523:. After reading his short treatment of the topic I have much greater appreciation of the subtlety of how SR leads to the full picture of magnetism. As Jackson doesn't go into depth on the topic, I'd highly recommend the sources he mentions in the footnotes either on the bottom of page 578 or 580. Schwartz's "Principles of electrodynamics" is very enlightening (it also was on the same shelf as the Jackson 2nd ed - I've got the 3rd ed and he completely rewrote chapters 11 and 12 so I had to hit the library to look at your reference). Schwartz does the classic derivation found in Griffith and then shows how it is slightly inadequate in cases outside of the realm of electrostatics. He does however go through and derive all of the electromagnetism based on only three assumptions: charge invariance, Coulomb's law, and that all physical laws must be Lorentz covariant. That last assumption is slightly different and broader (but more accurate of SR's postulates) than the kinematic transformations of SR that Jackson states are insufficient (and that I had previously thought sufficient). The correct derivation is not through the force, but through the sources to the potentials to the fields framing the relationships within SR. The only real hard thing to show is that the 2-rank field tensor has to be antisymmetric with only 6 independent values (Schwartz says in the text that God was trying to avoid complications, but does begin the argument of why this must be in the footnotes but leaves the rest as an exercise for the reader). So to sum up, when it is stated that magnetic behavior is a relativistic effect, it means that for Coulomb's law to be Lorentz covariant (as SR requires), there must be a moving charge dependent behavior. Sommerfeld does a nice description of this by saying that the differences in observed fields in different inertial frames is really a matter of space-time perspective. --
494:
wires using only electrostatics and relativity, Barut pg 127, exercise 5 has the reader derive the electric and magnetic fields of a moving particle using just electrostatics and
Lorentz transformations, and Panofsky pg 331-332 discusses how the fields accurately transform according to relativity. I'm sure I've missed a few others that have been mentioned. Also, while perusing the shelves at the library, I found a low-level but highly technical university text "Conceptual Physics" (Hewitt, 2006) which states that "a magnetic field is a relativistic by-product of the electric field." Once again, this is a mainstream concept first introduced by Page in 1912. Now, seeing as I have checked the books you have mentioned, I think I have every right to demand that you go check the sources we have mentioned which do contain proofs before continuing this debate. --
403:"Find me a moving charge that is not somehow part of a closed electric circuit." Solar wind. What is wrong with simply leaving the introduction the way it is? It's not "shy about declaring electric current to be the source of magnetic fields", it's right there in the first sentence. If you're that fixated on getting every word in the article exactly your way, you're going to have a tough time on wikipedia. (Not that I'm opposed to mentioning current.. A few days ago, I actually changed the first sentence of the intro to mention current more prominently, but some anon who isn't participating in this discussion changed it back, so...)
1647:
non-moving observer). All laws of electromagnetism (Bio-Savar, Amper's, Faraday, Gauss law for magnetic field) follow mathematically. They were empirically discovered in different order, but mathematical logic is just as I described above: Gauss's law (inverse square in 3-d space) + relativity = magnetism. This is true not only for electric field but for any inverse square field (say, gravitational - there is corresponding gravimagnetic field too). The inverse square law in turn comes from exchange by spin 1 particles (photons) constrained in 3-dimensional space.
546:]. It's quite recent but it's written by a CERN physicist and is published in "Physica Scripta". Starting with the simplest system - two isolated charged particles obeying Coulomb's Law - he constructs the most general Lorentz invariant Lagrangian out of the only six Lorentz invariant quantities available in the system and then moves to the simplest version by insisting that this Lagrangian reduce to the non-relativistic Lagrangian in the non-relativistic limit. Then, using Hamilton's principle and the Euler-Lagrange equations, he
3491:"Magnetic fields can do no work"...I know Griffiths says this (in boldface, in a big box, no less), but I haven't seen it in other textbooks and I think there are cases where it's arguably false, depending on definitions (e.g. an electron, with its spin magnetic moment, accelerates in a non-uniform magnetic field). I don't think this should be stated without some more research and references and examples and detailed discussion. You certainly can say that it doesn't do work on charged particles, though.
3338:"Magnetic fields can do no work"...I know Griffiths says this (in boldface, in a big box, no less), but I haven't seen it in other textbooks and I think there are cases where it's arguably false, depending on definitions (e.g. an electron, with its spin magnetic moment, accelerates in a non-uniform magnetic field). I don't think this should be stated without some more research and references and examples and detailed discussion. You certainly can say that it doesn't do work on charged particles, though.
489:. We have provided numerous reliable sources that state this - Jackson section 11.9, Griffiths pg 522-523, Purcell ch 5 ("he magnetic interaction of electric currents can be recognized as an inevitable corollary of Coulomb's law. If the postulates of relativity are valid, if electric charge is invariant, and if Coulomb's law holds, then the effects we commonly call "magnetic" are bound to occur."), Sommerfeld pg 240-241 ("Thus our primed observer, unlike one moving with the electron, is aware of a
3508:
of "you can calculate the magnetic attraction via the attractions and repulsions of the poles in the magnets, in an analogous way to attractions and repulsions of electrical changes. One should keep in mind, though, that this is a calculational tool, and not meant to be a literal model of what's going on inside a magnet. In fact, all the forces physically arise because the microscopic dipoles in one magnet respond to the non-uniform B field of the other magnet." I dunno, something like that.
3355:
of "you can calculate the magnetic attraction via the attractions and repulsions of the poles in the magnets, in an analogous way to attractions and repulsions of electrical changes. One should keep in mind, though, that this is a calculational tool, and not meant to be a literal model of what's going on inside a magnet. In fact, all the forces physically arise because the microscopic dipoles in one magnet respond to the non-uniform B field of the other magnet." I dunno, something like that.
1797:: "Due to SR, electricity cannot exist without magnetism" (this is true). BAD: "The reason that magnetism exists is because it's created by electricity in a different frame of reference" (The 'reason magnetism exists' is the same as the reason electricity exists: spontaneous symmetry breaking of the electroweak field, or string theory, or 'it just does', or whatever. Electricity without magnetism or vice-versa is self-contradictory, so the existence of the two fields are certainly caused
3464:
it, north pole and south pole. Moreover, you may not have known this (I didn't until someone corrected a similar edit that I had made), but I think people who actually design magnets have precise definitions of "poles", such that a realistic magnet doesn't have a single north pole and single south pole, but rather a spatial distribution of each. So you shouldn't say things like "magnetic fields always enter a magnet at the S-pole and leave at the N-pole of a magnet"...rather they enter
3311:
it, north pole and south pole. Moreover, you may not have known this (I didn't until someone corrected a similar edit that I had made), but I think people who actually design magnets have precise definitions of "poles", such that a realistic magnet doesn't have a single north pole and single south pole, but rather a spatial distribution of each. So you shouldn't say things like "magnetic fields always enter a magnet at the S-pole and leave at the N-pole of a magnet"...rather they enter
2143:
one involving the time derivative of the charge denisty, the other involving the time derivative of the current density. dB would have a term proportional to the time derivative of the current density. The extra terms basically come from the inhomogenous wave equation version of
Maxwell's equations and thus needing to introduce the concept of retarded time. If you have access to it, chapter 10 of Griffiths basically derives the general and exact solutions.
1970:
as separate phenomena, except when you've already finished computed something and want to translate that result into experimentalists' language (if you don't believe me, read any QFT textbook). In this underlying theory, electricity and magnetism aren't quite interchangeable, but certainly neither is more fundamental than the other. Remember, the only way you can show that electricity is truly more fundamental than magnetism is to find a reference
31:
1735:
system. I understand that you know how to set up an axiom system like that, but systems of axioms are not unique. For any two equivalent statements A and B, you can say "assume A and then B follows from A", or you can say "assume B and then A follows from B". But now it's obvious that neither of those is enough to say "the real reason, at some deep and meaningful level , that B is true, is because A is true". (A=electricity, B=magnetism) --
1478:
2557:. 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.--
639:"In many text books on classical electrodynamics the question of what are the fundamental physical hypotheses underlying the subject, as distinct from purely mathematical developments of these hypotheses, used to derive predictions, is not discussed in any detail. Indeed, it may even be stated that it is futile to address the question at all. For example, Jackson states:
3087:, and so forth. The flip side of that is, given that there are already nice, thorough, specific articles on all these topics, you should think hard about whether it would be better to include a clear and prominent link to one of those articles, instead of repeating all the content and making the article so long that it becomes hard to navigate and scares off readers.
505:
states that it is impossible to attempt "to derive magnetic fields and even
Maxwell's equations from Coulomb's law of electrostatics and the kinematics of special relativity." Perhaps this has changed, but the main point here is that the exact meaning of the assertion is unclear and that makes it unsuitable for inclusion in the article on magnetic fields.
859:
and interlocking solenoidal loops of magnetic lines of force, rather than in relation to single moving charged particles. Single moving charged particles only give a fragment of the overall picture. I think alot of this argument began because there had been attempts to eclipse the broader picture and focus on the single moving charge scenario.
