Talk:Magnetic field

Template:AIDnom

Pgadfor 13:38, 10 April 2006 (UTC)

New comments at the bottom please

$\epsilon ,\mu$ instead of $\epsilon _{0},\mu _{0}$?

It's been a while since I've done this stuff, and I don't have my textbook here to verify, but shouldn't we be using $\epsilon ,\mu$ instead of $\epsilon _{0},\mu _{0}$? Or we can use H and D fields instead... am I correct?

Yes, you're correct. Using ε and μ would only be correct for linear media, using H and D would be more general. I fixed it by saying that the equations are only for free space -- generalities can stay at Maxwell's equations I think. -- Tim Starling 06:14 Apr 1, 2003 (UTC)

To Stephen: either magnetic field can be called "B" accurately, or we move some or all of this page to magnetic flux density. I don't like this "really it's H but we'll just call it B" business. It's too confusing. -- Tim Starling 08:49 11 Jun 2003 (UTC)

---

Tim: Too bad, life (and the English language) is confusing. =) The point is, that people are not entirely consistent in their terminology, and an encyclopedia should describe this. (In most cases, μ=1 so B=H and the point is moot. It's only when you're talking about both at once that you need two different names. In this case, Jackson goes by the historical names of magnetic field for H and magnetic induction for B. Purcell writes:

Even some modern writers who treat B as the primary field feel obliged to call it the magnetic induction because the name magnetic field was historically preempted by H. This seems clumsy and pedantic. If you go into the laboratory and ask a physicist what causes the pion trajectories in his bubble chamber to curve, he'll probably answer "magnetic field," not "magnetic induction." You will seldom hear a geophysicist refer to the earth's magnetic induction, or an astrophysicist talk about the magnetic induction of the galaxy. We propose to keep on calling B the magnetic field. As for H, although other names have been invented for it, we shall call it "the field H" or even "the magnetic field H".

And this is just Purcell's take. As you say, Griffiths calls H the auxiliary field, and Jackson (the god of electromagnetism) uses the historical names only when he has to distinguish B and H.

In most cases mu=1 so B=H - this is completely wrong. What most cases? Give references. There is no such situation in real world, because B = mu_0 * mu_r * H, where B - flux density (magnetic induction) in (T), mu_0 - permeability of free space 4*pi*10^-7 (H/m), mu_r - relative permeability (referred to the mu_0) of a given medium (dimensionless), H - magnetic field (A/m). Even if mu_r = 1 then B = mu_0 * H and still B is not equal H. Calling B a magnetic field is just plain wrong and this is caused mostly by shortened notation used commonly in physics. EVERYWHERE in international electrotechnical standards (the whole series IEC:60404) the only correct notation is that H is magnetic field and B is flux density (magnetic induction). Moreover, there is also J which is magnetic polarisation. H is a completely different quantity to B - similarly we could say that since resitance = 1 then voltage is synonymous with current, which is obviously not. I am going to change the whole article soon. If someone is interested please talk to me on my discussion page, because it gets too much text here. --Zureks 15:25, 26 March 2007 (UTC)

mu=1? That is incorrect. mu is most often (for non-ferromagnetic materials) much closer to mu_0 or 4 x pi x E-7 H/m ! What is this mu=1 idea? ... I just realized that someone is probably confusing mu_r with mu! He may have read that mu_r is close to 1 for non-ferromagnetic materials -- which is indeed correct. ... I just read the remarks by Zureks above. Zureks is correct and even if mu_r=1, that in no way makes B=H. (I should have read the remarks by Zureks first.) -Emfieldtheory 09:28, 6 June 2007 (UTC)

Sure mu can equal one, when you use units such that mu_0 is also one. I don't have Jackson in front of me, but I'm pretty confident that's the usage intended. --Starwed 07:56, 7 June 2007 (UTC)

Yep! That is correct. I stand corrected. Thank you. mu can be close to 1.0 for many materials (except ferromagnetic ones -- which are way different by many orders of magnitude) when the units for mu_0 are chosen for that result. I naturally assumed SI units for permeability (mu_0= 4 x pi x E-7 H/m) before thinking about it more carefully. Jackson was probably doing as you state. I never read Jackson, but he, being a physicist (assuming that he is a physicist or his doctorate is in physics), probably has an inclination towards dealing with equations where all of the constants have their value exactly equal to 1. Many physicists tend towards this approach (no offense to the many physicists here). But this approach is very misleading for permeability since all materials differ slightly from having the exact same value for mu (pick any value -- 1.00000000 or something else). Even given mu_0=1, the only material that will exactly have mu=1 is the same material that has mu=mu_0 and that is free space -- itself an often disputed concept! This is hardly the general case! I would argue that Jackson is not doing his readers any favors by misleading them into thinking that all materials have a value of mu exactly equal to 1.0000 (where mu=mu_0), or even generally close to 1.0 (since the ferros are way different). Further, as Zureks pointed out above, even when mu=1.000000 for some single material in the universe (given the proper units), that in no way makes B=H! Writers who assume that will get into difficulty when dealing with the practical interaction of EM fields with materials. -Emfieldtheory 23:07, 7 June 2007 (UTC)

- Steven G. Johnson

At no point does Purcell say that B is formally, technically, or more accurately called magnetic induction. We are not bound by historical nomenclature, and the historical terms are not a priori "correct". We no longer refer to refractive index as "refrangibility" or to Uranus as "George's star". Common usage is what goes in dictionaries, historical usage is for the history books. This is my point: if B is magnetic field in common usage, then that definition is as "correct" as any other. But if, as you claim, B is "more accurately" called magnetic induction, it would be inappropriate to write an entire article referring to B as the magnetic field. The current situation is confusing in that we claim that the entire article is inaccurate. A student learning the material wishes to hold accurate information in their head, therefore every time they see "magnetic field" on this page, they will be distracted by a little mental note telling them that this usage is not to be trusted. -- Tim Starling 00:14 12 Jun 2003 (UTC)

Tim, people aren't consistent in their usage, and that sucks, but both usages need to be reported; describing usage is not the same thing as describing "correctness." On the one hand, the term magnetic induction is a historical one for B (a fact that would arguably be worth mentioning by itself), and it remains in present day usage when people want to disambiguate B and H (e.g. in Jackson, one of the most respected advanced electromagnetism texts, but also in 2003 physics journal articles, as a quick literature search will tell you). On the other hand, many many people (including physicists and Jackson himself) call B the magnetic field, especially when μ=1. - Steven G. Johnson

Not to put too fine a point on this, but if this Jackson (renown physicist?) says that mu is usually or closely =1 for most materials, then he is somehow very confused or he more likely may have a typo in his book and really intended mu_r! -Emfieldtheory 09:28, 6 June 2007 (UTC)

The article looks good now. Thanks. -- Tim Starling 01:04 12 Jun 2003 (UTC)

---

"...the magnetic field is the field produced by a magnet." Straightforward enough, and there is a nice handy link to magnet. However, in the magnet article, I'm told that a "magnet is an object that has a magnetic field". That's not useful! That's just frustrating in a very tired and cliche manner. Could someone make one of these articles more primitive than the other? Suggestion: Make it clear to a non-physicist like me why an electron does not count as a magnet (or why the force field associated with an electron is not a magnetic field, if you prefer that point of view). (Okay, so an electron only has one pole. But having two poles can't be part of the definition of "magnet", else the article on magnetic monopole makes no sense at all and someone should fix that.)

It's certainly not clear to me why an electron does not count as a magnet. Steven may well disagree -- he has some funny ideas about classical limits and pseudovectors. But an electron has two poles. It can be modelled as a very small current loop. It even has angular momentum.

Pfftbt. I agree that an electron is a magnet; it has a magnetic moment, after all. But it's not a classical magnet, since its moment is not a vector (and various other quantum funniness). (I don't know what you mean by the electron having "only one pole", though; it's a quantum dipole, after all.) —Steven G. Johnson

Speak of the Devil...  :) -- Tim Starling 00:20, Dec 18, 2003 (UTC)

Note also that, as soon we have things like μ and ε (as in the Wikipedia Maxwell's equations), one is talking about a macroscopically averaged field, as opposed to the rapidly-varying microscopic field generated by individual particles. Sophisticated textbooks like Jackson are careful to distinguish the two (Jackson even goes so far as to use different symbols—lower-case letters—for the microscopic fields). —Steven G. Johnson 05:07, 18 Dec 2003 (UTC)

A magnetic force is that force caused by moving charges. Whenever I say that, of course, someone has to add "or spin", which may be true but I happen to think it's pretty irrelevant at your level. -- Tim Starling 22:24, Dec 17, 2003 (UTC)

(Or by a changing electric field—this was Maxwell's big contribution, after all, and leads to wave propagation in vacuum.) Anyway, the historical understanding of the magnetic field came first from the Lorentz force law, and only later was an independent "physical existence" attributed to the field in its own right, and this is a reasonable pedagogical practice as well. (Freshman physics courses typically talk about the effects of magnetic fields before describing how they are generated, which is more complicated.) —Steven G. Johnson 00:13, 18 Dec 2003 (UTC)

Good point about the changing electric fields. -- Tim Starling 00:20, Dec 18, 2003 (UTC)

To Steven:

Just a note to your comment about μ generally equaling 1. For a lot of the work that is done by Geophysicists (and maybe others), we cannot assume that. At least for me, I make a concerted effort not to exchange B and H, at least while writing. I would suggest that we all try to do the same. It gets really hairy when measuring "magnetic field decays" when they are really "changes in magnetic field flux with time."

However, no big deal. It all comes out in the wash anyway and you all make good points. Andykass 18:56, 21 March 2007 (UTC)

velocity with respect to what ?

In the equation

$\mathbf {F} =q\mathbf {v} \times \mathbf {B}$

what frame of reference is v measured with respect to? If any inertial frame will do, then v can take on arbitrary values, which would change F and therefore the acceleration applied to the charged particle, which seems absurd. Is v measured with respect to the magnetic field flux lines? Is so, what does that really mean?

If an answer to this question is added to the article, perhaps the article on the Lorentz force should be updated to also include the answer or to point to this article. MichaelMcGuffin 21:36, 30 Aug 2004 (UTC)

Any inertial frame will do. When you change inertial frames of reference, of course, not only v but also B and E will transform ... and yes, the force will transform, too, according to relativity. (This is in contrast to the original conception of electromagnetism in Maxwell's equations, which did indeed postulate a "preferred" inertial frame, that of the ether.) Indeed, you can transform to a frame of reference where v is zero, and thus the magnetic force is zero...but in this frame of reference, there will generally be a non-zero electric-field force. (A famous thought-experiment along these lines shows how, in relativity, electric and magnetic fields are two aspects of the same thing.) —Steven G. Johnson 02:14, Aug 31, 2004 (UTC)

But 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 indeed ambiguous unless one specifies what v is referred to. I would think that this should be the center of mass of the 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

Of course the current in a wire depends on the reference frame—it's electrons moving! These issues were resolved in physics in the early 20th century, and the resolution is part of the foundation of all of modern physics. I can explain in great detail if anyone asks, but I warn you the answer is not short. -- SCZenz 16:58, 5 November 2005 (UTC)

No, the total current is the sum of the currents due to the negative and positive charges and thus independent of the reference frame (if you are comoving with the electrons you are then moving relatively to the positive charges, which results in the same current). -- Thomas

Current is not a concept limited to wires. What of the current due to a single charged particle, or many charged particles, with no balancing charges? There the current must depend on the reference frame. In fact, in electrodynamics, under Lorentz transformations, current and charge transform into each other as part of the same four-vector. See, for example, J. David Jackson's Classical Electrodynamics. -- SCZenz 17:27, 6 November 2005 (UTC)

Obviously, the concept of a current is not limited to wires (in general not even to charges). The question is whether these 'bare' currents (consisting only of unbalanced charges) produce any magnetic field. But I think this question may go too far for this article. Fact is that the article uses the example of a current in a wire as an illustration, and in this case the current (and hence the magnetic field strength) does not depend on the reference frame. The velocity v in the Lorentz force requires therefore a physical definition. --Thomas

You're simply wrong. The mathematics of proving it in the specific case of a current loop would be very hard, but relativity is fundamental to electrodynamics; velocities, magnetic fields, and currents all transform in a way that keeps the equation correct in any frame. In absolute generality. To argue this further, you would need to know electrodynamics in some detail; I've cited a book above, which is the graduate text for almost every university in the U.S. (and likely abroad, although I don't know for sure). If after reading it you still disagree, I can help get you in touch with Professor Jackson. -- SCZenz 18:01, 6 November 2005 (UTC)

To clarify, here's an expanded version of the equation in the presence of an electric field:

