 7 March 2008 (UTC)

BenRG, The curl of the E term does yield -(partial)dB/dt. You have no reason to have a problem with this fact. It is knowledge that goes back to the time of Maxwell at least.

This fact can be clearly seen from the more informative version of the Lorentz force that uses the A and Φ functions.

You and Steve seem to be engaged in some kind of surreal game whereby we write out the dummied down version of the Lorentz force and then pretend that we don't know the origins of the qE term.

We know that the E term caters for the case in which a changing magnetic field induces an EMF on a stationary particle. The original argument began because Steve was trying to deny this. But we know that it does. Only Steve didn't seem to know that. Hence from Faraday's law, we know that the E term must have a -(partial)dA/dt term.

The physics in Faraday's Law and in the Lorentz force is equivalent in every respect.

You have still to give me an axample of a single electromagnetic effect that can be explained by one of these laws but not by the other.

Maxwell didn't even include Faraday's law in his original eight equations because all the effects were already catered for by the Lorentz force equation (D) which he actually derived from Faraday's law.

So let's not get away from the point. The point is that Steve prefers to use the dummied down version of the Lorentz force at the head of the article because he doesn't like exposure of the contents of qE. This in turn is because he likes to view E as some kind of primitive real entity in its own right even when there is no charged particle present to feel its effects.

I have conceded on this point. But it seems that that is not good enough. He now wants to move the full version to a place where it is less visible and perhaps even preferably split it up. he doesn't want anybody to know that E = -(partial)dA/dt because until a few days ago, he didn't know it himself.

That is why is he so uncomfortable with the more informative full version?

I'm not going to get into a semantics debate. If you believe that only the dummied down version is entitled to the name 'Lorentz Force' then so be it. I don't think like that. I use names according to the physical substance of an equation irrespective of what symbols or versions are being used.

I can see absolutely no good argument for not leaving the head of the page exactly as it is.

It concedes Steve's point that the dummied down version is the Lorentz force. It then goes on to give a more informative version below.

What argument can you possibly have against that? 58.69.126.123 (talk) 14:17, 7 March 2008 (UTC)

The Full Lorentz Force Expression

Regarding the Eric Weisstein web link http://scienceworld.wolfram.com/physics/LorentzForce.html is was interesting to note that when such a reference is presented that disproves somebody's point, the reference is immediately denounced as being wrong, or unreliable etc.

That web link wrote out the Lorentz force in full. The controversial bit as regards the above argment ie. -grad(phi)- (partial)dA/dt is exactly as is shown in the main article. But since Steve Byrnes doesn't like that version because it exposes the meaning of qE, we find ourselves being told that it's not actually the same and that I need to find a better article. (What about Grant and Phillips? That's where I first learned the full expression.)

The difference with the Weisstein version is in fact in the manner in which the non-controversial third term vXB has been written. In the Eric Weisstein article, it has been written as grad(A.v).

According to Goldstein's classical mechanics, in the Lagarangian section, the term (A.v) is the Lagrangian for vXB, and hence grad(A.v) will equal vXB. But I agree with BenRG that this is wrong.

At any rate Weisstein and I are agreed about the fact that qE is equal to -grad(phi) - dA/dt

So why should there be a problem with inserting the more informative version of the Lorentz Force in the article? 202.69.172.152 (talk) 00:17, 7 March 2008 (UTC)

The reason that Weisstein is not a reliable source is not because I don't like it. It's because it's self-published, and moreover we know that it has errors in it.

Can you please find the page number in Grant and Phillips where they say "This is the Lorentz Force law", and write F=q(-grad Phi - dA/dt +vXB)? Or for that matter, any page where they write that equation?