1726:, but it's equally true that electricity follows from magnetism plus special relativity! And that time follows from space plus special relativity! And space from time! And momentum only exists because of energy plus special relativity! ...In reality, theoretical physicists treat electricity and magnetism on an
3507:
to be using. Also, as I mentioned before, you come across as awfully judgmental against the
Gilbert model, which as I understand it is a quite widespread and rigorously correct and convenient model, when used correctly. Anyway, maybe you could try phrasing it in a less judgmental way, along the lines
3354:
to be using. Also, as I mentioned before, you come across as awfully judgmental against the
Gilbert model, which as I understand it is a quite widespread and rigorously correct and convenient model, when used correctly. Anyway, maybe you could try phrasing it in a less judgmental way, along the lines
3114:
In this article, within the paragraphs, some vectors are bolded using math mode and other are bolded using wiki markup. The difference is that the math mode is bigger and, I think, has a different font. Looking at other articles it appears to me that most in-paragraph-variables are not in math mode.
2644:
As best as I can tell, this is saying something like "Some people think that when you draw in magnetic field lines, that means that the magnetic field is zero wherever you didn't draw a line. But that's not true, because then the magnetic field wouldn't satisfy
Maxwell's equations." Is this accurate?
2487:
Hm? I've heard that postulate stated several times but HOW exactly does the magnetic field do work? If referring to
Griffiths he's pretty clear on the subject (as far as I remember anyway) with the standard v perpendicular to F argument. Tried searching for some decent sources supporting the claim of
2070:
was only bringing up QFT in the context of arguing that it's not true that "magnetism is less fundamental than electricity" or "the underlying cause of magnetism is electricity (and SR)". Quasi-philosophical claims such as those certainly cannot be justified without considering the underlying quantum
2029:
I've seen books on gauge theory state that the electric field arises from global gauge invariance, while the magnetic field arises from considering local gauge invariance. So even in the context of QFT, there are ways to consider the electric and magnetic field as arising separately. However, there
650:
This is, perhaps, a true statement. However, if the additional assumptions are weak ones, the derivation may still be a worthwhile exercise. In fact, in the case of
Maxwellās equations, as shown in References , the āadditional assumptionsā are merely the formal deļ¬nitions of the electric and magnetic
3463:
more common than either "N-pole, S-pole", or "North seeking pole, south seeking pole". Maybe you could say once near the beginning that it's helpful to think of the term "north pole" as shorthand for "north seeking pole", but once you establish that, maybe you should call it what most everyone calls
3439:
The second sentence of the article may be too early to bring up the fact that it takes a non-uniform B-field to exert a force on a magnetic dipole. How about something like "...magnetic field is a field that permeates space and which CAN exert a magnetic force on moving electric charges and magnetic
3310:
more common than either "N-pole, S-pole", or "North seeking pole, south seeking pole". Maybe you could say once near the beginning that it's helpful to think of the term "north pole" as shorthand for "north seeking pole", but once you establish that, maybe you should call it what most everyone calls
3286:
The second sentence of the article may be too early to bring up the fact that it takes a non-uniform B-field to exert a force on a magnetic dipole. How about something like "...magnetic field is a field that permeates space and which CAN exert a magnetic force on moving electric charges and magnetic
3234:
For instance, there needs to be some sort of description of the H field. This is going to take a lot of thought as I am not quite sure if most textbooks themselves understand what the H field is. Some people seem to use it effectively as an applied magnetic field. Many gloss over the fact that
3173:
One complication to be aware of in the question of wiki-markup-bold versus mathbf is that different viewers can set up their wikipedia "preferences" regarding math differently, so something that looks good with one set of preferences might look bad with another. I imagine most people use the default
2142:
Actually, the reason that the derivation is correct for low velocities only is that the equations for dE and dB are not completely general. They aren't consistent with
Maxwell's equations except in the limit of static charges and currents. For instance, the full equation for dE has two more terms,
1691:
Dear
Enormousdude, I'm well aware of that beautiful derivation of B=(vxE)/c^2, but the derivation only works for a point charge moving at a constant velocity (which can be Lorentz boosted to a point charge at rest). The law does not hold for a point charge that is accelerating, even if (for example)
1304:
865:
In fact, on thinking about it for a few hours, it is possible that the solar wind might actually be the one case of an open radial electric current. If the radial symmetry is perfect, I doubt if it could have a magnetic field at all. But in all probability, the symmetry will not be perfect and there
854:
I myself once mentioned lightning as being a possible case of a broken electric circuit, but that then brings us to the subject of Maxwell's displacement current and whether or not magnetic fields can be broken. It's hardly likely that a solenoidal magnetic field can be broken. Displacement current,
785:
The common factor in the two proofs is that they both convert Coulomb's law into the Biot-Savart law. In Grant&Philipps, the method used is to arbitrarily extend the charge density term in Coulomb's law to include a current density term with the correct coefficient needed to make it commensurate
235:
does not equal zero we have problems. It's actually hard to imagine any moving charge anywhere that is not part of a closed electric circuit, so why not be bold and simply state that magnetic fields occur around bar magnets and electric circuits? They are the most common scenarios. The single moving
3557:"Maybe a better way of saying this is that a magnetic monopole is a property of a particle(s)." I don't think this is the place to be wondering about how best to refer to monopole-ness...everyone just says that the particle would be called a magnetic monopole. Also, you forgot to put "main article:
3468:
each, usually. Likewise, you make it sound like the earth's magnetic-field south pole is just below the surface in Canada, when in fact it's probably deep in the earth's core. Finally, maybe it would make more sense to rename the section something like "field lines for a bar magnet", and then start
3404:"Maybe a better way of saying this is that a magnetic monopole is a property of a particle(s)." I don't think this is the place to be wondering about how best to refer to monopole-ness...everyone just says that the particle would be called a magnetic monopole. Also, you forgot to put "main article:
3315:
each, usually. Likewise, you make it sound like the earth's magnetic-field south pole is just below the surface in Canada, when in fact it's probably deep in the earth's core. Finally, maybe it would make more sense to rename the section something like "field lines for a bar magnet", and then start
3039:
I also very much dislike the B vs. H discussion currently there, but rather than outright deleting it, it might be better to move what's currently there to a new section or subsection, something like "History of B and H", and put it at the bottom of the article. The primary discussion would then be
1969:
axiom system that matters. And in standard model QFT, electricity and magnetism only occur through F (and its gauge field A), which is the combination of electricity and magnetism into a Lorentz-covariant tensor. When dealing with the standard model, you never even discuss electricity and magnetism
858:
I'm not going to change the present wording in the introduction because it is basically correct. I'm merely drawing attention to the fact that there are reasonable grounds to believe that the full picture of the magnetic field really needs to be viewed within the context of closed electric circuits
812:
relegated to the relativity section! Also, the textbook you cited seems to think it's worthy of mention that "it can be made very plausible that the laws embodied in Maxwell's equations represent the simplest conceivable generalization of Coulomb's law which is consistent with relativity", why not
504:
This is very interesting but not relevant to the claim that: magnetism is a relativistic effect. Show me where this statement appears in the books and what the statement purports to mean with respect to an understanding of magnetism. My second edition of Jackson's Classical Electrodynamics page 578
297:
over a volume is only zero you have no sources or sinks, ie ways for charge to enter or leave that volume. It's also encoded into Maxwell's equations - take the divergence of Ampere's law (with Maxwell's correction of course) and you get the continuity equation. Got a reference that Ampere's law is
97:
So where do we draw the line? If Prof. AKT Assis publishes something in a reputable journal in 1992 does that then become acceptable mainstream theory? Prof. Assis has shown, based on the electromagnetic theories of Weber, that magnetism is a velocity dependent extension to Coulomb's law. Should we
3241:
Any additional changes will be broken into smaller pieces. (I think I made somewhat of a mistake in doing too much with this one edit. I probably should have done one big change that just reorganized followed by a number of smaller committs. Nothing I can do about that now without doing a lot of
2599:
My concern is that the original template was getting too long, such that it could not fit on one screen and messed up the formatting of host pages with images near the top. There are different ideas that could be implemented, such as having lists that could be expanded without leaving the current
2502:
Dipoles are comprised of moving charges and the magnetic work on them individually is 0, so the net work on the dipole is also 0. The work which textbooks usually assign to magnetic dipoles is actually electric work done by the charges which are being deflected by the magnetic field. It's a useful
2432:
Main article doesnt seem to have the formula for B near a straight wire. Perhaps it should; and similar formulae eg the force between parallel wires. Of all the related electromagnetism articles this seems the most appropriate for people to look for these formulae in. Or is there a better placeĀ ?
2225:
Please can someone check the formula for the strength of the B-field around a wire conductor. I think it should just be "r" and not r-squared on the bottom. We already have r-hat as a unit vector on the top line. It's a while since I did my physics undergrad, and I don't have my textbooks to hand.