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

There is only one reference frame in which there is no electric field, the one where the wire was stationary, and it is in this frame that F=qvxB holds. In other frames, the velocity transforms, and the B field transforms into an E field, but if you use the equation above you still get the same force. Does that help? -- SCZenz 18:10, 6 November 2005 (UTC)

So you are suggesting then also that v in F=qvxB (which is the formula given in the article for the Lorentz force) refers to the stationary wire? -- Thomas

In this example, if you leave off the qE, yes it refers to the stationary wire. If you leave in the qE, it could refer to anything; the real point is that in the frame with the stationary wire, E=0, whereas in the others it doesn't. -- SCZenz 06:25, 8 November 2005 (UTC)

Well, this should answer then the original question of this topic. I have allowed myself therefore to add a corresponding statement to this effect in the 'Definitions' section of the article.--Thomas

Yea, J (just like F) changes with a Lorentz transformation, but the dependence is only second order in v_t/c (where v_t is velocity of transformation) for a charge-neutral wire. So for practical purposes, B, E, and v depend on reference frame but J and F don't. Walk first, run later.Petwil 05:20, 8 September 2006 (UTC)

In a frame of reference in which v is equal to zero, the Lorentz force will be equal to zero. In a frame of reference in which v is not equal to zero, the Lorentz force will not be equal to zero. Not even relativity can explain how a particle could have acceleration in one frame of reference but zero acceleration in another frame of reference. (58.69.250.10 16:24, 21 February 2007 (UTC))

First mention of the thought experiment

Thanks, I see now that a sketch of a thought experiment has been added to the article. Something still confuses me though. In the thought experiment, call the first observer A (i.e. the observer that is "stationary") and the second observer B (i.e. the observer moving with the lines of charge). The current description points out that, from A's point of view, B's clock ticks more slowly, thus A perceives the net force F_A between the lines of charge as weaker, i.e. F_A < F_B. This weakening corresponds to the magnetic field that A perceives, attracting the moving lines of charge and opposing the repulsive electric force. However, couldn't we also change our perspective to that of B, and say that from B's perspective, A's clock ticks more slowly, thus we should expect F_B < F_A ? Surely there's something basic about special relativity that I don't understand. We can't have both F_A < F_B and F_B < F_A. MichaelMcGuffin 18:01, 8 Dec 2004 (UTC)

Stop thinking about the thought experiment, talk of special relativity and the twins

Isn't that the classic "twin paradox" of special relativity? I do not know how to resolve that paradox (I hear that general relativity is necessary) but both inertial observers see the other's clock as ticking more slowly than their own. How can that be? However, the two lines of charge are moving along only with observer B. You can think of B and the two lines of charge are stationary and *all* that B observes is the electrostatic repulsion of the lines of charge. Since observer A is moving relative to B and the parallel lines of charge, that observer will not see it the same as B. r b-j 18:15, 8 Dec 2004 (UTC)

(General relativity is not required to understand the twin paradox. There are various ways to show conclusively what the observed result would be, but one of the simplest is to imagine keeping the twins in constant communication by having them send radio pulses of their respective clocks towards one another. At the end of the trip, they compare their cumulative "clock" counts, and you can see that they both agree that the stationary one is older. French (Special Relativity) has a simple discussion of this. —Steven G. Johnson 21:29, Dec 8, 2004 (UTC))

It's funny, because while the "moving" twin is at a constant velocity, there is no sense that he is moving and the other is stationary. How do they view each other's clock during that period? It's only that the twin that goes to the far away planet and returns younger relative to his brother, is experiencing acceleration over the stationary twin, that you can differentiate them. I didn't think that SR had anything to say about acceleration (other than the normal Lorentz transformation in SR) whereas GR has a lot to say about acceleration (and gravitation). Anyway, my 28 year old "Elementary Modern Physics" textbook says literally that the paradox is explained by use of GR (without explaining it). Steven, could you translate that French explanation and put it in the English version of Special relativity? r b-j 22:19, 8 Dec 2004 (UTC)

Let me clear up two confusions. First, you're right that the fact that one observer has to accelerate at some point is the key difference between them — one observer does not remain in a single inertial frame of reference. However, you don't need general relativity to explain what happens, because you can make the acceleration itself a negligible fraction of the trip (and even with acceleration, you can still use special relativity as long as you describe the acceleration from the rest frame...you only need GR if you want to make the laws of physics have the same form in the accelerated frames). Second, A. P. French is the name of the author (a former MIT professor who wrote many physics textbooks in the 60's); the explanation itself is in English. Many other modern textbooks on special relativity contain a similar explanation (e.g. Basic Concepts in Relativity by Resnick and Halliday). Further, French (1968) writes:

One last remark. It has been argued by some writers that an explanation of the twin paradox must involve the use of general relativity. The basis of this view is that the phenomena in an accelerated reference frame (including the behavior of a clock attached to such a frame) are regarded in general relativity as being indistinguishable, over a limited region of space, from the phenomenon in a frame immersed in a gravitational field. This has been interpreted as meaning that it is impossible to talk about the behavior of accelerated clocks without using general relativity. Certainly the initial formulation of special relativity, although it leads to explicit statements about the rates of clocks moving at constant velocities, does not contain any obvious generalizations about accelerated clocks. And, as Bondi has remarked, not all accelerated clocks behave the same way. The clock consisting of a human pulse, for example, will certainly stop altogether if exposed to an acceleration of 1000g — in fact, a mere 100g would probably be lethal — whereas a nuclear clock can stand an acceleration of 10¹⁶g without exhibiting any change of rate. Nevertheless, for any clock that is not damaged by the acceleration, the effects of a trip can be calculated without bringing in the notions of equivalent gravitational fields. Special relativity is quite adequate to the job of predicting the time lost. It had better be, for (as Bondi has facetiously put it), "it is obvious that no theory denying the observability of acceleration could survive a car trip on a bumpy road." And special relativity has amply proved itself to be a more durable theory than this.

When I first took a course in special relativity, some years ago, I distinctly remember my professor saying that the notion that general relativity was required to describe the twin paradox had been disproved years ago. —Steven G. Johnson 22:54, Dec 8, 2004 (UTC)

that must have been some time ago. anyway i'm looking at http://www.sysmatrix.net/~kavs/kjs/addend4.html as well as twin paradox here on wiki. i understand this stuff a lot less than signal processing and FFTs. not sure if you would say the same :-) r b-j 04:51, 9 Dec 2004 (UTC)

A lot of the trouble here is that the accelerated twin is assumed to have set up a bunch of clocks synchronized within his own reference frame. They are synchronized by exchanging light signals with his clock (and/or each other). When he suddenly changes velocity he finds that these clocks are way out of synch, the difference being proportional to their (signed) distance from him. The "paradox" always results from comparing one clock with a set that are all synchronized within an inertial frame. The "traveling" twin cannot compare a "stationary" clock with his; he compares it with a sequence of clocks he has synchronized beforehand (but after he was in motion); comparisons are done between clocks instantaneously in justaposition. General relativity is not needed for the analysis. Pdn 13:47, 28 July 2005 (UTC)

You've got it all right, I think. But it is actually quite a common mistake to make among non-GR-specialist physicists. -- SCZenz 15:44, 28 July 2005 (UTC)

now, back to the thought experiment, which is messed up in its current form

This twin paradox stuff is interesting, but it doesn't seem to address my original question. In the thought experiment I was asking about, neither observer ever accelerates or changes direction, so there is never any change of "simultaneity planes" as illustrated in the twin paradox article. Each one observes a net force, F_A and F_B, between the lines of charge, according to their frame of reference. Each observer's clock ticks more slowly from the other's point of view. If we want to conclude that F_A < F_B, and not F_B < F_A, I think there's some missing reasoning or logic that should be added to the explanation of the thought experiment. Or, at least, could someone add a reference to a textbook or academic paper/article that explains the thought experiment in more detail? Thanks. MichaelMcGuffin 18:50, 9 Dec 2004 (UTC)

For reference, here is the thought experiment in its current form, which I believe is wrong: "A thought experiment one can do to show this is with two identical infinite and parallel lines of charge having no motion relative to each other but moving together relative to an observer. Another observer is moving alongside the two lines of charge (at the same velocity) and observes only electrostatic repulsive force and acceleration. The first or "stationary" observer seeing the two lines (and second observer) moving past with some known velocity also observes that the "moving" observer's clock is ticking more slowly (due to time dilation) and thus observes the repulsive acceleration of the lines more slowly than that which the "moving" observer sees. The reduction of repulsive acceleration can be thought of as an attractive force, in a classical physics context, that reduces the electrostatic repulsive force and also that is increasing with increasing velocity. This pseudo-force is precisely the same as the electromagnetic force in a classical context."GangofOne 07:59, 28 July 2005 (UTC)

The problems: First it says "lines of charge having no motion relative to each other", but then you say they experience "repulsive force and acceleration", so they ARE moving relative to each other? Second, an infinite line of CHARGE against another infinite line of charge will feel and infinite force, but it also has an infinite mass, so who knows what the acceleration will be. The force will be infinite for either observer. You say below a = F / m = (1/(4*pi*epsilon_0)*2*lambda^2/R)/rho , if this is a force; but it is force /(mass/lenght), so it's acceleration / length, whatever that is. Jumping down a few paragraphs....GangofOne 07:59, 28 July 2005 (UTC)

this following is a quantitative expression of that thought experiment. i think the twin paradox is applicable. in addition i do not see any of this "F_A < F_B, and F_B < F_A" conclusion that you have brought up. think about perceived acceleration in a direction that is perpendicular to the lines and on the same plane for both observers. i do not think you get a_A < a_B, and a_B < a_A. i think you only get a_A < a_B . the observers are not qualitatively in the same situation. both can observe the other as moving and themselves as stationary, but both do not observe the lines of charge in the same way because one is moving relative to the lines of charge and the other is not. r b-j 21:45, 9 Dec 2004 (UTC)

The classical electromagnetic effect is perfectly consistent with the lone electrostatic effect but with special relativity taken into consideration. The simplest hypothetical experiment would be two identical parallel infinite lines of charge (with charge per unit length of $\lambda \$ and some non-zero mass per unit length of $\rho \$ separated by some distance $R\$. If the lineal mass density is small enough that gravitational forces can be neglected in comparison to the electrostatic forces, the static non-relativistic repulsive (outward) acceleration (at the instance of time that the lines of charge are separated by distance $R\$) for each infinite parallel line of charge would be:

$a={\frac {F}{m}}={\frac {{\frac {1}{4\pi \epsilon _{0}}}{\frac {2\lambda ^{2}}{R}}}{\rho }}$

If the lines of charge are moving together past the observer at some velocity, $v\$, the non-relativistic electrostatic force would appear to be unchanged and that would be the acceleration an observer traveling along with the lines of charge would observe.

Now, if special relativity is considered, the in-motion observer's clock would be ticking at a relative *rate* (ticks per unit time or 1/time) of ${\sqrt {1-v^{2}/c^{2}}}$ from the point-of-view of the stationary observer because of time dilation. Since acceleration is proportional to (1/time)², the at-rest observer would observe an acceleration scaled by the square of that rate, or by ${1-v^{2}/c^{2}}\$, compared to what the moving observer sees. Then the observed outward acceleration of the two infinite lines as viewed by the stationary observer would be:

$a=\left(1-v^{2}/c^{2}\right){\frac {{\frac {1}{4\pi \epsilon _{0}}}{\frac {2\lambda ^{2}}{R}}}{\rho }}$

or

$a={\frac {F}{m}}={\frac {{\frac {1}{4\pi \epsilon _{0}}}{\frac {2\lambda ^{2}}{R}}-{\frac {v^{2}}{c^{2}}}{\frac {1}{4\pi \epsilon _{0}}}{\frac {2\lambda ^{2}}{R}}}{\rho }}={\frac {F_{e}-F_{m}}{\rho }}$

The first term in the numerator, $F_{e}\$, is the electrostatic force (per unit length) outward and is reduced by the second term, $F_{m}\$, which with a little manipulation, can be shown to be the classical magnetic force between two lines of charge (or conductors).

jumping to here. The above shows you have an understanding of what's wrong, but missed it. The '2 lines of charge' is different than '2 current carrying conductors' (overall charge is 0). What your analysis ends up with is the result for 2 current carrying conductors.GangofOne 07:59, 28 July 2005 (UTC)

The electric current, $i_{0}\$, in each conductor is

$i_{0}=v\lambda \$

and ${\frac {1}{\epsilon _{0}c^{2}}}$ is the magnetic permeability

$\mu _{0}={\frac {1}{\epsilon _{0}c^{2}}}$

because $c^{2}={\frac {1}{\mu _{0}\epsilon _{0}}}$

so you get for the 2^nd force term:

$F_{m}={\frac {v^{2}}{c^{2}}}{\frac {1}{4\pi \epsilon _{0}}}{\frac {2\lambda ^{2}}{R}}={\frac {\mu _{0}}{4\pi }}{\frac {2i_{0}^{2}}{R}}$

which is precisely what the classical E&M textbooks say is the magnetic force (per unit length) between two parallel conductors, separated by $R\$, with identical current $i_{0}\$.