You refuse to participate in a discussion of which physical phenomena are part of the "Lorentz Force Law" and which are not, dismissing it as "semantics". On the contrary, it's very important. Bernoulli's law of fluid flow is true, and everyone knows it's true, but it's not part of the Lorentz Force Law. It would be a mistake to put it in the article. Again, the fact that something is true does not constitute evidence that it's part of the Lorentz Force Law. If you're going to argue that something is part of the Lorentz Force Law, such as Faraday's law, you can't just keep saying that it's true and that everyone knows it. Of course it's true. Of course everyone knows it. But that does not prove that it's part of the "Lorentz Force Law". To prove that a physical phenomenon is part of the "Lorentz Force Law", you need reliable sources to back up the fact that it's part of the Lorentz Force Law, not just the fact that it's true. --Steve (talk) 22:38, 7 March 2008 (UTC)

The Reasons for the Argument

Steve, The article appears to be in good shape now. I would certainly agree with you that the Weisstein article got it wrong as regards the vXB term. I can't think of any gauge condition that would allow grad(A.v) to be equal to vXB. But then the original argument was never about the vXB term.

I don't think that you should lose track of the original reasons for why the argument began. The reasons for the argument were entirely because of this passage that you wrote last month,

I don't think that it's correct to say that the Lorentz force "is the solution to the differential form of Faraday's Law" or that they "both express the same physics", as added by 61.7.150.6 last April. They are different laws, expressing different physics, and are related only by special relativity.

Say you drop a loop of wire through a fixed, inhomogeneous magnetic field. A current will be generated, to be sure, but the electric field will be zero everywhere. In Faraday's law, an electric field is created by a changing magnetic field, but here the magnetic field is constant, and the electric field is zero. This is called motional EMF, and it's a direct consequence of the Lorentz force (qv x B), and has nothing to do with Faraday's law (which is responsible for something different, induced EMF).

If, on the other hand, you hold the loop of wire steady while moving the device that generates the inhomogeneous magnetic field, then the Lorentz force (qv x B) does nothing (since the charges aren't initially moving), but Faraday's law says that the changing magnetic field creates an electric field, which in turn pushes the electrons around the loop.

"Motional EMF" and "Induced EMF" are different physics, applicable in different situations, as explained in any good textbook. The reason people get them confused is: (1) Inertial transformations can turn one into the other (a fact which Einstein used in the introduction to his paper on special relativity), and (2) Some physics teachers will teach the so-called "Faraday's law" in a particular form (namely, in terms of "flux through a loop of wire") which encompasses both induced EMF (when the wire is fixed) and motional EMF (when the wire is moving). I don't think this is standard, though, and the most standard ways in which Faraday's law is written (its "differential form" and "integral form") do not include motional EMF.

If no one objects, I plan to edit the article accordingly.--Steve (talk) 00:45, 21 February 2008 (UTC)

By this passage, you demonstrated a total lack of understanding of the link between the Lorentz force and Faraday's law. The two laws contain exactly the same physics. If that were not the case, then why did Maxwell not include Faraday's law in his original set of eight equations? The reaon is that equation (D) catered for all the effects covered by Faraday's law. It was equation (D), which is the Lorentz Force, that Maxwell used in conjunction with curl A = B and Ampère's circuital law to derive the EM wave equation.

Modern textbooks use Faraday's law to derive the EM wave equation in conjunction with Ampère's circuital law. That of course is the restricted form of Faraday's law that drops the vXB effect. 58.69.126.123 (talk) 11:18, 8 March 2008 (UTC)

Well, as we now know I was using a different definition of Lorentz Force than the article's (just the magnetic part) and a different definition of Faraday's law than the one you like, so that may be part of why you find what I wrote so objectionable. I do, however, stand by (100%) my claim that Faraday's law and the Lorentz force do not contain exactly the same physics, under any standard definitions. You are the only one who believes this, as you'll find by searching in vain for a reliable source that makes this statement. You are also the only one who believes, for example, that it would not be totally incorrect to use E5 as the definition of the Lorentz Force law. But in any case, if we can both agree on the article, so much the better. :-) --Steve (talk) 16:59, 9 March 2008 (UTC)

So what aspect of physics is catered for by Faraday's law that is not catered for by the Lorentz force? And what aspect of physics is catered for by the Lorentz force that is not catered for by Faraday's law?