1677:
currents, which a single moving point charge is not. If you don't believe me, look up Griffiths "Example 10.4" (eqns (10.68,10.69,10.70)), which says explicitly that the equation B=v x E/c^2 is exact for a point charge moving with any constant velocity, but that B=(mu_0/4pi)(q/r^3)v x r is only an
931:
Thanks for correcting my error re para/diamagnetism. But the paragraph doesn't "ignore paramagnetic and diamagnetic force", it just doesn't mention it. We mention it above and below, so that's fine with me. I'm sure the intro could be improved further. Your extra point of interest sounds good,
590:
be a function of the four-velocity. Thus, the four-force is given by contracting a rank 2 anti-symmetric tensor with the four-velocity - it is the antisymmetry that ensures the orthogonality condition. Further, any rank 2 anti-symmetric tensor is the exterior derivative of a four-vector and this
493:
field in addition to the electric field."), Cullwick in EM and Relativity pg 4 and pg 105-107 where he shows how Einstein and someone else derived electromagnetic relations using only SR and electrostatics, Cullwick's "The fundamentals of electro-magnetism" pg 136-139 derives the force between two
3565:
Anyway, I'm just one guy, and you're welcome to disagree with and ignore any of those suggestions. Also, I don't know if anyone else will offer feedback, you may want to sit on it a few more days before posting, at your discretion. Also, I tend to prefer big all-at-once changes to a zillion small
3412:
Anyway, I'm just one guy, and you're welcome to disagree with and ignore any of those suggestions. Also, I don't know if anyone else will offer feedback, you may want to sit on it a few more days before posting, at your discretion. Also, I tend to prefer big all-at-once changes to a zillion small
3223:
I have made some major reorganizational changes following my above outline and it is posted on my personal wikipedia page. This also includes some extra material as well. In addition, I removed some stuff that I felt was too technical for an overview article such as the equation for the Lorentz
1734:
reason to set up axioms that privilege one over the other -- the only reason, I think, is that in our everyday lives and intuitions, an attractive/repulsive electric force seems easier to understand and accept than a velocity-dependent magnetic force, so it's appealing to put that into your axiom
1704:
be definitions (at least classically): "B is the field that you get when you solve Maxwell's Equations"; or "B is defined so that the Lorentz force law holds for test particles"; or (this is what I think you're getting at, but see below) "B is the field that you get when you try to generalize the
2207:
in two different ways; by the force on the second the charge (the B-field), or by the motion of the first (the H-field). OK; that explanation could do with a little work, but you get my drift, and it squares with the physicist who is quoted as saying that the pion trajectories are curved by the
1809:
way charges affected each other, special relativity would be violated. So charges additionally affect each other in other, less intuitive ways, and these are described by magnetism..." (This is both true and hopefully intuitive. The key is that it starts with electricity as being well-known and
915:
Mainstream encyclopaedie tend to give an introduction in a similar vain to the existing one, including references to units. They then tend to follow on with an extra point of interest for example, that a magnetic field surrounds the Earth and that it has been useful to mariners for navigational
710:
Some editors have been writing in overnight claiming to have found sources which say that magnetism can be derived directly from Coulomb's law, charge invariance, and relativity. I would fully believe their claims because I have a similar source right in front of me now. Contrary to what I said
1496:
definition, since it's not at all general -- for example, the field from an accelerating point charge does not follow from it. The "proper" definition, in my view, is to say that (at the classical level at least) B is what you get when you solve Maxwell's Equations. Someone should change this.
2877:
Here is a proposal for a new way of organizing this wiki. I am writing it here to: get feedback, to help any one who may be considering fixing this, and as a reminder to myself to how I can restructure this should I get the time later to fix it. (Currently I am working on a wiki for gauge
1646:
Actually B=(vxE)/c^2 (sometimes not divided by c^2 depending on system of units used) is just accurate definition of magnetic field. It comes from Lorentz transformation of Coulomb force between moving charges (from the reference frame co-moving with one of charges to the reference frame of
827:
Agreed. Mention it in the relativity section by all means. But bear at the back of your mind for your own good, that the fraud lies in the bit where they convert the charge term in Coulomb's law into an electric current term. Likewise with Purcell's version too, only he uses a different and
752:
This is hardly a basis for deciding that this is a mainstream idea which ought to take prime place in an article about magnetic fields for lay readers. Why not take a leaf out of the mainstream encyclopaediae and drop the controversy altogether, or at least relegate it to the relativity
2852:
I'm also not fond of the phrasing "simply the relativistic part of an electric force...". I'd be fine with it being deleted. More generally, there seem to be very different opinions among editors about what the relationship is between electricity, magnetism, and SR; I wrote the article
884:
The bits that you deleted were indeed superfluous to requirements because magnetism goes back long before Faraday, and Maxwell's equations are more suited to the 'electromagnetism' article, although perhaps a delegation to 'Maxwell's Equations' could be added to those other links.
2589:
topic (it is only defined for static or very slowly varying fields); clicking electrostatics opens the list including electric potential. You raise a valid point, that switching between two pages in different subtopics of electromagnetism requires navigating via an intermediate
643:
At present it is popular in undergraduate texts and elsewhere to attempt to derive magnetic ļ¬elds and even Maxwell equations from Coulombās law of electrostatics and the theory of Special Relativity. It should immediately obvious that, without additional assumptions, this is
230:
Yes Pfalstad. This is the aftermath discussion. The introduction is not too bad now, but it is still shy about declaring electric current to be the source of magnetic fields. It declares this fact in an oblique and indirect way. AmpĆØre's law is all about closed loops. If div
3496:
Is there a reason that you took out the Fleming's left-hand-rule and its diagram? A google search confirms that it's in pretty widespread use. Certainly your made-up replacement ("F.I.B.") is inadequate, since there's no diagram indicating how you're supposed to orient your
3343:
Is there a reason that you took out the Fleming's left-hand-rule and its diagram? A google search confirms that it's in pretty widespread use. Certainly your made-up replacement ("F.I.B.") is inadequate, since there's no diagram indicating how you're supposed to orient your
347:
FyxizFighter and :16, don't you find it amusing that whenever anonymous states something that is, shall we say, questionable and is then called on it, the response is "try to look at the broader picture"? In other words, "try not to pay attention to the silly thing I just
2376:
2202:
and for those out-of-date engineers). However, I'm not going to claim that it necessarily signifies the H-field either, so put down your weapons. A magnetic field is a physical phenomenon; the influence of one moving charge on another moving charge. The field can be
2831:
parts of the Force are changed as is the Force. Second, having this statement in the same paragraph as the description of how the fields transform has a tendency of confusing the reader. A charge in its own stationary reference frame does not experience a magnetic
1692:
you define v to be the retarded velocity. The fields from a point charge undergoing arbitrary motion are different and non-equivalent -- see, for example, Griffiths eqns (10.65) and (10.66) (but it's in any advanced E&M textbook). So that formula is a very nice
786:
with the Biot-Savart law. The basis of this extension is the fraud in the derivation. It is based on the idea of playing about like a child with the three components of current density within a symmetry matrix, all disguised under big words such as 'Four Vector'. (
742:"The answer to this question is that although a rigorous deduction is not possible, it can be made very plausible that the laws embodied in Maxwell's equations represent the simplest conceivable generalization of Coulomb's law which is consistent with relativity."
775:
is in total contradiction of Purcell's 1963 version of the same proof. Purcell depends on the fact that charge density is altered due to selective application of the Lorentz-Fitzgerald contraction. This textbook operates on the basis that charge density must be
2032:
really' think that this article should mostly discuss the "classical" behavior of the magnetic field, and have a small section discussing its role in more "advanced" theories such as QFT, SR, and (if there's anything interesting to say) even string theory.
2464:, surprised me at first. On reflection, I think it's saying that for a moving charge, the acceleration is perpendicular to the velocity. But surely a magnetic field can do work on a magnetic dipole can't it? If so, then this statement should be moved to the
1955:
Dear antiXt, You can't get a physical reason out of analyzing precisely what happens and what goes wrong if you use Galilean transformations, since Galilean transformations have nothing to do with the physical universe. But all this is beside the point---we
3502:
When describing the Gilbert model, you say "could express this force in terms of the magnetic moments of the poles". I think "...in terms of the attractions and repulsions of the poles" would be clearer. After all, "magnetic moments" are exactly what you
3349:
When describing the Gilbert model, you say "could express this force in terms of the magnetic moments of the poles". I think "...in terms of the attractions and repulsions of the poles" would be clearer. After all, "magnetic moments" are exactly what you
1296:
1678:
approximation valid for nonrelativistic velocities. Approximations are fine and inevitable, but more accuracy is always better, and it's rarely appropriate to "derive" a law that's actually more accurate by combining two laws that are less accurate.
3227:
I tried to follow Steve's suggestions above, since on further thought I agree with them. My first thought was to make it more technical and more physics like. Here I am aiming to make it more general with links to the more technical content.
711:
yesterday, one of my university textbooks does indeed mention this idea. 'Electromagnetism' by I.S. Grant and W.R. Phillips deals with this issue in a special section entitled 'Electromagnetism and Special Relativity' at the very end of the book.
2095:
someone said that the equation B = v E K is just valid for low velocities, and for a unique point chage moving. But... Look at my first equation, i use Integrals, since the total MAgnetic field is numerically equal to the sum of infinitessimal.
3040:
free to discuss B versus H as modern scientists think about it (in terms of magnetization and matter and free current and bound current, just as you suggest), as opposed to how 19th-century scientists thought about it ("the vortex sea"...).
1031:
722:"Accepting charge invariance and conservation, what else do we need to know? If we start with Coulomb's law for the force between stationary charges, is it possible, by using arguments based on relativity, to deduce the laws of magnetism?"
846:
There is no theoretical reason why we can't have a single moving charged particle, and I would certainly expect such a charged particle to be surrounded by concentric solenoidal magnetic field lines, possibly tapered backwards in a cone.
700:
I sent in a comment this morning which gave a quote from a mainstream textbook which categorically made it clear that there is no proof that magnetism is a relativistic effect. As my comment was ignored and archived, I'll repeat it again
1487:
One reason not to do that is because both the Biot-Savart law and the Coulomb field are only approximate for a moving point charge (the errors cancel each other such that the law as given is correct). Another is that we're saying it's a
3058:
If you get around to making these changes, don't forget to take advantage of the hard work of other editors in other, related articles. Feel free to liberally copy-and-paste descriptions, diagrams, or whatever, from articles such as
2749:. This shows that magnetic and electric phenomenona are already different manifestations of the one electromagnetic field even in the same frame of reference. The electric field can be a force per unit charge with magnetic origins.