Thought experiment needs to be reworded and analysis to fit. I leave it you, since I see you are competent. GangofOne 07:59, 28 July 2005 (UTC)

i'm still not clear as to what to fix without bringing in the quantative analysis. (is that what you want me to do?) even if there is outward acceleration between the two lines of charge, there is an instant of time where the relative velocity is zero (therefore not moving relative to each other). it is only this instant of time that i was referring to in the thought experiment.

two infinite lines of charge do exert an infinite force on each other, but the force per unit length is finite and if the mass per unit length is also finite, then the outward acceleration is determinable. no?

let's be specific about what needs to be fixed. i'm happy if it is fixed. r b-j 03:26, 1 August 2005 (UTC)

I have a number of comments and unclarities, maybe some are my own inadequacy of understanding. I will continue anyway. What you say directly above about the instanteaous acceleration, if it is infintesially short moment, what relevance does the speed of clock ticks? That would only apply in a finite interval of time. Anyway, my original idea was that these infinite lines of charge as an example would be better as an example as two parallel conductors, which I think your analysis is really referring to. But then the next question is , does this examplify that which it is supposed to be an example? I'm still thinking about this. But consider this: let's say we have a long but finite pair of lineal charges, just to work around the red herring of the the infinites involved. Assume the charged wires are contrained to only move away from each other, not arbitrarily freely. A force meter is put betweem them and reads some value. (The force is related to the acceleration it WOULD experience if free.) So another observer flies by in a differnt frame of reference and reads the same number on the meter. So, where's the relativity come in? GangofOne 05:26, 1 August 2005 (UTC)

i dunno how Lorentz transformation of special relativity would deal with the numerical force meter but i do know that, assuming the motion is in the x direction, Lorentz transformation does not change the perspective of distance in the y or z directions but does change how one observer views the other's flow of time and that the lengths in the x direction is changed. when the two lines are infinitely long, then they remain infinitely long after the application of length contraction.

it's just a thought experiement, not a real experiment. in a real experiment, to measure acceleration just by looking at position, we would need snapshots at at least 3 instances of time. in the thought experiment, we know there is this concept of instantaneous acceleration and we are asking what it would be at a single instance of time.

the issue about charge neutral conductors vs. these lines of charge can be dealt with by just thinking about it a little. it does not negate the physics of the thought experiment at all. the charge neutral conductors have a net magnetic field, but no net electrostatic field. the lines of charge have both electrostatic field and electromagnetic field for the "stationary" observer that observes the lines of charge moving past him/her. the "moving" observer that is moving alongside the two lines of charge observes no electromagnetic effect. it is simply electrostatic for him/her. i don't want to do this thought experiment with charge neutral conductors, but i can still use the results of current in conductors as a basis for determining the classical magnetic field. r b-j 05:07, 2 August 2005 (UTC)

ugly math symbols

I really don't like the ugly $\mathbf {B}$ in the text. Why not B for vector, or B for scalar. Much cleaner. dave 04:04, 6 Jan 2005 (UTC)

personally, i think it's cleaner if precisely the same symbol (except possibly smaller) that is used in the math equations are used in the text. whether it's $\mathbf {E}$ or $E\$. i think it's particularly cleaner if the Tex math is used for greek and exponents and subscripts and other special symbols than the kludge that many use. $x^{y}\$ vs. x^y . r b-j 17:36, 6 Jan 2005 (UTC)

Your point still has some validity, but don't cheat. Do it right—in text it should be x^y with italic symbols. A serif font would make it look better; I don't know if there's an acceptable way to do that in Wikipedia articles. The disparity in size often makes the Tex math look weird when written inline (the bottom of your E letters descending below the line is real ugly). Gene Nygaard 18:48, 6 Jan 2005 (UTC)

Depends on your screen resolution. I turn on "always render PNG" and it looks fine for me. Remember that you aren't the only person who views it. - Omegatron 02:41, Apr 26, 2005 (UTC)

I gotta add my 2 bucks. The current B and H look pretty bad. And as a programmer, anything that "depends on screen resolution" is broken. It should work the same for all resolutions. Precisely the same symbol is a good idea, but the text is pretty broken right now. Maybe the wiki redering needs to be enhanced, but something really ought to be done.

According to my corrections instead of all this mumbo jumbo with all these letters and stuff, why dont you just say R=B+C?

moving with respect to what?

"moving electric charges (electric currents) that e"

One thing I guess I never learned. Because of relativity, don't we need to specify what the particles are moving relative to? Do they not see each others magnetic field if they are not moving relative to each other? I guess they would behave as if they were only electrostatically repelling or attracting each other? Oh man, now I have confused myself... - Omegatron 23:41, Apr 25, 2005 (UTC)

This is why the presence of a magnetic field depends upon your frame of reference. Consider a charged particle moving at a constant velocity (i.e. in an inertial frame). If I am in an inertial frame of reference where the particle is moving with respect to me, I see a magnetic field. If I am in the same inertial frame as the particle, so that it is at rest with respect to me, I see no magnetic field. In general, when you change frames of reference, magnetic and electric fields get mixed up (together, they form a rank-2 tensor). —Steven G. Johnson 02:04, Apr 26, 2005 (UTC)

'O', the bottom line is that magnetic effects are a result of special relativity. That is, if you start with Coulomb's Law and then impose Lorentz invariance (or is it covariance?), you get magnetic effects. It turns out that there is an analog to magnetism in gravity - so called gravito-magnetism. I think it is also called 'frame-dragging'.Alfred Centauri 12:39, 2 September 2005 (UTC)

field line flow? field shells in open space?

I've added a little item about the orientation markers vs actual field flow. I've been unable to find anything that says if the magnetic field lines actually move or if they are simply static lines through space. (The arrow is just a reference to mark field orientation, as far as I've been able to determine.)

They don't move. In fact, they don't even exist, see below. -- Tim Starling 12:32, Jun 24, 2005 (UTC)

I'm not a professional physicist by any means, but I've also never determined if the field actually exists as separate concentrated lines/shells as iron filings demonstrate, or if the lines form only as a RESULT of the iron filings being there, building up into thicker lines as more iron filings enter the field. Is a magnetic field in empty space "ridged" as the filings suggest, or is a field in open space simply an even undifferentiated gradient from strong to weak? DMahalko 09:31, 24 Jun 2005 (UTC)

Field lines are just diagrammatic. The number drawn in any given diagram is arbitrary, the field is smooth, not ridged. Lines are just one way to show the direction and magnitude of a vector field at every point on a plane. Iron filings tend to mimic the shape of diagrammatic field lines, because adjacent lines of iron filings tend to repel each other, and because grains that are in contact tend to line up end-to-end with unlike poles touching. -- Tim Starling 12:32, Jun 24, 2005 (UTC)

This particular explanation needs to be included in the main text. It also should delve cautiously into more fundamentally what the field may consist of (e.g. alignment/coherence of virtual photons or e/p pairs from the vacuum, conceptual vortex mechanisms versus vacuum "permeability" changes leading to repulsion/attraction, etc (never liked the descriptions using compression of field lines/rubber bands for attraction). (Dfwrunner 20:54, 8 June 2007 (UTC))

Rotating magnetic field

I do not think that long quotes on Tesla's philosophy are appropriate for this article. -- SCZenz 18:13, 27 July 2005 (UTC)

I agree. I'm not sure if anything beyond the first paragraph in that section is appropriate for this article. Salsb 18:19, 27 July 2005 (UTC)

Ok, I'm paring that stuff down now... -- SCZenz 18:27, 27 July 2005 (UTC)

The people should be in the section. JDR 18:30, 27 July 2005 (UTC)

Why? The discussion strikes me as a historical interlude about an engineering application. Shouldn't it be in say an article about the history of motors as opposed to a basic article on magnetic fields? Salsb 18:37, 27 July 2005 (UTC)

It should be with the topic. The RMF concept is redirected here, so the history should be with that (as it is the history of the RMF). JDR 18:49, 27 July 2005 (UTC)

Yeah, people really aren't appropriate here. This article is about the concept of the Magnetic field, in great generality. My objection to your additions, Reddi, is that you are going into great detail on an issue you care about in particular, when no other sub-topic of magnetic field has such detail. A separate article really is more appropriate. -- SCZenz 18:41, 27 July 2005 (UTC)

SCZenz, people were in the see also section before. A separate article (which would be ideal) has been redirected here over and over again (lately by Salsb, WMC; earlier by Starling). JDR 18:49, 27 July 2005 (UTC)

People are appropriate for the see also section, not for the main article. As for the redirects, I think perhaps the issue is that the history of rotating magnetic fields, and the engineering applications, should be in separate places. In particular, I rather suspect that electrical motors and power plants have their own extensive articles already. But a separate article that brings it all together, if it's important to you to organize it like that, wouldn't be the end of the world to me. -- SCZenz 18:56, 27 July 2005 (UTC)

I removed the history except the two main, Ferriari and Tesla.

As for the redirects, the concept of "rotating magnetic field" is redirected here, and the engineering applications and it's history should have (in the least) a summary here.

A separate article on the RMF should exist. JDR

There is a place where this would fit in nicely: Electric_motors#AC_motors. As you point out, this is an important engineering principle, and your text seems to be part of the history of motors. Salsb 18:54, 27 July 2005 (UTC)

The concept redirects here. It wasn't even mentioned before, which it should have been, and it should have a brief summary, in the least. JDR 19:09, 27 July 2005 (UTC) (eg., The concept redirects here. The history of the concept should be at the article where the concept is.)

Since there is minimal history in this article, I disagree, I would include it in a nice history of engineering article but its not too important Salsb 19:28, 27 July 2005 (UTC)

The one other objection I have to this section, is the inclusion of the Earth's magnetic field from dynamo theory. This is about convection and rotation in fluids creating a magnetic field not about a rotating magnetic field. So if it should be placed in this article, which I am not sure it should be, it shouldn't be in this section Salsb 19:28, 27 July 2005 (UTC)

The Earth is one big dynamo (core rotor; atmosphere stator), directly related to rotating magnetic fields. JDR 19:41, 27 July 2005 (UTC)

As written it does not follow well, since the earth does not have a rotating magnetic field. There are articles on the Earth's magnetic field, on dynamos and on the dynamo theory, so I don't think there needs to be an additional discussion here, as opposed to a see also. Salsb 19:57, 27 July 2005 (UTC)

Salsb, you have to understand that you are talking to someone who thinks that the Earth's magnetic field is rotating because "it goes from south to north. THIS movement is the rotation of the field. It's rotating back and forth ... from the south pole to the north and back again. That's why compasses work." (see Talk:Rotating magnetic field.) —Steven G. Johnson 02:38, August 5, 2005 (UTC)

Stevie ... contrary to your negative implication via the link ... the inner core and outer core are rotating (akin to a rotor and stator) conducting (north-south) the magnetic field of the earth ... "THIS movement is the rotation of the field" and this action does make a compass work. JDR

Rotating magnetic field proposal

To find a way out of the impasse thus far, I propose that we have Reddi put his material for rotating magnetic fields into rotating magnetic fields, in place of the redirect. The concept isn't important enough for the space taken up in magnetic field, but it is true that a rotating magnetic field is a concept, independent of its applications, and that it could be useful. It might end up being a longer article than I would have written, but I don't think of that as a realy problem. But we certainly need a consensus somehow... thoughts? -- SCZenz 20:00, 27 July 2005 (UTC)

A rotating magnetic field in of itself is not special, its useful though its applications. I suggest that this text be added to the Motors article under AC motors, since there is a small history section there already which could be expanded. Salsb 20:05, 27 July 2005 (UTC)

What I'd consider even better, if Reddi would take the text on rotating magnetic fields and expand it into an article on the history of electric motors, that would be very cool indeed. Although admittedly a fair amount of work. Salsb 20:09, 27 July 2005 (UTC)

That sounds interesting ... I have been aquiring much of Edison's patents and Tesla's patents (as well as others). Alexanderson (sp?) built huge machines ...and this would include the early work in electrostatic machines. I'll kick this history of electric motors around in my head abit. Sincerely, JDR 18:19, 8 November 2005 (UTC)

I think the Magnetic Field article as it stands now is OK We'll keep a short section on rotating fields, and leave rotating magnetic field as a redirect. Sound ok? -- SCZenz 23:18, 27 July 2005 (UTC)

More velocity relative to what

I just reverted the edit made assigning v a specific reference frame in F = qvxB, because it was not correct. I then made an edit that I hope clarifies the situation. Here's a fuller explanation, for reference.