If what you say is true, then why did Maxwell not include Faraday's law in his original eight equations? And how come Maxwell derived the Lorentz force from Faraday's law?122.3.108.118 (talk) 19:18, 9 March 2008 (UTC)

If what you say is true, why is it impossible to find a reference that says that Faraday's law and the Lorentz force contain exactly the same physics? Why would it be that most textbooks don't even cover them in the same chapter? :-) --Steve (talk) 22:32, 9 March 2008 (UTC)

Steve, Maxwell derived the Lorentz force from Faraday's law. See between equations (54) and (77)of his 1861 paper. He derived the A vector from Faraday's law as being a more fundamental 'Momentum' from which both E and B could be derived. He then worked backwards to the Lorentz force equation.

And putting aside semantics about the definition of E, we are agreed that the first two equations in the main article are physically equivalent to the historical equation (D) in Maxwell's 1865 paper that is listed in the history section. And you can see with your own eyes that if you take the curl of this equation, you end up with the full version of Faraday's law.

So why would I waste my time hunting down a reference that precisely states that the two laws are equivalent when it is patently obvious to anybody who has any knowledge about these two laws? The problem with you is that you have only just learned about the similarity and it is still taking a bit of time to sink in bearing in mind that on 21st February 2008 you announced your intention to amend this whole article in line with your erroneous belief that the two laws were quite different in substance. And you even proclaimed yourself to be a bit of an authority on the matter.

Part of your problem may have been the fact that most of the EM textbooks written in the last twenty years are very much dummied down compared to the older books. They tend to favour your attitude of wanting to conceal the source of E. 203.115.188.254 (talk) 07:47, 10 March 2008 (UTC)

I'm happy to hear you acknowledge that your opinion is different from "most of the EM textbooks written in the last twenty years". This article, of course, must side with the textbooks, in accordance with Misplaced Pages "reliable source" guidelines. :-) --Steve (talk) 14:23, 10 March 2008 (UTC)

Steve, just because I said that the modern EM textbooks are dummied down doesn't mean that I am disagreeing with them. All I'm saying is that they aren't giving you the full picture. The first equation in the main article is correct but it doesn't give you the full picture, because it doesn't reveal the source of E. Hence you went through university totally unaware of the link between Faraday's law and the Lorentz force. 222.126.43.98 (talk) 18:12, 10 March 2008 (UTC)

You need a reliable source that says modern EM textbooks don't give the full picture. No original research. See WP:NOR. --Steve (talk) 21:03, 10 March 2008 (UTC)

Steve, I don't need a reliable source. I was telling you for your own benefit because your own misunderstanding arose from the fact that you didn't know the contents of E, as the modern textbooks that you have been referring to don't seem to highlight it. I'm beginning to see now that you are not a physicist at all but merely somebody how knows how to play a silly little game with wikipedia rules in order to win arguments.203.115.188.254 (talk) 09:19, 11 March 2008 (UTC)

I can't believe I'm getting involved in this again, but... anonymous, you keep talking about how F = q(E+v×B) hides the nature of the E field. That's the point! When you talk about a part of a theory, you have to pretend as though the rest of the theory doesn't exist. That's the only way to give meaning to the concept of a "part"! The division into parts is arbitrary. It's just convention. Physicists happen to use the letter sequence "Lorentz force law" to refer to three particular relationships between variables in electromagnetism. They may all be equivalent to each other in the presence of the rest of electromagnetism, but the rest of electromagnetism can't be present. If it were present, every true statement in electromagnetism would be equivalent to every other and the names would become meaningless. Your relationship between variables is also a part of electromagnetism, and maybe even an interesting part, but it happens not to be one of the three parts called "Lorentz force law" in the literature. This is just English word usage. No amount of physical or mathematical argumentation can make you right. Only an example from the literature of the use of the phrase "Lorentz force law" to refer to a particular relationship can make it correct to refer to that relationship as "Lorentz force law". -- BenRG (talk) 13:18, 11 March 2008 (UTC)