1473:{\displaystyle d\mathbf {B} ={\frac {\mu _{0}}{4\pi }}{\frac {id\mathbf {s} \times \mathbf {r} }{r^{3}}}={\frac {\mu _{0}}{4\pi }}\mathbf {v} \times {\frac {\mathbf {r} }{r^{3}}}dq=\mathbf {v} \times {\frac {1}{c^{2}}}d\mathbf {E} }
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It's certainly fine and proper to have an article on classical magnetism, although as said, it would be good to be state the scope more explicitly and perhaps put in a small section about the underlying physics -- quantum and SR.
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axiom system is: It's the standard model! (Or string theory or whatever which reduces to the standard model.) Classical electromagnetism is certainly an emergent phenomenon from the underlying standard model, and this is the
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3473:-subsection called "Earth's magnetic field and pole labeling confusions", where the north-vs-south issue could be mentioned. I think that might be a better organizational fit to the section, with material you've now added.
3320:-subsection called "Earth's magnetic field and pole labeling confusions", where the north-vs-south issue could be mentioned. I think that might be a better organizational fit to the section, with material you've now added.
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When dealing with the standard model, you never even discuss electricity and magnetism as separate phenomena, except when you've already finished computed something and want to translate that result into experimentalists'
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It sounds like you think the term "magnetic field" should properly refer to B, not H. I, personally, would agree, but lots of engineers would not. (I'm a physicist.) I would slightly change the phrasing to something more
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Split main discussion into 5 sections. The two sections with subsections should probably enumerate the list first with links to the the subsections and include a short description with longer descriptions following:
519:(after a bit of an edit conflict) You should actually use the full quote from Jackson; he states (paraphrasing a bit here) that it's not possible to do it with just electrostatics and the kinematics of special relativity
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Mr. 235 says, in the portion of the talk page which is now archived: "Why not take a leaf out of the mainstream encyclopaediae and drop the controversy altogether, or at least relegate it to the relativity section." It
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the relativistic generalisation of the Biot-Savart Law, the Lorentz force equation, and "those describing electromagnetic induction effects with uniformly moving source currents and test charges". See what you think.
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I don't like this. As a reader who is trying to understand electrostatics and magnetism and constantly goes back and forth its difficult. For example, how do I go from this article to "electric potential" using the
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I'm sorry however that you felt the need to pander to the elements that oppose the term 'Lines of Force'. It is a pretty well known mainstream term and depicts the concept very well.It was good enough for Faraday.
808:"Why not take a leaf out of the mainstream encyclopaediae and drop the controversy altogether, or at least relegate it to the relativity section." As my earlier comment was ignored, I'll repeat it again here. It
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However, in practice, most situations involving moving charged particles are within the context of closed electric circuits or bar magnets, and it is within that context that the laws of magnetism are formulated.
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of any thing. The force is purely Electrical in nature in one reference frame; it is a mixture of magnetic force and electric force in another reference frame. When moving from one reference frame to the other
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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.
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If you want to argue that Maxwell's displacement current is not real, then you needn't also try to tell me that modern textbooks are interpreting Maxwell correctly, and that I am interpreteing Maxwell wrongly.
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FyzixFighter, Grant and Phillips derives AmpĆØre's circuital law by beginning with a closed electric circuit. Besides, the div of a curl is always zero and Hence AmpĆØre's law can only hold for closed circuits.
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with the phenomenon of electricity" but then said "an attractive/repulsive electric force seems easier to understand and accept than a velocity-dependent magnetic force". Steve, IMHO, that's a pretty
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My thinking is that an article called "magnetic field" is be the perfect central place to discuss B versus H, since after all they are both called "magnetic field". In fact, I'd say B versus H is the
1805:: "The most well-known way that charges affect each other is that like charges repel, and opposites attract, as described quantitatively by the Coulomb law. Less well known is that if this were the
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Pfalstad, you may be right on that point. However, I simply don't know enough about the solar wind to be able to see the full picture. I don't know for sure what exactly it is, or where it goes to.
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In the case of the derivation of the Lorentz force equation given below, not even the latter assumption is required, as the magnetic ļ¬eld deļ¬nition appears naturally in the course of the derivation.
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What is wrong with simply writing in the introduction that magnetic fields are solenoidal lines of force that are found in the region surrounding bar magnets, electric currents and moving charges? (
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In "magnetic field of a steady current", you might consider taking out the equation and just describing how the field lines tend to circle around the currents, as in the figure. You could say, See
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In "magnetic field of a steady current", you might consider taking out the equation and just describing how the field lines tend to circle around the currents, as in the figure. You could say, See
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Correct me if I'm wrong, but isn't this article about magnetic field in classical electromagnetism, and not in QED, or even worse in string theory, about which we don't even know if it is correct?
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Wow, that was quick! There's a lot here that I like. Reading through, here are some suggestions that occurred to me. Not meant to be a complete list, and anyone else is welcome to comment too.
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Wow, that was quick! There's a lot here that I like. Reading through, here are some suggestions that occurred to me. Not meant to be a complete list, and anyone else is welcome to comment too.
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I know that none of you are ever shy to make it quite clear that you hold any of my opinions in total contempt, and that you don't consider my opinions to be in the least bit of any importance.
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simplification but it's not correct. As for elementary dipoles like an electron with an intrinsic magnetic moment, the question hasn't been settled. So, I'm changing that part of the article.
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If the solar wind does spread out radially and indefinitely, is raises rather interesting questions regarding the shape of the solenoidal magnetic field lines that are associated with it.
2241:. No doubt if you integrate over the chain of elements in a long wire (with the wire passing close to the observation point, but starting and ending relatively far away), then one of the
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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
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reason to set up axioms that privilege electricity over the magnetism and to stop with futile attempts of finding some nonexistent symmetry between electric and magnetic fields, such as
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will be an axis around which the magnetic solenoidal field loops can form. This would be a case of the magnetic field forming on an ongoing basis at the leading edge of the solar wind. (
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unlike B, the divergence of H is not zero and therefore there is an divergence source in addition to a curl source. The result is strange things like 'demagnetization factors'.
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that privileges the former over the latter. I strongly believe such a reference does not exist, but there's plenty of literature on axiomatic QFT which you're welcome to check. --
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B and H section: I like it. I don't think it's necessary to give the units of D. You should make it very, very clear that there's another B and H section later on in the article.
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B and H section: I like it. I don't think it's necessary to give the units of D. You should make it very, very clear that there's another B and H section later on in the article.
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under Galilean boosts that is self-consistent and describes consistent forces on test charges, I would be interested in seeing that too. So show me the details or it's wrong.
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i just dont know why put a equation, if the derivation and consequently, the proper equation, is not general, if put the equation, put the deduction! just simple as wind
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Pfalstad, to the best of my knowledge, all materials are either paramagnetic or diamagnetic to a greater or lesser degree. Your latest wording implies that only some are.
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Field lines: Your edits, which I generally like, seem to have had the (presumably unintentional) consequence of using the term "magnetic field lines" a couple of times
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Field lines: Your edits, which I generally like, seem to have had the (presumably unintentional) consequence of using the term "magnetic field lines" a couple of times
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I suspect this argument is nonsense because it ultimately depends either on forgetting that moving magnets generate electric fields, or on an asymmetric absorption of
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charge is only a fragment of the overall picture, although I admit that some mainstream encyclopaediae do refer to that scenario in addition to electric currents.(
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In no-where in a lot of articles have deductions of some simple equations like that, just as "Take this, if you dont understand, sorry, it's not my problem"
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Someone the other day claimed that an original research article published in 2006 was not original research because it was published in a reputable journal.
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is just as quantum physics, there is no need to know the velocity or position of a particle, but people dont understand it and need help from heisenberg...
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whether real or not, ensures that a magnetic field is not broken. Displacement current effectively completes an electric circuit whether it is real or not.
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by talking about how the field lines pass in and out of the magnet, and define north and south pole in terms of where they enter and exit, and then have a
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by talking about how the field lines pass in and out of the magnet, and define north and south pole in terms of where they enter and exit, and then have a
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page. Would this or other changes address your concerns, or are you in favour of simply keeping the original template? I appreciate your feedback.--
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In Relativity, there is no force called Gravitational Force, it is just a inertial force. so we can study relativity without talk about gravitation.
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I'm not sure how you imagine discussing magnetic field lines without putting it in terms of vector fields. But by all means, you're welcome to try.
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can be non-zero. That's the whole point of any continuity equation, whether you're talking about charges, or water flow, or people in a room - div
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though. For my part, I have no opinion, I usually stick with whatever formatting is already being used. Change it if you think it would help.Ā :-)
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do not exist in the absence of dipole interactions with matter, and so cannot be considered an intrinsic property of the magnetic field itself."
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only for closed current loops, cause all the textbooks I've seen introduce it without any caveats and freely apply it to any kind of current? --
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May I know why would it be hard to imagine any moving charge anywhere that is not part of a closed electric circuit? I have no such problems. --
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of those sections than B versus H. But that's just my opinion, and of course you're welcome to go for it and see how it turns out.Ā :-) --
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Second, would it be okay if I create another wiki for B vs H? Magnetic_Field_(B_or_H?) that I can shove most of the B vs H stuff into?