F = qv x B is always the correct force due to the magnetic field in any reference frame. However, the magnetic field can turn into an electric field as you change reference frames, so this equation will not remain constant for a system that produces a B field with moving charges (i.e. a current loop). However F = q(E + v x B) does remain constant in all reference frames; i.e. the total electromagnetic force can be defined unambiguously. F = qv x B is only the correct electromagnetic force when E = 0. In the case of a current loop, this occurs in the frame where the loop itself isn't moving.

However, the first part of the definition section doesn't refer to any example; it's a general example for force on a particle due to a B field. It doesn't say where the B field is from, so it is the correct equation for the force due to the B field in whatever frame you choose—you just have to pick the particle velocity and B field for the same reference frame. Hope that helps. -- SCZenz 21:12, 8 November 2005 (UTC)

I don't agree that the addition I made by referring v to the rest frame of the wire was incorrect. Given that F=qvxB in the article it was correct (I thought you agreed with this above). The total electromagnetic force is not written out here, so it should not be referred to either. As it is now, it is only counter-intuitive and in fact inconsistent (note also in this context my further comment under Talk:Lorentz force#Should the Lorentz Force Include the Electric Field?).--Thomas

The article states that the force due to the magnetic field is qvxB, which is correct in any reference frame. It's just not the same force in every reference frame, because you don't have the same magnetic field in every reference frame. -- SCZenz 19:58, 10 November 2005 (UTC)

How should the magnetic field depend on the reference frame if it is produced by the current in a wire? Assuming the wire is overall electrically neutral, the electric field is zero (in all reference frames) and the total current (and hence the magnetic field) is independent of the reference frame as well, as it depends only on the relative drift velocity of the ions and electrons in the wire (which has nothing to do with the test charge velocity v).--Thomas

Charge and current transform into each other under Lorentz transformations. Thus the magnetic field and electric field produced from them change under Lorentz transformations. A mathematical discussion of this is at an advanced undergraduate or graduate level, and non-trivial, so if you want a detailed proof I would do far better to refer you to a textbook than to try to reproduce the explanation myself. I recommend reading J. D. Jackson's Classical Electrodynamics, chapter 11, particularly section 11.9. I believe Griffiths' electromagnetism textbook also has a discussion; both texts are in the reference section of the Magnetic field article itself. -- SCZenz 19:13, 11 November 2005 (UTC)

Consider this heuristic, handwaving argument. You say: "Assuming the wire is overall electrically neutral, the electric field is zero (in all reference frames)...", but is it? If the e- are moving w.r.t. the wire (the positive charges), then there is a relativistic length contraction, and the charge per length of the e- is no longer the same as the charge per length of the positive charges, so there is a "net charge" per length, (or , better stated, something that acts like a charge, that can cause forces, etc). It "is" the magnetic field. The magnetic field is a relativistic effect. (And that's why the E and B are mixed up together, and mutually change, depending on the motions of the charges and point of space. (This could be better expressed, but maybe it's helpful. Continue your questions, maybe we can generate some explanations suitable for the article.) GangofOne 20:17, 11 November 2005 (UTC)

To continue, you say: "and the total current (and hence the magnetic field) is independent of the reference frame as well," No the current depends on the ref. frame. If I am static with the wire and "see" the e- move, I "see" one value for the current. If I move with the e- so it is the wire that moves, I "see" the opposite value for the current. If I split the difference, and move half the speed, so that the wire is moving one way and the e- the other, I see no current. So the current is NOT reference frame independent.

The idea is that from any inertial frame of reference, current, E, B, v, ALL change, but is such a way that F=qE +qvxB is still true. GangofOne 20:39, 11 November 2005 (UTC)

I am afraid what you are saying above is incorrect in several respects:

First of all, you seem to forget that electrons and ions are oppositely charged, so if you change the rest frame from one to the other, the velocity changes direction but also the charge, i.e. the current does not change sign (contrary to what you stated above).

Secondly, it would be quite a funny wire if the charge density of the ions would become different from that of the electrons depending on the reference frame: this would mean that charge neutrality would not be fulfilled anymore and hence corresponding electric force fields would be set up along the wire in addition to the electric field that you propose to be created perpendicular to it. So overall you would have a net force depending on the reference frame, which is physically not acceptable.

Thirdly, one should bear in mind that a magnetic fields doesn't do any work on a charged particle as the associated force is always perpendicular to the velocity. This property should obviously not depend on the reference frame. However, the proposed relativistic 'charging' of the wire however should always create an electric field directed towards to or away from it, i.e. it is only perpendicular to the velocity if the charge velocity is parallel to the wire. In all other cases, the resultant field would do work on the charge and change its kinetic energy. Again this is physically not acceptable.

For clarification, just consider the case of a charged particle in the magnetic field of a wire from a kinematical point of view: in the rest frame of the wire the orbit of the particle is a circle around the corresponding field line (assuming the velocity v to be perpendicular to the magnetic field and the field as homogeneous i.e. the Larmor radius as sufficiently small). Now if you view this scenario from a different inertial reference frame moving with velocity U, the latter velocity will simply be superposed to the Larmor circle which the charge traces out in the wire's frame i.e. we will have a Cycloid motion, which is however just the result of the superposed linear velocity but not of an electric field. --Thomas

You're right that GangofOne made an error in the bit about moving along with the electrons above. Ignoring relativity, you'd be right that the current wouldn't change with reference frame. However, because the electrons are moving at a different rate than the protons, they are affected differently by Lorentz transformations. Thus current does transform into charge (a fact which, even if we explain it poorly, is cited in every sufficiently advanced physics textbook on the subject).

Your second argument that, when the wire becomes charged, there is an electric field along the wire is rubbish; a charged wire has an electric field that points radially outward, as is solved in elementary E&M textbooks (see, e.g., Halliday, Resnick, and Krane's Physics, Volume 2, section 29-5). This removes the new, unexplained force and the phantom work you were concerned about.

A suggestion: if you want to keep trying to understand what's going on, that's great—the charged wire obscures the physics principles a bit, which makes it interesting. But you're not going to succeed in overturning the learned consensus of physicists on an issue that's been settled for over half a century, whether you win an argument with a lowly grad student like me on Wikipedia or not. -- SCZenz 18:49, 12 November 2005 (UTC)

I would agree that Wikipedia is probably not the right place to overturn learned consensus, but on the other hand, the contributors should also have some responsibility regarding the factual correctness of the articles. In this sense I think the points I mentioned are at least worth considering here.

I could actually go much further and discuss the Lorentz transformation in the first place, but I think this would go too far off topic here (for anyone interested, see my web page http://www.physicsmyths.org.uk/lorentz.htm ).

In any case, I don't agree that my argument connected with the charge invariance is rubbish: if the charge densities of the negative and positive charges are different in the wire, charge invariance requires that there is a corresponding surplus charge external to the wire, or in other other words, the negative and positive charges are merely distributed over different lengths, with the total charge being identical and unchanged. Now this may not make a significant difference if the wire is much longer than the distance to the wire, but consider the opposite case where the distance d is much larger than the length of the wire: in this case, the electric field is basically that of a point charge and does not depend on the charge density of the wire i.e. a different Lorentz contraction for the electron and ion distribution would not result in a net charge (there would only be a second order effect decreasing like 1/d^4 and which could therefore be made arbitrarily small compared to the magnetic field (which goes like 1/d^2 for the short wire)). So in this case the Lorentz contraction would not yield the required electrostatic force when changing reference frames.

Another point that I find very questionable in corresponding derivations is the fact that reference frame of the moving charge (i.e. the one where the v in F=qvxB is zero) is apparently being treated as an inertial frame when in fact the particle is accelerated due to the Lorentz force in the wire's frame (if you treat for instance the earth as an inertial reference frame and assume that the sun rotates around it, you would obviously arrive at vastly incorrect results regarding the force between the two). So there is actually no additional electrostatic force required in the frame of the moving charge as this frame is not inertial but itself accelerated by the force on the charge in the wire's frame (an exact definition of 'wire's frame' is still missing as well by the way, not only here but also in some textbooks that I checked out). --Thomas

Basically, what you're point out is that treating a current loop in the context of relativistic electrodynamics is complex, and you have to be very careful if you care about all the details. But nobody does care--there are far more interesting tests of relativity and electrodynamics. That's why textbooks don't discuss it. -- SCZenz 19:22, 15 November 2005 (UTC)

Suggestion to merge articles

I strongly disagree with the suggestion to merge this article with magnetic flux density. These are two different, though related, concepts. For starters, the two have different units of measures (dimensional decompositions). Magnetic field is amps per meter, magnetic flux density is webers per square meter. -- Metacomet 15:06, 31 January 2006 (UTC)

The article magnetic field discusses in detail both fields B and H. Therefore, there is no reason to have a separate article discussing B. (The units of B and H are indeed different. But the units of B from "magnetic field density" and of B from the article "magnetic field" are the same, and this is exactly the same quantity). Yevgeny Kats 17:13, 31 January 2006 (UTC)

In my opinion, there should be an overview article that discusses both B and H, including high-level definitions, differences between the two, and the relationship between them. Then there should be two separate, more detailed articles, one article on each of the two fields. For historical reasons, and because of the way electromagnetics is often taught in introductory courses, there is a lot of confusion between B and H. It would be a shame if WP were to reinforce the confusion, instead of trying to clarify the distinction and explain where it comes from. Again, these ideas are simply my opinion. -- Metacomet 17:28, 31 January 2006 (UTC)

As a suggestion, the three articles might be called:

• Magnetic field (overview) to give high-level overview
• Magnetic field intensity to give detailed discussion of H
• Magnetic flux density to give detailed discussion of B

-- Metacomet 17:32, 31 January 2006 (UTC)

I think it's not possible to discuss H separately from B. It is possible, however, to discuss B without discussing H. Therefore, I'd suggest to divide it to

• "Magnetic field", which will discuss only B.
• "Magnetic fields in matter", which will discuss B and H in matter.

Each article will include a major link to the other.

Currenly we have some random division of the content between the articles "magnetic field density" and "magnetic field"

Yevgeny Kats 18:47, 31 January 2006 (UTC)

I disagree. I prefer the approach that I suggested above. You can easily discuss either field by itself, as long as you have a definition that does not involve the other, which is quite easy to do. I don't really want to get into a huge argument about it though. You are entitled to your opinion, and I am entitled to mine. -- Metacomet 19:56, 31 January 2006 (UTC)

I think we may put the whole discussion about B and H in the same "magnectic field" article, but we should create a separate magnetic flux density article, with some description, and pointing to the magnectic field article... There (here) we can explain B as being an macroscopic effect of atomic phenomena... But I strongly disagree that "it's the same thing", or that the same "magnetic field" name applies to both, that's an absurd. At least this doesn't happen in the books I've read, or in my university.

In the electric field and electric displacement field case, the two articles exist without problem. The only problem is some confusion about what this "macroscopic thing" means... I may try to rewrite some of the four pages! Is there anybody who believe that the current versions are untouchable!? -- NIC1138 03:19, 20 April 2006 (UTC)

The question is not what you prefer, or what I prefer, but what is actually used by professionals and by educators. A little dose of reality here: the name "magnetic field" is used for both B and H. See any recent professional literature, or a respected textbook such as Jackson. IIRC, Griffiths uses "magnetic field" for B and "auxiliary field" for H. Other textbooks insist on the historical usage of "magnetic induction" for B and "magnetic field" for H. Living languages are sometimes ambiguous...learn to deal with it. (As for B and H having different units, that's a totally artificial consequence of SI units.) Which is not to say that B and H are the same thing, but you are doing readers a disservice if you oversimplify the terminology situation or proscribe certain common usages as "wrong". I would suggest a single "Magnetic field" article that describes both B and H, with the focus on B (a more intuitive concept since it appears in the Lorentz force), and sub-articles on specific topics such as magnetization of matter, etc. —Steven G. Johnson 02:33, 21 April 2006 (UTC)

I don't know how physicists teach the concept of magnetic field but for me B is the flux density and H is the magnetic field and I was quite shocked to read the article. How do you teach hysteresis and saturation without having the two. All the books I know about motor design (ie applied electromagnetism) separates these two because we need them. Ckoechli 15:40, 8 September 2006 (UTC)

You still talk about H when relevant, it's just that in physics, B is considered more fundamental and thus is normally what when means when one says "the magnetic field." Griffiths offers the quote below. --Starwed 20:55, 30 January 2007 (UTC)

Many authors call H, not B, the "magnetic field." Then they have to invent a new word for B: the "flux density," or magnetic "induction" (an absurd choice, since that term already has at least two other meanings in electrodynamics). Anyway, B is indisputably the fundamental quantity, so I shall continue to call it the "magnetic field," as everyone does in the spoken language. H has no sensible name: just call it "H".