The above paragraph by BenRG made absolutely no sense from what I could make out.Tim Carrington West (talk) 13:50, 11 March 2008 (UTC)

Byrnes, Why Did you delet my edits Which clarified the meaning Of The Term Lorentz Force

You have wasted hours of careful research by deleting my edits. You are arbitrary and irrational. Your actions were unjustified. Please explain why you insist upon keeping misleading information on this page. From what I have seen of your actions, you dont understand anything about what you are doing on this page. You are justifying the opinion that the information found on Misplaced Pages is not accurate. 72.64.58.151 (talk) 19:23, 10 March 2008 (UTC)

I was deleting information that was either not backed up by a reliable source, or, worse, explicitly contradicted by one of the "gold standards" of reliable sources on Misplaced Pages--namely, widely-used modern university-level textbooks. Doing this is actually encouraged by Misplaced Pages policy. See WP:V. If you feel that widely-used modern university-level textbooks are wrong or misleading, then I'm sorry to tell you that Misplaced Pages is not the place to set forth your better understanding. If you find particular statements in the article that you feel are misleading, I will be happy to back them up with specific quotes from modern textbooks. I'm sorry that you've been spending so much time on this article (as have I) and I would encourage you to start your own website where you can explain the Lorentz force any way you please, without having to spend your time finding reliable sources that agree with your presentation. --Steve (talk) 21:00, 10 March 2008 (UTC)

Role of the vector potential A ( r, t )

The articles Dirac_equation#Coupling_to_an_electromagnetic_field and Quantum_electrodynamics#Euler-Lagrange_equations and Hamiltonian_mechanics#Charged_particle_in_an_electromagnetic_field, and several others use the momentum in a field p-qA and the Hamiltonian (p - q A) / (2m) to set up the coupling with the EM field. That so, is A more fundamental than the present article suggests? Brews ohare (talk) 05:17, 11 March 2008 (UTC)

Of course A is more fundamental than both E and B as both the latter derive from A.

My understanding is that Dirac once said that A is a velocity. And I know that Maxwell treated it as a momentum, from which he then derived the Lorentz force from Faraday's law.

Hydrodynamically, A is a velocity, whereas E is an acceleration dA/dt, and B is a vorticity curl A. The velocity v is taken to be relative to Maxwell's sea of molecular vortices.203.115.188.254 (talk) 09:26, 11 March 2008 (UTC)

Unconfirmed, but I've heard that Franz Ernst Neumann used the A vector before Maxwell did.George Smyth XI (talk) 12:46, 11 March 2008 (UTC)

The article (in particular, that footnote) only says that in most modern presentations of classical electromagnetism, E and B are treated as more fundamental, a statement which is clearly true if you look at classical electromagnetism textbooks. So the footnote is definitely okay.

More generally, I think that given the idea of gauge transformations, it's hard to argue that A is particularly fundamental--after all, one hundred physicists can look at exactly the same situation, and each could write down a different, correct vector potential. This goes against my understanding of the term "fundamental". But the question of "what is more fundamental" really can't be answered without quantum field theory (since everything in classical electromagnetism emerges from that). There, a gauge is a "choice of local section of some principal bundle", which still makes it sound like the bundle is "fundamental" and the gauge is an arbitrary choice...but here, I'm definitely not knowledgeable enough to say for sure.

Anyway, the article only makes the relatively guarded statement that that's how it's usually treated in classical electromagnetism, and that statement is definitely on solid ground. --Steve (talk) 15:34, 11 March 2008 (UTC)

Steve, You can't play real physics with arbitrary constants of integration. In hydrodynamics, if A is the velocity, dA/dt is the acceleration and curl A is the vorticity, then you can't start fooling everybody that A + dΦ/dt is just as fundamental as A.

Gauge theory is the point at which physics departs from reality.Tim Carrington West (talk) 16:05, 11 March 2008 (UTC)

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