3030:: "The term "magnetic field" refers to two different but related fields, also called the B-field and the H-field" or something like that.
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Differences between B and H should be delayed until after all of basics are covered. A short acknowledgment of the difficulty such as
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A magnetic force can be considered as simply the relativistic part of an electric force when the latter is seen by a moving observer.
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I don't think so. biot-savart equation is valid for a moving point charge, because this is the definition of current, charge moving.
2632:"Though useful, modeling the magnetic field as lines can be misleading since field lines themselves are not vacuum solutions of the
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By saying that magnetism follows from electricity and STR one usually means that it follows from electricity and fact that we have
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What i'm doing is the same as deduction quatum equations from semi-classic view. they are good approximations for the real case.
1843:. Time does not follow from space and this fact, nor space from time, nor momentum from energy,... So your analogy doesn't work.
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I have been following the discussion here on Magnetic field and relativity. Consider for instance the statement from the wiki
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2371:{\displaystyle \mathbf {B} _{\mathrm {longwire} }={\frac {\mu _{0}}{2\pi }}{\frac {I\times \mathbf {R} }{\mathbf {R} ^{2}}}}
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with the phenomenon of electricity, and then say that magnetism follows from that plus special relativity. Of course that's
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Hey. I am still looking for that proof from you that "magnetism is a relativistic effect". So far nothing. You giving up?
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I really like a lot of the ongoing changes about magnetic field lines, but I'm a bit mystified by the following quote:
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And dont forget that Maxwell Equation is only an Approximation for the real word, just like all equations in physics.
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3156:(I cannot seem to figure out how and why wikipedia is logging me out or not logging me in hopefully this will take.)
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Anyways, I'm glad that you're thinking about this article, and I hope you get around to editing it eventually.Ā :-) --
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is the only magnetic force. It ought to be removed and a new section opened up on the Lorentz force in its entirety (
912:), although even that doesn't cover paramagnetism or diamagnetism, which Maxwell explained using centrifugal force.
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To me one should either math mode all variables and inline equations or math mode none of them. My question is:
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the term magnetic dipole can be replaced or explained as a small magnet or magnet early on then elaborated on later
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2636:, and Maxwell's equations are considered the most complete formulation of magnetic theory. Magnetic field lines
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of the textbook citations several editors have provided here. IMHO, any further discussion on these matters is
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Magnetic field lines and their properties (postpone vector field stuff though and rewrite a little to simplify)
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The article does mention "lines of force" four times, so I don't see what you're going on and on about, 235.
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And I don't see any quantum aspects of magnetic field in the article, perhaps it would be good to fix this.--
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However, the paragraph below still ignores paramagnetic and diamagnetic force and gives the impression that
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2768:, your definition of "electric field" is the same as Maxwell's definition (force per unit charge), and is
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2208:"magnetic field" (by the "B-field" would be a poor answer, as that's more-or-less the definition of B). --
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113:"Original research" means "original to Knowledge", that is, unpublished anywhere else but Knowledge. See
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Certainly, in certain contexts, it is a good reason. To make myself more explicit, here's some examples:
1291:{\displaystyle id\mathbf {s} ={\frac {dq}{dt}}d\mathbf {s} ={\frac {d\mathbf {s} }{dt}}dq=\mathbf {v} dq}
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Oh, and one more thing - regarding why the rank 2 tensor must be antisymmetric. That seems easy to me -
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Hi. I can see this is a contentious issue, but nevertheless I want to challenge the view that the term
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Paul, this is one of the reasons why I archived the talk page. Further, to the best of my knowledge,
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dipoles"? or "...which can exert forces and torques on moving electric charges and magnetic dipoles"?
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dipoles"? or "...which can exert forces and torques on moving electric charges and magnetic dipoles"?
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definition of electric field, before you go around changing articles to reflect outdated terminology.
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into the definition of the magnetic field, or possibly both. If you are claiming a transformation of
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is zero but this due to the zero velocity.) We should either eliminate this sentence or expand it.
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published source that advances the same claims or makes the same argument as you." (emphasis mine)
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Nevertheless, I will point out that the attempted proof which follows in this textbook and states
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Force Law. I am thinking about getting rid of the equations for the Biot-Savart Law as well.
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If start with electricity (assume that electric forces are nonzero and finite) we get that with
1026:{\displaystyle d\mathbf {E} ={\frac {1}{4\pi \varepsilon _{0}}}{\frac {dq}{r^{3}}}\mathbf {r} }
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So this excerpt concurs with you remarks about Jackson but clarifies the important case of the
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The term 'magnetic field' is often used for another quantity that physicists simply call the '
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Once again, I think you are in denial of the higher picture of interlocking solenoidal loops.
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saying what they are. Is there a way to change the order or change the phrasing to fix that?
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saying what they are. Is there a way to change the order or change the phrasing to fix that?
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Pole labeling confusions: The terms "north pole" (and "south pole") are, as far as I know,
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Pole labeling confusions: The terms "north pole" (and "south pole") are, as far as I know,
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After review from enough people I will commit this change to the magnetic_field article.
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We need to delay the introduction of terminology until after the basics are explained.
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if the equation is wrong, or not "correcT" just delete if from the begin of the article.
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source. Material that counts as "original research" within the meaning of this policy is
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What variables and equations Superscript text should be in math mode within a paragraph?
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from the definition that is now universally accepted. Please educate yourself as to the
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the relativistic formulaes for eletromagnetismos we leave for relativity, not MAXWELL.
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773:"the search is made considerably easier by the fact that we know the answer beforehand"
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This is still work in progress, but I hope it is enough better to post the way it is.
2732:{\displaystyle \mathbf {E} =-\nabla \Phi -{\frac {\partial \mathbf {A} }{\partial t}}}
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theory, and I believe that no quantum field theorist would agree with those claims. --
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be (Minkowski) orthogonal to the four-velocity from which we immediately deduce that
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I am leaning toward the latter. Although the former seems to be much more common.
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Misrepresenting the statements of other users is against wikipedia policy... --
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Hi, here's some feedback on your suggestions, which by the way I generally like.
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2007:
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1565:{\displaystyle d\mathbf {B} =\mathbf {v} \times {\frac {1}{c^{2}}}d\mathbf {E} }
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If you wish to start a new discussion or revive an old one, please do so on the
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All discussions of units should be postponed until after the relevant equations
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If not, what does it mean? If so, could it be stated more clearly? Thoughts? --
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identically zero which is a statement of the conservation of electric charge.
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Find me a moving charge that is not somehow part of a closed electric circuit.
157:. The only way to show that your work is not original research is to produce a
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they would be nonzero and finite. If we start from magnetism we get that with
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I thought that for a moment, but reading it closely I see it's for a current
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Since the field is conservative, I can sum (integrate) all possible results.
620:]is a paper from the same author (J. H. Field) where he states the following:
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Force on charge due to time varying magnetic field (induced electric fields)
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http://www.ifi.unicamp.br/%7Eassis/Commun-Theor-Phys-V18-p475-478(1992).pdf
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part of the electric field, and hasn't been for probably 100 years. There
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intuitive, without implying that it's more fundamental than magnetism.) --
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such a thing as an "electric force" qE, and a "magnetic force" qvXB, and
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Yes, the magnetic field on an elementary dipole can certainly do work. --
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the drift speed of the electrons is very very low! some meters per hour!
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Why don't we put this small deduction of the first equation of the page?
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put something like that here in the article, in the relativity section?
651:ļ¬elds in terms of the spaceātime derivatives of the 4āvector potential .
3478:"charged particles spiral along magnetic field lines"...I think "form a
3325:"charged particles spiral along magnetic field lines"...I think "form a
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is only zero if the charge density is static and, when you integrate div
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four-potential (not necessarily the electromagnetic four-potential).
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The maxwell equations is not valid for Eletromagnetism + relativity.
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Steve said "By the way, I should note that there's no good reason to
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First, FYI, I think the more standard term is "article", not "wiki".
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is from the closest point on the wire to the observation point (the
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As stated before, we don't need to provide a proof; that would be
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Questions about formating vector fields and about Moving articles
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Force on Magnets due to uneven (varying in space) magnetic fields
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Changing electric field: You have a typo in the first sentence.
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Changing electric field: You have a typo in the first sentence.
1793:: "Electricity is more fundamental than magnetism" (it's not).
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I slightly clarified the deleted text, and put it back in. --
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Hi Bless sins. I'll start by simply answering the question:
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we work with newtonian mechanich without maxwell or einsten.
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electric forces would indeed be nonzero and finite, but with
2546:, however I don't think many people are watching that page.
2793:(according to the universally-accepted modern definitions).
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From Faraday's law of electromagnetic induction we obtain,
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Your current idea works, and addresses my concerns. Thanks.
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and gave an explanation on the old (i.e. current) template
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Dear 201.58.7.211, The Biot-Savart law applies exactly to
1134:{\displaystyle c^{2}={\frac {1}{\varepsilon _{0}\mu _{0}}}}
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Paul, I think the payoff quote from WP:OR is the following:
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my derivation is complete and beautiful and is not wrong.
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In "electrical currents", you should link to the article
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In "electrical currents", you should link to the article
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Eliminate discussion of left hand rule including diagram:
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To see an example of a similar template style, check out
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By the way, I should note that there's no good reason to
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First Attempt at editting Article up on my personal page
1184:{\displaystyle \mathbf {v} ={\frac {d\mathbf {s} }{dt}}}
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the magnetic field as such. They're really more about "
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the magnetic field, but they're not really, centrally,
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Eliminate comparison of B = Ī¼H to J = Ļv starting from
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Coulomb law to be consistent with special relativity ".