— David J. Griffiths, Introduction to Electrodynamics

Question of validity - biot savart law

$\mathbf {B} ={\frac {\mu _{0}}{4\pi }}{\frac {q}{r^{2}}}\mathbf {\hat {r}} \times \mathbf {v}$

is this equation right, or should r hat and v be switched (in the cross product). Cause i just had a physics HW problem that contradicted. Still doing the HW, so don't have time to check up on anything. User:Fresheneesz

The Biot-Savart Law is usually applied in differential forms, like in the following two expressions:

$\mathbf {dB} ={\frac {\mu _{0}}{4\pi }}{\frac {dq}{r^{2}}}\mathbf {v} \times \mathbf {\hat {r}}$

$\mathbf {dB} ={\frac {\mu _{0}}{4\pi }}{\frac {i}{r^{2}}}\mathbf {ds} \times \mathbf {\hat {r}}$

This law is important in studying magnetic fields. May somebody please add more detail about that in the article? Thanks.
- Alanmak 23:35, 12 February 2006 (UTC)

Yes, I agree with you. I am not a wikipedia user myself so I am not going to do any kind of correction or whatever in this article, but a friend of mine called me and asked me to explain some magnetics because she was trying to get some general idea first using this article before starting serious studies usin textbooks. When she showed me, I could immediately understood the source of her confusion. This article is too focused in relativity and simply ignore the basics like Gauss' Law and Biot-Savart Law. They have very significant practical and historical value, the second Maxell Equation is the Gauss Law, not that formula derivated from the Lorentz Transformation. By the way, the Gauss Law, in its both "shapes" have more practical value than the Lorentz transformation. If I wasn't an engineer I wouldn't understand more than a half of information in this article. This article is in an Encyclopedia and should not be just a badly-done gathering of formulas. Who ever wrote this article, if you think you are cool showing far too advanced formulas and definitions, then you are very wrong. No wonder why wikipedia is not respected in serious academic environments. —The preceding unsigned comment was added by 222.150.226.168 (talk) 14:21, 13 April 2007 (UTC).

About the picture at the beginning of the article

This picture looks nice. But there are a few things that could be improved:

1. Magnetic field lines should form closed loops.
2. It is a widely accepted convention to use "B" instead of "M" as the symbol for magnetic field.
3. As the positive and negative ends of the electric wire has already been indicated, it is not necessary to specify that the current is "DC". It would be better to use "I", which is the common symbol for electric current.

Would anybody like to modify that picture for a little bit?----

I think the current (and the mag field) should be shown in the opposite directions. Its easier for me to think CW rotation than CCW.--Light current 14:49, 10 April 2006 (UTC)

The picture looks ok to me. The current flow is fine. In physics/engineering, there are two types of current flow: conventional and actual. The diagram is merely being very explict and indicating conventional current flow (+ to -). For an introductory type of explaination, being brain-dead and explicit is good. And I think the magnetic field orientation is correct, but I'd have to check and my books are in storage. Summary: don't touch anything yet, untill we're sure. —The preceding unsigned comment was added by 69.109.242.191 (talk • contribs) 12:32, 11 April 2006 (UTC)

For an easy mnemonic that doesn't require checking your reference books, see Right hand rule. --Blainster 23:05, 25 April 2006 (UTC)

Yes, this picture is really well designed to be easy to check with the right hand rule. Whoever drew it was clearly thinking ahead. I'd vote that we keep it as is. --- Markspace 18:37, 4 May 2006 (UTC)

Im not saying its wrong, Im saying it would look better to me if the picture was turned around thats all. BTW can you please sign and date your posts by typing 4 tildes ~~~~. THanks--Light current 19:55, 11 April 2006 (UTC)

I think this picture is actually quite confusing: it seems to imply that the ends of the rod are charged - and thus that density of charge plays a role in magnetism, while only the density of current actually matters. _R_ 23:19, 4 July 2006 (UTC)

I think the picture is fine. In fact, it helps explain why parallel wires with like currents attract each other. In the "Symbols & Terminology" section, there appears this sentence, which I don't like: "While like charges repel and unlike ones attract, the opposite holds for currents: if the current in one of the two parallel wires is reversed, the two will repel." It's misleading to suggest "the opposite" of some principle holds for currents. What holds for everything is that opposites attract. The two wires attract because they present opposite magnetic polarities to each other, which becomes obvious if you stare at that swell picture for awhile. The arrows pointing down in the picture would be pointing up in an identical wire right next to it, since the magnetic field lines form a circle.Charlie Raeihle 21:53, 12 July 2006 (UTC)

I may be mad but I would take the plus and minus signs to indicate the ends were connected to positive and negative sources respectively and since electrons are negative the current would flow from negative to positive. I suggest changing to the +/-ve notation commonly used in physics to give a sense of the potential at each end of the wire, that will be more intuitive for readers I feel in respect to what way the electrons are moving. Apart from that its fine.

Iron filings pic.

I suggest that the picture does not show the magnetic lines of force due to an 'isolated' magnet. What it shows is the magnetic lines of force with a lot of iron filings scattered in the magnetic field. The picture is therfore misleading in that if you plotted the field lined using one tiny isolated bar of metal, the pattern you would get would not be the same as that shown! Comments? --Light current 18:20, 12 April 2006 (UTC)

I agree it is confusing and i do not like it, i also cannot speak english good.

Electric and magnetic fields- whats the difference?

If the presence of a dielectric (E >1) can distort an electric field, does the presecnce of a ferromagnetic material (U>1) distort a magnetic field from a magnet. If so, what do iron filings do to the magnetic filed lines when spread around a bar magnet? 8-?--Light current 00:12, 4 May 2006 (UTC)

Yes. The field lines are nearly perpendicular to the surface of a high permeability material. Madhu 14:36, 10 August 2006 (UTC)

So the iron filings actually distort the magnetic field?--Light current 00:08, 11 August 2006 (UTC)

Here's an image of distorted field lines. It's not great, but it's the first one I could find quickly. Of course, iron filings are usually light enough to be shifted by the field of a typical bar magnet, so each affects the other. If the iron filings were not permitted to move (or the field strength was not sufficient to move them), the field lines would follow the filing, rather than the other way around. Think about the field lines within an iron core transformer. Without the core, the field lines would be all over the place :-( Madhu 04:29, 11 August 2006 (UTC)

Right hand rule

um...this is the left hand rule, no? reverse thumb vector...Gatoatigrado 03:32, 6 June 2006 (UTC)

No that picture is of the right hand rule. For magnetic fied, if the current flows in the direction of your thumb, the magnatic field goes in a circular path in the direction of your fingers. You need to make a kind of thumbs-up sign with your right hand for that. The left hand rule is motion of charged particles. --H2g2bob 16:21, 6 June 2006 (UTC)

Can anything block magnetic fields?

I know that many objects are not magnetic (i.e. wood) but magnetic fields still go through them. For example when you place a metal object behind a thin piece of wood and place an attracting magnet on the other side, the force pulling them together is the same as it would if there was nothing in between them(given they were the same distance appart). So the magnetic field goes through these things, is there anything that magnetic fields do not pass through? So basically an easy way to understand would be: if there was a strong magnet in the center and you surrounded it behind a wall of substance X which then makes it so nothing outside the wall would feel any pull from the magnet inside. Is there any such substance? Thanks ~Matt Email, Demostheness@hotmail.com

See http://en.wikipedia.org/wiki/Permeability_%28electromagnetism%29 and mumetal.--Light current 11:32, 5 August 2006 (UTC)

A superconductor (read Meissner effect) will block a magnetic field up to a limit depending on the material the superconductor is made from and its temperature. Conductors will dampen changes in the magnetic field flowing through them as the changes induce a current which in turn induces a magnetic field which perfectly opposes the applied field change. This is very short lived as the currents induced die away due to resistance in the material and so stop blocking the field. Its still worth knowing about becuase it leads to Inductance and a few effects to do with fluctuating magnetic fields CaptinJohn 11:15, 13 March 2007 (UTC)

Intuitive explanation of B

Hello. I came to this page hoping for an intuitive explanation of the measure B of an electic field, but I can't find one. I have searched the web for several hours and I still can't find one.

The measure E of an electric field make sense to me, the amount of force in the direction of E, per unit of charge of a test charge placed in the field. However B is a bit of a mystery.

Why didn't physicists define B as being in the direction of the force as well - something like force in the direction of B per unit charge per unit velocity. It seems a bit ugly to me to have the force of an electric field with E, but the force of the magnetic field is at right angles to B. I'm sure there is a deep reason for it, but I don't see it. It would be helpful, on this page, to have an intuitive explanation of exactly what B is in a physical sense, and why it is at right angles to the velocity of the test charge and the force on the test charge. Can anyone please enlighten me? Nicolharper 16:33, 9 August 2006 (UTC)

The difference is that electric charges move in the direction of E and magnetic domains line up in the direction of B. I believe magnetic field lines were theorized based in orientation of other magnets or iron filings within a B field. Michael Faraday, James Clerk Maxwell, and others observed and formalized the relationship between moving charges and magnetic fields. It wasn't planned, it was discovered long after magnetism was observed. I guess it would possible to redefine B in the direction of a moving charge, but then it would be at right angles with intuitive notions of field lines based on simple experiments with a compass or iron filings. Madhu 14:32, 10 August 2006 (UTC)

Thanks. Much appreciated. It would be good if this could be explained in the article. Maybe I'll do it if I find time. Nicolharper 15:38, 10 August 2006 (UTC)

What is all this about pressure??

I noticed this bit in the section about energy density : << For example, a magnetic field B of one tesla has an energy density about 398 kilojoules per cubic metre, and of 10 teslas, about 40 megajoules per cubic metre.

This is the same as the pressure produced by magnetic field, since pressure and energy density are essentially the same physical quantities and thus have the same units. Thus, a magnetic field of 1 tesla produces a pressure of 398 kPa (about 4 atmospheres), and 10 T about 40 Mpa (~400 atm). >>

Does anyone understand what this means about pressure, as a physics PhD student i just dont get what its on about. Pressure on what? Physical pressure? what does it mean? A magnetic field on its own does not exert pressure it only exerts pressure on a magnetic substance inside the magnetic field and then the force is proportional to the field gradient, not field strength.

Any comments.

This was supposed to be force (or pressure) on ferromagnetic materials as described in slightly greater detail in the electromagnet article. The old section included a complete, but short derivation. Since then, it has been edited to the point where it no longer appears to make sense. I'm not completely sure why it was whittled down, but you are welcome to improve it. Madhu 23:02, 12 September 2006 (UTC)

Magnetic Field's

The diagram showing the magnet and iron filings is not acuate for when you use an electromagnet http://www.ndt-ed.org/EducationResources/CommunityCollege/MagParticle/Graphics/coil1.gif Also magnetic feilds can be alternating by using an electromagnet and alternating current insted of direct current Does anyone know much about the effects of AC magnetic feild's? Im esspecally intrested in verry high frequencies Alan2here 15:15, 1 October 2006 (UTC)

I Know that alternating magnetic fields are very difficult to generate at high frequencies. This is because to alternate : I Know that alternating magnetic fields are very difficult to generate at high frequencies. This is because to alternate the field requires you to dump all the energy in that field. If you look at the above numbers (I'm not sure they are correct but I have no reason to doubt them) then to make a 1000cc (a 10cm cube) volume field of 1T oscillate at 1kHz would need a 400kW of power to be generated and dumped. The problem you have is that it would also need a lot of very thin wire wound very tightly to actually generate the field. The wire would melt very easily if not cooled and what is difficult to do. I ran a 1T water cooled magnet in DC (direct field) mode when I did my masters and it took about 5 minutes to get it up to 1 T because if you went any faster it burned out. So with our cooling system (which was huge) we could have had a 1T field oscillate at 0.833mHz (one cycle per 20mins). On that basis Id say it is the cooling system that limits suck work.

I should note here that the magnet I used was NOT superconducting. It you use a superconducting magnet that power is dumped in the power supply rather than the coils so its easier to cool but I think you still have the same problem of needing ever bigger cooling systems to run even small, low frequency fields. CaptinJohn 11:31, 13 March 2007 (UTC)

major error in lead

The lead stated:

In physics, a magnetic field is that part of the electromagnetic field that exists when there is a changing electric field. A changing electric field can be caused by the movement of an electrically charged object, as in an electric current; or a combination of the orbit of an electron around an atom and the spin of electrons themselves, as in a permanent magnet.

That was just completely wrong. A constant electric current, for example, does not create a varying electric field, but it does create a magnetic field. There are two physically distinct mechanisms for creating a magnetic field, which are expressed by two separate terms in Maxwell's equations. I've fixed the error.--24.52.254.62 04:54, 2 November 2006 (UTC)

Although I've fixed that error in the lead, the whole rest of the article is in a horrible state. The explanation section is extremely poorly written, and has bizarre, mispelled sentence fragments floating around in it. The article is also not written so as to be intelligible to the general reader. I've added a cleanup tag.--24.52.254.62 05:05, 2 November 2006 (UTC)

Still somewhat of an error in "a magnetic field is that part of the electromagnetic field that exerts a force on a moving charge." Particles with spin can have intrinsic magnetic moments, and thus interact with a magnetic field. A point particle with spin isn't quite the same as a moving charge. Glancing through the article I see that the explanation section needs serious work. (There seems to be some confusion between the electric field and the electromagnetic field. Also, it implies that the electromagnetic field has a non-relativistic portion?) --Starwed 07:50, 2 December 2006 (UTC)

Clean Up Is Required

I Think A Clen Up Of This Article Should Be Ordered. Meanwhile, can anyone suggest other articles??? — Preceding unsigned comment added by 89.241.123.153 (talk • contribs)

Yeah, it could probably do with a bit of a review. Meanwhile..., other articles for what? --h2g2bob 19:58, 21 November 2006 (UTC)

Large error in explanation

Note on the following presented text in the main article:

"A thought experiment one can do to show this is with two identical infinite and parallel lines of charge having no motion relative to each other but moving together relative to an observer. Another observer is moving alongside the two lines of charge (at the same velocity) and observes only electrostatic repulsive force and acceleration. The first or "stationary" observer seeing the two lines (and second observer) moving past with some known velocity also observes that the "moving" observer's clock is ticking more slowly (due to time dilation) and thus observes the repulsive acceleration of the lines more slowly than that which the "moving" observer sees. The reduction of repulsive acceleration can be thought of as an attractive force, in a classical physics context, that reduces the electrostatic repulsive force and also that is increasing with increasing velocity. This pseudo-force is precisely the same as the electromagnetic force in a classical context."

This explanation is incorrect. In the first place the "reduction of repulsive acceleration" as a "reduction of the electrostatic repulsive force" violates the requirement that lorentz force must be conserved in all inertial frames. Also additional problems arise from the implied direct relation between force and acceleration. The proper explanation is to first insist on charge conservation in all frames, then insist on the fundamental correctness of coulomb interaction in all frames. Then under the transformation of inertial reference frames, notice that the force also changes even though charge and coulombic interaction is invariant. Then and only then can a force every bit as real as that suffered by two neigbhoring charges be surmised to force the invariance of coulomb interaction. Just my small contribution if anyone is interested.

                                        The shadow

WTF does "B" stand for anyway?

What does it stand for, seriously? I know it's the Magnetic Flux Density or Magnetic Field Strength, but I have no idea what word it's actually supposed to stand for, if any. You know the way "v" is the initial letter of "velocity" and the way "c" is the inital letter of "capacitance"? Well, WTF does "B" mean? It's driving me mad, I can't find its meaning anywhere! (Of course, I don't actually care, as long as I understand the actual physics, but still I like to know what it means...) Perhaps it stands for "Bloody Victorians and their crap notation." Stuart Morrow

It doesn't stand for anything im afraid. Its like s for distance CaptinJohn 11:05, 13 March 2007 (UTC)

I think there is, at least, an explanation for why the letter B is the convention. At the very least, I'v heard such an explanation, but I can neither remember it nor vouch for it's veracity. --Starwed 21:34, 21 March 2007 (UTC)

the s for distance is an abbrevation for "spatium" (latin).

Extension to theory of relativity section

To me, this section seems like it could be unclear or misleading.

Einstein explained in 1905 that a magnetic field is the relativistic part of an electric field.

This makes no sense as written. If the magnetic field is the "relativistic part", what is the nonrelativistic part of an electric field? I would prefer to say that both are components of an electromagnetic field.

It's true that the magnetic force between two moving charges can be deduced from their interaction in one particles reference frame and special relativity. That's an entirely different matter than the magnetic field being "part" of the electric field.

One of the products of these transformations is the part of the electric field which only acts on moving charges — and we call it the "magnetic field".

Again, this isn't how the issue is normally presented. The author of this section seems to be using the phrase "electric field" to refer to what is more commonly called the Electromagnetic field. Even if this is valid terminology in some literature, it isn't what's used elsewhere on wikipedia and should definitely be avoided.

The quantum-mechanical motion of electrons in atoms produces the magnetic fields of permanent ferromagnets. Spinning charged particles also have magnetic moment.

This phrasing makes it seem like the particles are always physically spinning on some axis, which of course isn't necessarily the case. I would also say that the phrase "quantum-mechanical motion" should link to the article on Spin (physics), rather than the word spinning.

A magnetic field is a vector field: it associates with every point in space a (pseudo) vector that may vary through time. The direction of the field is the equilibrium direction of a magnetic dipole (like a compass needle) placed in the field.

Currently this is simply a one liner; it doesn't seem to belong in this section. Perhaps a broader description of how the magnetic field behaves under transformations should go here?

We use the symbol ${\vec {B}}$ for the magnetic field and for the sake of mathematical simplicity (one symbol instead of seven).

I'm probably missing something here, but what are the seven symbols referred to? I know a previous version of this section discussed writing the magnetic field as combinations of the electric field and velocity; is this an orphaned ref. to that? Also, the text following this statement is just a general discussion of the meaning behind the magnetic field vector, which is needed somewhere in the article, but probably in a more general section.

My thoughts are as follows:

• Details of the relativistic transformation of the electric field into the magnetic are not needed in this article; they belong at Electromagnetism and related pages.
• The section should be renamed, and be devoted to briefly explaining the role of the magnetic field in "advanced" theories like relativity and QED.
• Some of the content in this section belongs in a more general dicussion of the properties of the magnetic field; conversely, the entire introduction to the properties section is actually about special relativity. It would be nice if some dicussion could happen on this talk page about exactly how the article should be laid out!

--Starwed 12:04, 23 February 2007 (UTC)

thanks to anon 132.236.59.30 for fixing spurious duplication from me.

it must have been a spurious "paste", but i do not know how it happened nor how i didn't see it afterward. r b-j 06:30, 10 April 2007 (UTC)

Relativity and the Magnetic Field

This quote is taken from the main article,

"Einstein explained in 1905 that a magnetic field is the relativistic part of an electric field".

The main article then goes on to say that the magnetic field arises as a by-product of the Lorentz transformations.

However, the Lorentz transformations as applied to electric and magnetic fields already include the inter relationships determined by Maxwell's equations. The magnetic field therefore already exists independently of relativity or Lorentz transformations. We cannot therefore state that magnetism is a relativistic effect of the electric field under a Lorentz transformation.

It would be more correct to state that Einstein's Theory of Relativity effects the magnetic field relativistically, but that the magnetic field as affected relativistically doesn't differ in nature from the classical magnetic field.

If we were to suggest that the classical magnetic field was merely an effect of coordinate frame transformation, this would be tantamount to suggesting that the magnetic field is only fictititious.

The magnetic field is clearly a different concept altogether from the electric field. The electric field measures force per unit electric charge. The magnetic field, whatever it is, doesn't even have the same dimensions. (58.10.102.2 15:12, 29 April 2007 (UTC))

The E and B fields have the same units relativistically speaking. They only appear to have different units because a factor of 'c' has been taken out of the time unit and placed into the electric field unit. Measuring time as a distance means qE and qB have units of momentum per meter. Alternately, if distance is measured as a time, qE and qB have units of energy per meter (AKA force). Alfred Centauri 18:35, 29 April 2007 (UTC)

I still dislike how this is presented in the article. Clearly the magnetic field and the electric field are inter-related, and it's reasonable to think of them as two aspects of the same thing, but I'd really like to see a source for the electric field being considered the more fundamental. And if I don't see a specific source for the claim that Einstein said that "a magnetic field is the relativistic part of an electric field." I'm going to remove it from the article. --Starwed 07:04, 30 April 2007 (UTC)

Defining the magnetic field is actually a very tricky business. The mathematical definition is given by the Biot-Savart law but this doesn't assist any as regards giving a physical picture for the layman. Maxwell seemed to have been in the process of giving a picture of the magnetic field as lines of force acting along the angular momentum vector of a sea of molecular vortices that are aligned solenoidally along their angular momentum axes. However, this explanation has been disregarded by mainstream modern science. Since then, all definitions of the magnetic field, whether classical or relativistic have been purely mathematical.

Interestingly, the Lorentz force first appeared in Maxwell's original paper regarding molecular vortices and it appeared again as one of the original eight 'Maxwell's equations' in his famous paper 'A Dynamical theory of the Electromagnetic Field' 1865. The Lorentz force is actually the solution to Faraday's law of electromagnetic induction. However, in 1884, Oliver Heaviside reformatted Maxwell's equations and he presented a version of Faraday's law in partial time derivative format. This partial time derivative version of Faraday's law eliminates the convective component of the solution ie. E = vXB. The E = vXB component was once again introduced to physics when Heaviside's versions of Maxwell's equations were subjected to the Lorentz transformation. The Lorentz transformation had the effect of restoring the convective component that Heaviside had removed as well as introducing the relativistic factors.

This seems to have given rise to the misconception that the E = vXB, nowadays referred to as the Lorentz force, is purely a relativistic phenomenon. In fact the relativistic factors are relativistic, but the core formula goes back to Maxwell and it exists quite independently of Einstein's theories of relativity. David Tombe 30th April 2007 (210.86.146.100 07:53, 30 April 2007 (UTC))

The Simplification of the Article

Unfortunately magnetism is not a simple subject. It is considerably more complex than either gravity or electrostatics. There are therefore no half measures. As far as the layman is concerned, the magnetic field is a force field that exists around a bar magnet or an electric circuit and which aligns iron filings into a solenoidal pattern. A changing magnetic field induces an electric current in a wire. There is no point in making it more complicated than that for the layman.

For the student of physics, there is alot of hard work ahead. Alot of the hard grind was done in the nineteenth century by Ampère, Weber, Faraday, and Maxwell to name only a few. Our present day textbooks on electromagnetism lay out all the laws as established by these nineteenth century masters.

Einstein's theories of relativity came about in the twentieth century after electromagnetism had already obtained its final form. Relativity is a specialized topic of which the effects only become noticeable at very high speeds approaching the speed of light.

I can't therefore see why it has been felt necessary to cloud an already complicated topic with relativity, especially when most of the readers will be laymen. All matters relating to Einstein's theories of relativity should be kept to a special section further down. There is absolutely no need to mention relativity in the definitions when all those definitions and laws were established before Einstein was born.

The article should begin with a very simple overview of magnetism for the layman. It should proceed with an historical evolution of its dicovery and formulation going back to lodestones in Asia Minor, leading to Gilbert, and then to Oersted, Ampère, Faraday, Maxwell, Weber etc.

The various laws such as,

(1) Ampère's law (2) Faraday's law (3) Maxwell's Equations (4) The Biot-Savart law (5) The Lorentz Force

etc. should then be dealt with in separate sections further down.

Dr. Nelson White, Cambridge 28th April 2007 (61.7.165.234 13:57, 28 April 2007 (UTC))

I agree. I actually said two months ago that whoever wrote this article is just showing off that they have done a course on Einstein's Theories of Relativity. (58.8.1.227 15:49, 28 April 2007 (UTC))

I agree with most of this as well. There's no need to bring relativity into it straight off the bat, especially since there is a separate article on the Electromagnetic field. However, I do think that the introduction shouldn't be simplified to the point of being incorrect; defining it as "a force field that surrounds electric current circuits", for instance, is inaccurate and misleading. Define it correctly, and then offer up more everday examples. --Starwed 07:19, 30 April 2007 (UTC)

I first added the "technical" tag ("This article may be too technical for a general audience..."), because someone had got as far as complaining on the help desk about the article. Within minutes, someone made this edit [1]. I felt it was a little unfortunate, because (a) it didn't reduce the technical nature enough (b) it removed material which was built on in the article (c) it removed tags. But it would seem ungrateful to revert the edit, so I tried to put back what was most obviously deleted, in context.