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mention that in the introduction? Here is the citation
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I think this is misleading. First of all what is the
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Is valid, because In the deduction I never considered
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contradictory fraud to bring about this same result. (
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give a good argument and dont say non-sense, please
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magnetic fields doing work but without any results.
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most important thing that should be in this article
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to try to start to bring about some consistency. --
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the original thought of the Wikipedian who added it
3569:Happy editing, kudos, and hope all is well!Ā :-) --
3482:" is more unambiguous than "spiral". "Spiral" has
3416:Happy editing, kudos, and hope all is well!Ā :-) --
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172:Hopefully, this is plain enough for anonymous.
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2030:already exist articles on electromagnetism: I
678:arising naturally in the context of the STR.
2953:Magnetic torque on magnets (magnetic dipoles)
2814:Thoughts on the Magnetic Field and Relativity
2659:Update: I replaced this passage. Thoughts? --
1700:. Here are some things that (if fleshed out)
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2927:The difference between the B and the H...
2518:can anybody tell about MFM used in MO Media?
3183:...for example, Sections 2, 3, 5, 6, 7 all
2873:Proposal to reorganize Magnetic Field wiki
2764:As now two editors have confirmed over at
1972:about the actual underlying quantum theory
426:citation has been provided to support any
2713:
2707:
2687:
2685:
2407:
2405:
2385:
2383:
2360:
2355:
2348:
2339:
2323:
2317:
2286:
2285:
2280:
2277:
2246:
2226:Please check and verify before changing.
2099:is non-sense talk about Relativity here.
1599:
1579:
1577:
1557:
1546:
1537:
1529:
1521:
1516:
1465:
1454:
1445:
1437:
1420:
1411:
1409:
1401:
1385:
1379:
1368:
1358:
1350:
1341:
1325:
1319:
1311:
1306:
1277:
1252:
1246:
1238:
1215:
1207:
1199:
1165:
1159:
1151:
1149:
1122:
1112:
1102:
1093:
1087:
1049:
1041:
1018:
1010:
996:
987:
971:
963:
958:
3566:ones, but maybe that's just my opinion.
3413:ones, but maybe that's just my opinion.
2468:section, and some explanation added. --
1864:magnetic forces would be zero and with
449:I sent in a refutation citation below (
369:On another note, the divergence of the
216:relegated to the relativity section!
153:and which is therefore believed to be
44:Do not edit the contents of this page.
3547:for the exact quantitative equations.
3394:for the exact quantitative equations.
2978:Magnetic Fields and Matter
2964:Sources of Magnetic Fields
2624:Ongoing changes regarding field lines
1764:reason to start with Coulomb's law.
7:
2422:in the numerator is now hatless). --
544:FyzixFighter, take a look at this:
2947:Effects of Magnetic field
2114:we word maxwell without einstein!!
2903:. It is an unfortunate confusion.
2720:
2710:
2701:
2698:
2452:The statement in the introduction
2308:
2305:
2302:
2299:
2296:
2293:
2290:
2287:
2221:Magnetic field of a steady current
1072:{\displaystyle i={\frac {dq}{dt}}}
591:four-vector is nothing other than
521:without making further assumptions
24:
3517:...I think you mean the article
3513:You should fix the wikilinks to
3364:...I think you mean the article
3360:You should fix the wikilinks to
2791:neither is included in the other
2714:
2688:
2555:Template:Thermodynamic_equations
2408:
2386:
2356:
2349:
2281:
2162:i dont know why all this fuzz..
1580:
1558:
1530:
1522:
1466:
1438:
1412:
1402:
1359:
1351:
1312:
1278:
1253:
1239:
1208:
1166:
1152:
1019:
964:
29:
2950:Magnetic Force on Moving Charge
1696:, but as it stands, it's not a
2914:Eliminate confusing stuff
2483:06:57, 22 September 2007 (UTC)
2473:20:47, 21 September 2007 (UTC)
2427:16:23, 12 September 2007 (UTC)
2266:16:06, 12 September 2007 (UTC)
2231:15:36, 12 September 2007 (UTC)
2182:) 14:53, August 25, 2007 (UTC)
2159:the charge is quasi-statical.
2137:) 10:17, August 25, 2007 (UTC)
1639:) 11:44, August 22, 2007 (UTC)
877:Paramagnetism and Diamagnetism
1:
2669:21:51, 14 December 2007 (UTC)
2655:06:19, 13 December 2007 (UTC)
2614:17:48, 10 November 2007 (UTC)
2508:08:16, 25 November 2009 (UTC)
2213:01:43, 7 September 2007 (UTC)
2092:er... er... Deart everybody.
790:10:12, 18 July 2007 (UTC)). (
2674:Electric and Magnetic Fields
2605:22:48, 6 November 2007 (UTC)
2573:18:10, 6 November 2007 (UTC)
2562:16:43, 6 November 2007 (UTC)
2523:13:02, 5 November 2007 (UTC)
2415:{\displaystyle \mathbf {R} }
2393:{\displaystyle \mathbf {R} }
1587:{\displaystyle \mathbf {v} }
839:Lightning and the Solar Wind
3252:) 01:19, 18 May 2008 (UTC)
3133:all variables and equations
2466:Force on a charged particle
2443:05:13, 30 August 2008 (UTC)
2148:13:51, 25 August 2007 (UTC)
2076:02:10, 26 August 2007 (UTC)
2038:00:02, 26 August 2007 (UTC)
2011:09:40, 25 August 2007 (UTC)
1979:07:00, 25 August 2007 (UTC)
1930:18:10, 24 August 2007 (UTC)
1893:08:58, 24 August 2007 (UTC)
1876:they wouldn't be zero, but
1815:22:00, 23 August 2007 (UTC)
1769:17:41, 23 August 2007 (UTC)
1740:05:16, 23 August 2007 (UTC)
1661:20:40, 22 August 2007 (UTC)
1502:05:02, 21 August 2007 (UTC)
618:This is interesting. Here
90:Weber and Original Research
3594:
3519:Faraday's law of induction
3366:Faraday's law of induction
3077:Faraday's law of induction
2533:Template:Electromagnetism2
2233:Andrew (www.techmind.org)
2198:means the B-field (except
207:Relativity/Magnetism again
2808:23:22, 4 March 2008 (UTC)
2759:13:53, 4 March 2008 (UTC)
2529:Template:Electromagnetism
2514:Magnetic Field Modulation
937:13:55, 21 July 2007 (UTC)
925:10:48, 21 July 2007 (UTC)
871:10:23, 20 July 2007 (UTC)
833:22:51, 18 July 2007 (UTC)
818:22:44, 18 July 2007 (UTC)
795:22:34, 18 July 2007 (UTC)
683:02:09, 19 July 2007 (UTC)
600:23:33, 18 July 2007 (UTC)
556:23:25, 18 July 2007 (UTC)
528:23:00, 18 July 2007 (UTC)
510:21:19, 18 July 2007 (UTC)
499:19:56, 18 July 2007 (UTC)
479:19:30, 18 July 2007 (UTC)
469:18:38, 18 July 2007 (UTC)
454:22:46, 18 July 2007 (UTC)
439:14:20, 18 July 2007 (UTC)
432:just beating a dead horse
408:14:41, 19 July 2007 (UTC)
381:13:03, 19 July 2007 (UTC)
333:11:13, 19 July 2007 (UTC)
303:23:14, 18 July 2007 (UTC)
263:22:54, 18 July 2007 (UTC)
241:22:44, 18 July 2007 (UTC)
221:14:07, 18 July 2007 (UTC)
202:21:19, 18 July 2007 (UTC)
194:13:31, 18 July 2007 (UTC)
177:13:47, 18 July 2007 (UTC)
122:13:29, 18 July 2007 (UTC)
107:10:24, 18 July 2007 (UTC)
3579:17:03, 19 May 2008 (UTC)
3426:17:03, 19 May 2008 (UTC)
3272:22:41, 17 May 2008 (UTC)
3213:22:11, 16 May 2008 (UTC)
3168:17:52, 16 May 2008 (UTC)
3152:17:49, 16 May 2008 (UTC)
3104:17:13, 15 May 2008 (UTC)
3004:16:09, 14 May 2008 (UTC)
2901:Link to discussion below
2867:16:18, 15 May 2008 (UTC)
2498:11:58, 8 June 2009 (UTC)
1874:Galilean transformations
1862:Galilean transformations
1841:Galilean transformations
2973:changing electric field
1870:Lorentz transformations
1866:Lorentz transformations
1837:Lorentz transformations
732:It then goes on to say,
3541:Ampere's circuital law
3388:Ampere's circuital law
2733:
2416:
2394:
2372:
2255:
1611:
1588:
1566:
1474:
1292:
1185:
1135:
1073:
1027:
932:feel free to add it.
147:material for which no
3528:Jefimenko's equations
3375:Jefimenko's equations
3130:equations and vectors
2989:Miscellaneous
2929:and continuing until
2734:
2417:
2395:
2373:
2256:
1801:by a single source.)
1631:comment was added by
1612:
1589:
1567:
1475:
1293:
1186:
1136:
1074:
1028:
42:of past discussions.