I guess it might be useful to share my thoughts on the article and the process in general... I think the word "simplification" needs to be used carefully. It doesn't necessarily mean that articles should have technical content removed. Rather, the article can be structured to give people what they need at the level they need it. This is often an entirely different skill than being an expert in a subject, but I hope experts will appreciate the value of this. Above all, Wikipedia is written for a general audience: defences like "this is basic stuff, in any college textbook" don't work for a technical introduction.

It's worth commenting on the lead section since few people know what the Wikipedia style guide says. The lead section should be removable from the article without any actual information going missing; it should be a summary, drawing on the rest of the article. So this is the ideal place for a simple overview. However, it may be that the subject needs a rather longer overview, which could be placed as the first actual section in the article.

Also, I feel the article has too great an emphasis on physics, and far too little on the technology. These are not incompatible. People will often come to this article because they have heard that "(some technology) works with magnetic fields". Take a look at maglev for instance, which tells us that a Maglev train is a form of rail transport that works using magnetic levitation, and that Magnetic levitation is a method by which an object is suspended above another using magnetic fields. Would a layman be any the wiser after coming here? I think not. I'd like to see the "Applications" section expanded beyond a few bullet points (it looks as if it was grudgingly allowed). I'd like to see the lead section: explain magnetic fields without physics terms; talk about where magnetic fields are found naturally and how they are made artificially; give a few key applications of magnetic fields in the everyday world, and perhaps one or two more exotic applications like maglev (exotic unless you use Shanghai airport). Then, still in the lead section, and signposted by a few words like "In physics", a very general overview of the topics of discussion under physics.

If relativity complicates matters beyond classical physics, that should be mentioned, but not by replacing the classical discussion. After all, the articles on Newton's law have not been scrapped in favour of a relativity-modified form of the laws of motion. There is room in this article for a reasonable separation if that's how things are (and I honestly don't know, because I don't understand the article in its present form). Notinasnaid 07:48, 30 April 2007 (UTC)

Your point about Newton's laws is absolutely correct. When we are studying Newton, we don't need to keep labouring the fact that Einstein made amendments that come into effect when we approach the speed of light. Likewise with the magnetic field. But there is added confusion as regards the magnetic field because when Heaviside's equations are treated relativistically, the vXB component of the Lorentz force appears. This has led to the claims that the magnetic field is a relativistic effect. In actual fact, the Lorentz transformations are only restoring the convective component to Maxwell's equations, that was removed by Heaviside in 1884. The Lorentz transformations as applied to electric and magnetic fields do two things. (1) They introduce the relativistic factors, and (2) they restore the convective vXB component. But the convective component was there anyway in Maxwell's original equations independently of relativity and so it cannot be claimed that the magnetic field is the relativistic component of the electric field.

As such, any article on the magnetic field should leave all references to relativity to a special section. David Tombe 30th April 2007 (210.86.146.100 08:41, 30 April 2007 (UTC))

Reference to general relativity should be in the article beause special relativity is the very reason why magnetic fields actually exist. So it should be noted in the lead section that on the fundamental levem, magnetic field is only a relativistic manifestation of more fundamental electric field to help reader to not have common misconcepcions about magentic field. Thank you. --83.131.65.112 11:28, 30 April 2007 (UTC)

You are quite wrong. The Lorentz transformations only expose what is already inside Maxwell's equations and they add a convective term vXB that was already in one of Maxwell's equations before Heaviside removed it in 1884. Check equation (D) in Maxwell's paper 'A Dynamical Theory of the Electromagnetic field' 1865. Magnetism was around long before relativity was ever thought of. There are too many people who think that it is cool to show off that they know about relativity and they want to dominate an article about the magnetic field with relativistic effects that only occur as we approach the speed of light. (58.10.103.126 13:45, 30 April 2007 (UTC))

58.10.103.126, it should be at least mentioned that entire electrodynamics (not QED of course) can be derived from Coulomb's law and special relativity. Sometimes people have common misconcepcion that special relativity is consequence of Maxwell's equations just because they were discovered before. That's why it's worth to say that magnetic field is only a relativistic manifestation of more fundamental electric field. Thank you. --83.131.5.63 14:52, 30 April 2007 (UTC)

You're quite wrong. Relativity adds effects to electromagnetism but it doesn't create it. The Lorentz force and the Biot-Savart law are both present within Maxwell's original equations of 1864. All that the Lorentz transformation does is adds a relativistic factor which becomes noticeable if we travel close to the speed of light. You're assertion that the whole of electrodynamics can be derived from Coulomb's law and special relativity is totally wrong. Try deriving the whole of electrodynamics using only Coulomb's law and special relativity but without using Maxwell's equations and see how well you get on.

You seem to think that we have to dwell on this relativistic amendment. (58.10.103.126 15:40, 30 April 2007 (UTC))

I agree with the suggestions above that this article should focus on a qualitative description of the magnetic field and its applications and leave the quantitative material to one or more of the electromagnetic / relativity articles, e.g., four-potential, vector potential, EM field tensor, etc.). The key to doing this such that future editors won't be so tempted to simply add the quantitative 'stuff' back is to make mention (but only a mention) of the relativistic aspects in a separate section with a prominent link to the main article that the summary is taken from. This approach seems to work well in other articles. In other words, the subject of 'magnetic field' is so broad that this article should be primarily composed of summaries from other main articles with pointers to those articles for the benefit of those desiring more detail. Alfred Centauri 12:53, 30 April 2007 (UTC)

To 58:10:103:126: Consider the following quote from the textbook "Basic Concepts in Relativity and Early Quantum Theory" by Resnick & Halliday:

"In fact, starting only with Coulomb's law and the invariance of charge, we can derive (see Ref. 7) all of electromagnetism from relativiy theory - the exact opposite of the historical development of these subjects."

Ref 7 is "Electricity and Magnetism" by Edward M. Purcell. Alfred Centauri 23:02, 30 April 2007 (UTC)

Whoever made that quote seems to have forgotten that the relativity has to be applied to Maxwell's equations first in order to give it any meaning in the context of electromagnetism. The relativity itself cannot then claim credit for the relationships that were already inherent in Maxwell's equations. You cannot link up relativity directly with Coulomb's law and expect the Biot-Savart law and the Lorentz force to fall out. That quote is obviously a high handed quote and should not be taken seriously. (210.86.146.70 08:54, 1 May 2007 (UTC))

Maxwell's equations (and therefore entire electrodynamics) can be derived from Coulomb's law and special realtivity (assuming the invariance of charge). It is only historical incidence that Maxwell's equations were discovered before special relativity. It is also wrong to think that special relativity is due to laws of electrodynamics, quite opposite - if special relativity wouldn't be true (and if Galilean transformations would be true), there would be only electric fields. Thank you. --83.131.93.54 10:26, 1 May 2007 (UTC)

You are totally overlooking the fact that when relativity is applied to electromagnetism, the first step is to apply it to Maxwell's equations. I can't therefore see how it can then be inferred that Maxwell's equations are a product of relativity. If you believe in what you are saying, can we have a citation that demonstrates how Maxwell's equations are obtained from Coulomb's law and relativity? (58.10.102.198 12:18, 1 May 2007 (UTC))

On the contrary, beginning with just the Lorentz transformation (with c being understood as an invariant speed), it is straightforward to show that potential energy must be in the form of a four-vector. Deriving the four-force resulting from this four-potential yields a force law identical in form to the Lorentz force. The dynamics of the force fields also follow. Thus, as had been said above, assuming only Coulomb's law (in the 'rest' frame) and the invariance of charge, SRT is all that is needed to not only to see that a velocity dependent force must exist , but also to derive the resulting dynamics. See "Electricity and Magnetism" by Edward M. Purcell and [2] Alfred Centauri 13:22, 1 May 2007 (UTC)

What potential energy are you talking about? You begin with a Lorentz transformation and then suddenly you are talking about a potential energy. Where did this potential energy suddenly come from? It came from Heaviside's versions of Maxwell's equations. I've seen the derivation myself. Maxwell's equations are converted into a potential energy format using both the magnetic vector potential and the electrostatic potential. The Lorentz force comes out of Maxwell's equations and not out of relativity. There is no point in deluding yourself that relativity alone can produce the Lorentz force in conjunction with Coulomb's law.(58.10.102.198 13:38, 1 May 2007 (UTC))

But, Maxwell's equations are the ones that necessarily come from Coulomb's law, STR and invariance of charge. --83.131.1.164 15:44, 1 May 2007 (UTC)

83.131.1.164, you forgot about Faraday's law and Ampère's law which are the core equations in Maxwell's equations. Ampère's law and Faraday's law are most certainly not the product of relativity. You are getting confused with the fact that the Lorentz transformations are applied to Ampère's law and Faraday's law in four vector form and the Lorentz force falls out. How could Ampère's law regarding a current in a wire producing a magnetic field around it possibly be a consequence of relativity? That current in the wire has an absolute interaction with the surrounding magnetic field that it generates. Now see my reply below to Alfred Centauri for the rest.

You really aren't paying close enough attention to what I wrote. Please note that I wrote about a potential energy. In my comments above, I'm stating that a potential energy must be a four vector to be consistent with the SRT. That result does not come from Heaviside or Maxwell. Then, as should have been clear from my comments, the force associated with this potential must have a certain form and that form necessarily involves a velocity dependent part. None of the preceding involves any appeal to electromagnetism.

The Lorentz transformation alone requires that a force and its associated potential be of a certain form if they are to be covariant under the transformation. Thus, if all we know is that there is an inverse square law force that can be repulsive or attractive - call it whatever you want, the 'X' force - then, by the SRT, that force will necessarily obey a force law of the form of the Lorentz force. Further, the dynamics of the force fields associated with the 'X' force will necessarily obey laws of the form of Maxwell's equations. Alfred Centauri 15:16, 1 May 2007 (UTC)

I'm paying attention alright. First of all, your linked reference didn't cover the issue in question, but it doesn't matter because I've done all this anyhow. To get the vXB component from the Lorentz transformation, we need to apply it to the Heaviside partial time derivative versions of Maxwell's equations. What you have said above is total nonsense. Show me a citation. You are talking about a potential energy without specifying what that potential energy is. And you think that I don't know that it has to be the four vector potential energy associated with Maxwell's equations ie. the one that involves the electrostatic potential energy and also the magnetic vector potential A. It is ludicrous to suggest that the the vXB component of the Lorentz force comes about simply from any four vector potential energy that is consistent with SRT.

When the Lorentz transformation acts on the Maxwellian four vector potential, in respect of generating the vXB component, it is not doing anything that a simple Galilean transformation couldn't do. It is merely adding the convective component unto a partial time derivative and making it a total time derivative. That vXB term was already in Maxwell's equations before Heaviside took it away. In other words, the Lorentz transformation is merely adding on the velocity dependent term that the Galilean transformation could also add on. The vXB term is merely the difference between a partial time derivative and a total time derivative

If you are so confident that the magnetic field is only a relativistic effect, then can you please explain to me the role of relativity in paramagnetic attraction and diamagnetic repulsion. Paramagnetic attraction as you know is when a magnet picks up non-magnetized pieces of metal. Let's see you explain that relativistically. (58.10.103.214 16:19, 1 May 2007 (UTC))

The linked referenced most certainly does cover the issue in question and the fact that you dismiss it outright with an "it doesn't matter" speaks volumes.

Further, why would I need to specify the potential? A non-relativistic potential energy is simply an energy valued function of space. A relativistic potential energy is simply four energy valued functions of spacetime where the four functions are components of a four-vector. What more needs to be said???. If you had bothered to read the section in the linked textbook entitled "Forces from Potential Momentum", you would have seen an equation that has the exact form of the Lorentz force law but expressed in terms of an unspecified relativistic potential.

So please, let me suggest that you come down off of your high horse and address what you believe to be incorrect about that equation. Alfred Centauri 01:09, 2 May 2007 (UTC)

I saw the equation that you are talking about (15.12). That equation does indeed have an identical form to the Lorentz force which also happens to be equation (D) of the original eight Maxwell's equations in Maxwell's paper 'A Dynamical Theory of the Electromagnetic Field'(1865). See part III at [3]. But tell me what has that equation got to do with Einstein's theory of relativity? I can't see your point. That equation falls straight out of classical hydrodynamics yet you are trying to tell me that it is somehow a product of relativity.

I will now give you a web link that shows the Lorentz transformation producing that same equation (15.12) but with relativistic gamma factors added. The main point is that in order to do do, it has to act upon the Heaviside partial time derivative versions of Maxwell's equations, and in doing so it merely restores the convective vXB term that Heaviside removed from Maxwell's original equation(D). This is the way that the relativists do it, and you can see the result at equation (19). See the web link [4]

You have been trying to tell me that the Lorentz transformation can act on the Coulomb force alone and still produce the results at equation (19). I challenge you to show me how. Let me see you producing the Lorentz force using only the Lorentz transformation and Coulomb's law.