2684:
2404:
2382:
2276:
2245:
1598:
1576:
1515:
1305:
1198:
1148:
1086:
1040:
957:
900:= -gradĪ¦ -(partial)d
720:It says on page 460
3545:Maxwell's equations
3431:Feedback from Steve
3392:Maxwell's equations
3278:Feedback from Steve
3081:Maxwell's equations
2634:Maxwell's equations
151:source can be found
18:Talk:Magnetic field
2766:Talk:Lorentz force
2729:
2583:electric potential
2412:
2390:
2368:
2251:
1886:magnetic monopoles
1610:{\displaystyle dq}
1607:
1584:
1562:
1470:
1288:
1181:
1131:
1069:
1023:
3559:Magnetic monopole
3406:Magnetic monopole
3274:
3258:comment added by
2824:relativistic part
2727:
2366:
2337:
2254:{\displaystyle r}
2183:
2174:comment added by
2138:
2129:comment added by
1640:
1552:
1460:
1426:
1399:
1374:
1339:
1266:
1233:
1179:
1129:
1067:
1016:
994:
487:original research
87:
86:
54:
53:
48:current talk page
3585:
3253:
2970:magnetic dipoles
2781:The term vXB is
2738:
2736:
2735:
2730:
2728:
2726:
2718:
2717:
2708:
2691:
2421:
2419:
2418:
2413:
2411:
2399:
2397:
2396:
2391:
2389:
2377:
2375:
2374:
2369:
2367:
2365:
2364:
2359:
2353:
2352:
2340:
2338:
2336:
2328:
2327:
2318:
2313:
2312:
2311:
2284:
2272:Infact it'd beĀ :
2261:'s drops out. --
2260:
2258:
2257:
2252:
2190:H-field, B-field
2169:
2124:
1626:
1616:
1614:
1613:
1608:
1593:
1591:
1590:
1585:
1583:
1571:
1569:
1568:
1563:
1561:
1553:
1551:
1550:
1538:
1533:
1525:
1479:
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1476:
1471:
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1461:
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1446:
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1427:
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1415:
1410:
1405:
1400:
1398:
1390:
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1375:
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1372:
1363:
1362:
1354:
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1340:
1338:
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1297:
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1267:
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1256:
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1234:
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1224:
1216:
1211:
1190:
1188:
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1182:
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1170:
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1160:
1155:
1140:
1138:
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1132:
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1128:
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1116:
1103:
1098:
1097:
1078:
1076:
1075:
1070:
1068:
1066:
1058:
1050:
1032:
1030:
1029:
1024:
1022:
1017:
1015:
1014:
1005:
997:
995:
993:
992:
991:
972:
967:
68:
56:
55:
33:
32:
26:
3593:
3592:
3588:
3587:
3586:
3584:
3583:
3582:
3537:Biot-Savart law
3433:
3384:Biot-Savart law
3280:
3221:
3112:
3065:magnetic dipole
2875:
2816:
2719:
2709:
2682:
2681:
2676:
2626:
2585:is part of the
2536:
2516:
2450:
2402:
2401:
2380:
2379:
2354:
2341:
2329:
2319:
2279:
2274:
2273:
2243:
2242:
2223:
2192:
1766:Alfred Centauri
1627:āThe preceding
1596:
1595:
1594:independent of
1574:
1573:
1542:
1513:
1512:
1450:
1416:
1391:
1381:
1364:
1343:
1331:
1321:
1303:
1302:
1258:
1248:
1225:
1217:
1196:
1195:
1171:
1161:
1146:
1145:
1118:
1108:
1107:
1089:
1084:
1083:
1059:
1051:
1038:
1037:
1006:
998:
983:
976:
955:
954:
945:
879:
841:
680:Alfred Centauri
597:Alfred Centauri
553:Alfred Centauri
436:Alfred Centauri
378:Alfred Centauri
289:+drho/dt=0. div
209:
187:
174:Alfred Centauri
92:
64:
30:
22:
21:
20:
12:
11:
5:
3591:
3589:
3563:
3562:
3554:
3553:
3549:
3548:
3532:
3531:
3523:
3522:
3510:
3509:
3499:
3498:
3493:
3492:
3488:
3487:
3484:other meanings
3475:
3474:
3456:
3455:
3447:
3446:
3442:
3441:
3432:
3429:
3410:
3409:
3401:
3400:
3396:
3395:
3379:
3378:
3370:
3369:
3357:
3356:
3346:
3345:
3340:
3339:
3335:
3334:
3331:other meanings
3322:
3321:
3303:
3302:
3294:
3293:
3289:
3288:
3279:
3276:
3220:
3217:
3216:
3215:
3176:
3175:
3135:
3134:
3131:
3128:
3127:equations only
3125:
3121:
3120:
3111:
3108:
3107:
3106:
3091:
3090:
3089:
3088:
3053:
3052:
3051:
3050:
3044:
3043:
3042:
3041:
3034:
3033:
3032:
3031:
3020:
3019:
3018:
3017:
3011:
3010:
2993:
2992:
2991:
2990:
2987:
2986:
2985:
2982:
2976:
2975:
2974:
2971:
2968:
2962:
2961:
2960:
2957:
2954:
2951:
2945:
2938:
2937:
2936:
2935:
2934:
2923:
2918:
2912:
2911:
2910:
2909:
2908:
2905:
2891:
2886:
2874:
2871:
2870:
2869:
2815:
2812:
2811:
2810:
2795:
2794:
2778:
2777:
2751:202.69.178.230
2725:
2722:
2716:
2712:
2706:
2703:
2700:
2697:
2694:
2690:
2675:
2672:
2642:
2641:
2625:
2622:
2621:
2620:
2619:
2618:
2617:
2616:
2594:
2593:
2592:
2591:
2587:electrostatics
2576:
2575:
2535:
2526:
2520:194.94.133.193
2515:
2512:
2511:
2510:
2500:
2485:
2456:electric field
2449:
2446:
2430:
2429:
2410:
2388:
2363:
2358:
2351:
2347:
2344:
2335:
2332:
2326:
2322:
2316:
2310:
2307:
2304:
2301:
2298:
2295:
2292:
2289:
2283:
2269:
2268:
2250:
2228:130.138.227.40
2222:
2219:
2217:
2196:magnetic field
2191:
2188:
2186:
2151:
2150:
2091:
2089:
2088:
2087:
2086:
2085:
2084:
2083:
2082:
2081:
2080:
2079:
2078:
2052:
2051:
2050:
2049:
2048:
2047:
2046:
2045:
2044:
2043:
2042:
2041:
2027:
2026:
2025:
2013:
2004:
1990:
1989:
1988:
1987:
1986:
1985:
1984:
1983:
1982:
1981:
1960:what the real
1943:
1941:
1940:
1939:
1938:
1937:
1936:
1935:
1934:
1933:
1932:
1902:
1901:
1900:
1899:
1898:
1897:
1896:
1895:
1880:. This is the
1851:
1850:
1849:
1848:
1847:
1846:
1845:
1844:
1826:
1825:
1824:
1823:
1822:
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1820:
1819:
1818:
1817:
1778:
1777:
1776:
1775:
1774:
1773:
1772:
1771:
1747:
1746:
1745:
1744:
1743:
1742:
1711:
1710:
1709:
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1707:
1706:
1684:
1683:
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1681:
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1679:
1666:
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1663:
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1650:
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1606:
1603:
1582:
1560:
1556:
1549:
1545:
1541:
1536:
1532:
1528:
1524:
1520:
1511:This equation
1507:
1505:
1504:
1483:
1481:
1480:
1468:
1464:
1457:
1453:
1449:
1444:
1440:
1436:
1433:
1430:
1423:
1419:
1414:
1408:
1404:
1397:
1394:
1388:
1384:
1378:
1371:
1367:
1361:
1357:
1353:
1349:
1346:
1337:
1334:
1328:
1324:
1318:
1314:
1310:
1299:
1298:
1287:
1284:
1280:
1276:
1273:
1270:
1264:
1261:
1255:
1251:
1245:
1241:
1237:
1231:
1228:
1223:
1220:
1214:
1210:
1206:
1203:
1192:
1191:
1177:
1174:
1168:
1164:
1158:
1154:
1142:
1141:
1125:
1121:
1115:
1111:
1106:
1101:
1096:
1092:
1080:
1079:
1065:
1062:
1057:
1054:
1048:
1045:
1034:
1033:
1021:
1013:
1009:
1004:
1001:
990:
986:
982:
979:
975:
970:
966:
962:
944:
941:
940:
939:
878:
875:
840:
837:
825:
824:
823:
822:
821:
820:
801:
800:
799:
798:
780:
779:
778:
777:
766:
765:
764:
763:
757:
756:
755:
754:
747:
746:
745:
744:
736:
735:
734:
733:
727:
726:
725:
724:
715:
714:
713:
712:
705:
704:
703:
702:
694:
692:
691:
690:
689:
688:
687:
686:
685:
676:magnetic field
665:
664:
663:
662:
661:
660:
659:
658:
657:
656:
648:
647:
646:
628:
627:
626:
625:
624:
623:
622:
621:
609:
608:
607:
606:
605:
604:
603:
602:
565:
564:
563:
562:
561:
560:
559:
558:
535:
534:
533:
532:
531:
530:
502:
501:
482:
481:
462:
461:
460:
459:
458:
457:
442:
441:
419:
418:
417:
416:
415:
414:
413:
412:
411:
410:
392:
391:
390:
389:
388:
387:
386:
385:
384:
383:
358:
357:
356:
355:
354:
353:
352:
351:
350:
349:
312:
311:
310:
309:
308:
307:
306:
305:
272:
271:
270:
269:
268:
267:
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265:
249:
248:
247:
246:
245:
244:
208:
205:
186:
185:Lines of force
183:
182:
181:
180:
179:
167:
166:
165:
164:
163:
162:
134:
133:
132:
131:
125:
124:
91:
88:
85:
84:
79:
74:
69:
62:
52:
51:
34:
23:
15:
14:
13:
10:
9:
6:
4:
3:
2:
3590:
3581:
3580:
3576:
3572:
3567:
3560:
3556:
3555:
3551:
3550:
3546:
3542:
3538:
3534:
3533:
3529:
3525:
3524:
3520:
3516:
3515:Faraday's law
3512:
3511:
3506:
3501:
3500:
3495:
3494:
3490:
3489:
3485:
3481:
3477:
3476:
3472:
3467:
3462:
3458:
3457:
3453:
3449:
3448:
3444:
3443:
3438:
3437:
3436:
3430:
3428:
3427:
3423:
3419:
3414:
3407:
3403:
3402:
3398:
3397:
3393:
3389:
3385:
3381:
3380:
3376:
3372:
3371:
3367:
3363:
3362:Faraday's law
3359:
3358:
3353:
3348:
3347:
3342:
3341:
3337:
3336:
3332:
3328:
3324:
3323:
3319:
3314:
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3078:
3074:
3073:magnetization
3070:
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2981:magnetization
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2189:
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2176:201.58.21.236
2173:
2166:
2163:
2160:
2157:
2154:
2149:
2146:
2141:
2140:
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2020:
2019:
2017:
2014:
2012:
2009:
2005:
2002:
2001:
2000:
1999:
1998:
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1996:
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1993:
1992:
1991:
1980:
1977:
1973:
1968:
1963:
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1954:
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1729:
1728:equal footing
1725:
1721:
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341:
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334:
331:
330:217.44.98.235
326:
323:
320:
316:
304:
301:
296:
292:
288:
284:
281:Of course div
280:
279:
278:
277:
276:
275:
274:
273:
264:
261:
257:
256:
255:
254:
253:
252:
251:
250:
242:
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238:217.44.98.235
234:
229:
228:
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219:
215:
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112:
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110:
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104:217.44.98.235
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70:
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3188:
3184:
3180:
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3144:164.58.59.20
3142:
3139:
3136:
3124:no math mode
3113:
2994:
2930:
2926:
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2894:
2878:invariance)
2876:
2845:
2841:
2837:
2833:
2828:
2823:
2819:
2817:
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2786:
2782:
2773:
2769:
2746:
2742:
2740:
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2677:
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2643:
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2548:
2540:new template
2537:
2517:
2505:xtremepunker
2465:
2453:
2451:
2431:
2238:
2224:
2216:
2204:
2200:historically
2199:
2195:
2193:
2185:
2167:
2164:
2161:
2158:
2155:
2152:
2122:
2119:
2116:
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2110:
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2094:
2090:
2067:
2031:
2021:
1971:
1966:
1961:
1957:
1942:
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1918:
1914:
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1723:
1719:
1701:
1697:
1694:special case
1693:
1674:
1658:Enormousdude
1633:201.58.7.211
1624:
1621:
1618:
1510:
1506:
1493:
1489:
1482:
949:
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909:
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889:
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693:
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583:
579:
575:
547:
525:FyzixFighter
520:
507:72.64.45.198
503:
496:FyzixFighter
490:
463:
431:
427:
424:not a single
423:
373:
371:four-current
370:
327:
324:
321:
317:
313:
300:FyzixFighter
294:
290:
286:
282:
260:83.131.19.16
232:
213:
210:
199:72.64.45.198
197:
188:
158:
154:
150:
146:
142:
96:
93:
65:
43:
37:
3254:āPreceding
2931:In SI units
2741:where curl
2454:Unlike the
2170:āPreceding
2131:201.58.7.37
2125:āPreceding
1839:instead of
1656:Sincerely,
644:impossible.
586:four-force
578:four-force
466:72.64.48.88
36:This is an
3085:field line
2611:Bless sins
2570:Bless sins
2490:Phasespace
2205:quantified
1698:definition
1494:really bad
1490:definition
916:purposes.
776:conserved.
428:refutation
3242:work.)
3193:Magnetism
3069:magnetism
2917:Examples:
2885:Examples:
2770:different
2568:template?
2544:talk page
1799:as a pair
943:Deduction
82:ArchiveĀ 5
77:ArchiveĀ 4
72:ArchiveĀ 3
66:ArchiveĀ 2
60:ArchiveĀ 1
3497:fingers.
3344:fingers.
3268:contribs
3256:unsigned
3197:anything
2967:currents
2602:DJIndica
2559:DJIndica
2470:catslash
2424:catslash
2263:catslash
2210:catslash
2172:unsigned
2127:unsigned
2023:language
1962:physical
1927:Melchoir
1882:physical
1878:infinite
1732:physical
1629:unsigned
934:Pfalstad
815:Pfalstad
753:section.
491:magnetic
405:Pfalstad
218:Pfalstad
191:Pfalstad
159:reliable
149:reliable
143:reliable
119:Pfalstad
3185:involve
3028:neutral
2984:H Field
2480:Starwed
2239:element
2035:Starwed
548:derives
476:Starwed
39:archive
3452:before
3299:before
3260:TStein
3246:TStein
3160:TStein
3061:magnet
2996:TStein
2899:field
2774:modern
2638:per se
2378:where
2018:said:
2008:antiXt
1890:antiXt
1675:steady
348:said".
3571:Steve
3480:helix
3418:Steve
3327:helix
3205:Steve
3189:about
3096:Steve
2859:Steve
2846:force
2838:field
2834:Force
2800:Steve
2661:Steve
2647:Steve
2590:page.
2435:Rod57
2073:Steve
2016:Steve
1976:Steve
1812:Steve
1758:start
1737:Steve
1720:start
1702:would
1499:Steve
904:/dt +
701:here,
115:WP:OR
16:<
3575:talk
3505:want
3466:near
3461:much
3422:talk
3352:want
3313:near
3308:much
3264:talk
3250:talk
3209:talk
3164:talk
3148:talk
3100:talk
3000:talk
2863:talk
2842:not'
2840:is '
2829:both
2804:talk
2755:talk
2665:talk
2651:talk
2494:talk
2460:work
2448:Work
2439:talk
2180:talk
2135:talk
1967:only
1958:know
1921:and
1807:only
1803:GOOD
1795:GOOD
1762:good
1724:true
1637:talk
588:must
580:must
3543:or
3539:or
3471:sub
3390:or
3386:or
3318:sub
3201:any
3199:in
2783:not
2531:vs
2145:DAG
1888:.--
1791:BAD
584:any
576:any
434:.
3577:)
3561:".
3424:)
3408:".
3270:)
3266:ā¢
3211:)
3166:)
3150:)
3102:)
3083:,
3079:,
3075:,
3071:,
3067:,
3063:,
3002:)
2933:.
2897:H'
2865:)
2806:)
2787:is
2757:)
2745:=
2721:ā
2711:ā
2705:ā
2702:Ī¦
2699:ā
2696:ā
2667:)
2653:)
2496:)
2441:)
2346:Ć
2334:Ļ
2321:Ī¼
2033:--
1535:Ć
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1396:Ļ
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1356:Ć
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1120:Ī¼
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985:Īµ
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873:)
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810:is
374:is
335:)
214:is
109:)
3573:(
3530:.
3521:.
3486:.
3420:(
3377:.
3368:.
3333:.
3262:(
3248:(
3207:(
3162:(
3146:(
3098:(
2998:(
2861:(
2802:(
2753:(
2747:B
2743:A
2724:t
2715:A
2693:=
2689:E
2663:(
2649:(
2492:(
2462:.
2437:(
2409:R
2387:R
2362:2
2357:R
2350:R
2343:I
2331:2
2325:0
2315:=
2309:e
2306:r
2303:i
2300:w
2297:g
2294:n
2291:o
2288:l
2282:B
2249:r
2178:(
2133:(
2068:I
1923:B
1919:E
1915:c
1635:(
1605:q
1602:d
1581:v
1559:E
1555:d
1548:2
1544:c
1540:1
1531:v
1527:=
1523:B
1519:d
1467:E
1463:d
1456:2
1452:c
1448:1
1439:v
1435:=
1432:q
1429:d
1422:3
1418:r
1413:r
1403:v
1393:4
1387:0
1377:=
1370:3
1366:r
1360:r
1352:s
1348:d
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1333:4
1327:0
1317:=
1313:B
1309:d
1286:q
1283:d
1279:v
1275:=
1272:q
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1263:t
1260:d
1254:s
1250:d
1244:=
1240:s
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1213:=
1209:s
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1176:t
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1167:s
1163:d
1157:=
1153:v
1124:0
1114:0
1105:1
1100:=
1095:2
1091:c
1064:t
1061:d
1056:q
1053:d
1047:=
1044:i
1020:r
1012:3
1008:r
1003:q
1000:d
989:0
978:4
974:1
969:=
965:E
961:d
920:(
910:B
908:X
906:v
902:A
898:E
894:B
892:X
890:v
797:)
655:"
593:a
456:)
295:J
291:J
287:J
283:J
243:)
233:J
102:(
50:.
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