Your reference was supplied on the basis that it was going to show just that, but it didn't. It merely stated the Lorentz force as being a fact when the condition curl A = B holds. This is Maxwell's second equation and it is a hydrodynamical vortex equation. Whoever that contributor was who noted that B is an axial vector should perhaps take note of this fact as it might provide some clues as to what the magnetic field actually is.

Meanwhile until such times as you can produce a citation which demonstrates that the Lorentz transformations can produce the Lorentz force directly from Coulomb's law, then we can no longer maintain this myth that the magnetic field is the relativistic part of the electric field.

If you really believe that a magnetic field is the relativistic part of an electric field, can you then consider iron filings sprinkled on a sheet of paper over a bar magnet. Consider the solenoidal lines of force that become exposed and then tell me what reference frame I would have to go into for this pattern to convert into a radially divergent electric field pattern. (210.86.146.250 05:29, 2 May 2007 (UTC))

Anonymous said: "You have been trying to tell me that the Lorentz transformation can act on the Coulomb force alone and still produce the results at equation (19)". I hope your kidding because that's not what I've been saying all along. The idea here is to find the answer to the question "Knowing only the Coulomb force and the STR (and the fact that they are incompatible), how must the Coulomb force be modified to be relativistically covariant?". To find the answer to this question, one needs to know what a relativistic force field must 'look' like.

Right off the bat it is clear that the potential associated with the force cannot be a scalar but must instead be a four-vector. This implies that the 'gradient' (partial deriviative) of this four-vector potential will be a rank 2 tensor field on space time. The four-force will then be given by contracting the field tensor with the four-velocity.

Then, it is clear that this tensor field must be anti-symmetric since the four-force must be orthogonal to the four-velocity. This anti-symmetry is assured by taking the difference of the 'gradient' with its transpose. Thus, the 'gradient' operation on the four-potential will 'look' similar to a curl operation as the components of the tensor will consist of differences of partial derivatives.

Now, when this anti-symmetric field tensor and the four-velocity are contracted, the resulting four-force has a spatial part that is in the form of a Lorentz force law. This must be true for a force field in STR so, the Coulomb force must look this way to covariant. So, now we know that the Coulomb force must have a velocity dependent part in order to relativistically covariant. That is, knowing only Coulomb's force law and the STR, we deduce that there must be a magnetic field (part) and an associated magnetic force.

Further, the dynamics of the tensor field are constrained by STR and, when these tensor equations are written in '3 + 1' form, we get equations of the form of the Maxwell equations. Alfred Centauri 13:13, 2 May 2007 (UTC)

I'll now translate what you have just said into plain English.

The Coulomb force is not relativistically covariant but Maxwell's equations are.

That's it in a nutshell. I've never before seen such an illogical chain of total and utter nonsense as you have written above. You have presumed to work backwards to Maxwell's equations because of Einstein's theories of relativity. There wasn't a single grain of sense in anything that you said.

Maxwell himself deduced the Lorentz force from three dimensional hydrodynamics. You can see how he did it between equations (54) and (77) in his paper 'On Physical Lines of Force' 1861. It can't therefore be deduced from relativity also. What you are doing is taking a known result and then pretending to derive it using a language that nobody could possibly understand.

There is nothing to beat the benefit of hindsight, and what you have said above is totally unacceptable because it is totally incomprehensible.

At any rate we can prove the point far easier without even resorting to maths. You say that a magnetic field is the relativistic part of an electric field. OK then, tell me which frame of reference I need to go to in order to view solenoidal magnetic field lines around a bar magnet as radial electric field lines? (58.10.103.145 14:49, 2 May 2007 (UTC))

You need to cut back on the personal insults. I'm sorry if you don't understand what Alfred stated, but it's actually a pretty common line of argument in physics texts. For example, section 12.1.A in Jackson states that: "The general requirement that γL be Lorentz invariant allows us to determine the Lagrangian for a relativistic charged particle in external electromagnetic fields, provided we know something about the Lagrangian for nonrelativistic motion in static fields." The form of the Lagrangian is then deduced using similar arguments as above, although "Verification that [this] does indeed lead to the Lorentz force equation will be left as an exercise for the reader." --Starwed 22:16, 2 May 2007 (UTC)

Well Starwed, I'll leave you to do the excercise. Let me know when you have it completed. (210.86.146.200 04:41, 3 May 2007 (UTC))

Just to make a small point, I have to disagree with Anonymous' statement that "...It can't therefore be deduced from relativity also." Just because Maxwell could derive his equations well before relativity doesn't mean that starting from a different starting point (which may or may not include relativity) you can't get to the same conclusions. Certainly in classical mechanics and quantum theory there are multiple pictures and formalisms which give the same results. Both Newton's Laws and the Lagrangian will give you, say, the same equations of motion for planets going around a star (or for charged particles in a field I suppose; in the classical regime only, that is). And in quantum mechanics, there are a handful of formalisms (the Schroedinger Eqn and the Heisenburg Eqn come to mind). So, just because there exists a method X of getting to a result doesn't mean that method Y is invalid.

As to explaining complicated magnetic fields in terms of electrostatic-like fields, it seems to me that any such exercise would be too complicated to be meaningful. In some sense, for instance, a bar magnet's magnetic field is a result of all the magnetic fields of its constituent atoms and molecules. The fields of each of these are caused by effects which can be fudged classically (orbital angular momentum) and those which can't (spin). I would think you could fudge the former, but working with the latter would probably involve relativistic quantum theory, with which I am unfamiliar. But at the same time, it seems to me that according to someone sitting on a charged particle (with all its uncertainty in position and momentum) would only see a radial field (even if the rest of the universe seemed to be doing rather wacky things). Of course, the transformation from the rest frame of any given particle to a frame at rest with respect to the bar magnet as a whole would be horrendously complicated, if not impossible to write down. And it would only deal with one particle at a time. And of course, this has all the status of a thought experiment, and isn't rigorous. But I think it gets the idea across. DAG 23:20, 2 May 2007 (UTC)

Anonymous: your nutshell summary indicates to me that (at least) you didn't comprehend what I said. But, simply because you didn't comprehend it doesn't imply that it's utter nonsense. But don't take my word for it (OK, I know that you won't). Consult any advanced text on the STR written in the language of tensors to see what you've haven't seen yet.

You said "You say that a magnetic field is the relativistic part of an electric field." In fact, I have been arguing that the electromagnetic field equations can be derived from the STR and Coulomb's law (and invariance of charge) alone. Clearly, you disagree with this, however, you keep coming back to this example of a bar magnet as if it has a bearing on my arguments above. Why don't you see that it doesn't?

It (should be) clear to anyone with a reasonable grasp of the STR that it is not possible in general to find a frame of reference in which the the magnetic field vanishes everywhere. Consider the very simple case of a two charges moving parallel with different speeds. In what frame of reference does the magnetic field vanish everywhere for this most simple case? So why exactly is it that you keep bringing your example up?

Even better, please try to explain to me what relevance you believe your example has to my assertion that the STR (alone) requires that any force has a velocity dependent part?

Finally, if you didn't believe what I said earlier then your won't believe this either. In the context of the STR, all components of force depend on velocity. The 3-force we see coming from the gradient of a 3-potential is in fact a velocity dependent force that is orthogonal to the motion... the 'motion' through time that is. Enjoy! Alfred Centauri 02:35, 3 May 2007 (UTC)

No. What you said in your previous letter is what is known as 'Defensive Rubbish'. It is a strategy used when somebody is cornered in an argument. The strategy is to talk such absolute total and utter nonsense that nobody could possibly understand it. It then allows you to claim that the fault lies with that person for not understanding it. Stage two is to refer them to a big thick text book. And of course you will also have your allies such as Starwed backing you up and claiming that he understands it totally and without any difficulty at all.

The fact is that your assertion that a magnetic field is the relativistic part of the electric field is totally ludicrous. Even if what you said in your passage above happened to contain any truth at all, at the very most all that you would be saying is that in order for a force to be covariant under a linear transformation, it needs to have a velocity dependent term. This is so even with an ordinary Galilean transformation. A Galilean transformation can easily show that the vXB term is merely the convective component of the total time derivative of Faraday's law.

At the very most, you merely pointed out that the vXB term is commensurate with a linear transformation. You added in relativity as an extra without any justification whatsoever. All the relativity does is adds extra terms which we know as the 'Lorentz Factor' or the 'Gamma factor'. You slipped relativity in under a huge smokebomb of tensor field theory language .

Take the curl of vXB. You get -(v.grad)B. That's the convective component of a total time derivative. Add it to the partial time derivative and you've got Faraday's law in total time derivative format. Heaviside took the convective component away. A linear transformation puts it back again. All the relativity is totally superfluous and your incomprehensible passage, which Starwed fully understood, did not in any way link Coulomb's law to relativity.

Some other guy questioned the idea that if vXB can be derived hydrodynamically, why can it not also be derived from relativity. The answer is that three dimensional classical hydrodynamics is totally incompatible with relativity. They can't therefore both lead to the same result. At any rate, we still have to see how relativity can derive the vXB term. (210.86.146.200 05:06, 3 May 2007 (UTC))

This argument could be brought to a swift end if we had a reliable citation showing the mathematical link between Coulomb's law and Einstein's theory of relativity. From what I can see, the argument has centered on the link between the Lorentz Force and covariance. (58.136.112.127 06:52, 3 May 2007 (UTC))

To 58:136:112:127: There is no swift end to this argument. Anonymous is an anti-relativity troll from USENET and frankly, I've been feeding it a bit too much. Note that it doesn't provide any logical justification of its claims and pronounces all evidence contrary to its claims as nonsense, rubbish, superfluous, incomprensible, etc. Note I and others here have provided links and citations but anonymous has yet to do so. But, since you asked, here's another: [5]. And finally, here is an excerpt from the preface to the original edition of the textbook "Electromagnetics" by R. S. Elliot [6]:

This alternative retains the scope of the senior-graduate sequence but begins with a study of special relativity. With this as a basis, it is possible to develop all of electromagnetic theory from a single experimental postulate founded on Coulomb's law. An enriched understanding of magnetism results, and the Biot-Savart law is a consequence rather than a postulate. The Lorentz force law is seen to be a transformation of Coulomb's law occasioned by the relativistic interpretation of force. Upon accepting the Lorentz force law as fundamental, one is able to derive Faraday's emf law and Maxwell's equations as additional consequences. This procedure provides the further satisfaction of demonstrating that the fields contained in the Lorentz force law and in Maxwell's equations are one and the same, a conclusion not possible in the conventional development of the subject.

Alfred Centauri 13:15, 3 May 2007 (UTC)

The Definition of the Magnetic field

That definition of the B field in the main article only applies in special situations. I can imagine situations in which there is a B field but no E field. I think that we all need to take a closer look at the meaning of that E term. If that E term is causing the B field, then we need to know more about it. Is it a Coulomb force or is it a Lorentz force? Until we know, we may have to delete it. There is no point in trying to define the undefinable. (58.10.103.126 18:10, 30 April 2007 (UTC))

There should be no need to look too hard: just look at the references. Wikipedia editors should never have to make difficult calls like this; the original authors we cite have done that. Notinasnaid 18:13, 30 April 2007 (UTC)

What is the page number and the section number, and which reference are you referring to? (210.86.146.70 07:32, 1 May 2007 (UTC))

Yes, the 'definition' isn't one at all. Instead, the 'definition' section appears to be giving the B of a moving point charge. The (implicit) definition, according to a college textbook that I have is this:

"Given a test charge with velocity v, the magnetic force on the particle is given by F = qv X B".

Alfred Centauri 00:46, 1 May 2007 (UTC)

Even F = qv X B is not a definition of the magnetic field. That equation is merely one of the solutions to Faraday's law. It describes one particular effect of a magnetic field ie. that a charged particle moving at right angles to a magnetic field experiences a force that is at right angles to both its motion and the magnetic field. There are other aspects of the magnetic field not catered for by that formula. A stationary charged particle experiences a force in a changing magnetic field. That is the other part of Faraday's law. Then there is also the direct effect that magnetic field lines have on magnetic poles. In that capacity, the field lines are acting like lines of force. They pull along their axes and they push each other laterally. When two like poles repel the magnetic field lines spread outwards from each other. When two unlike poles attract, the magnetic field lines cross over directly between the two unlike poles.

There are many strands to the magnetic field. I have as yet to see a single definition. (210.86.146.70 07:32, 1 May 2007 (UTC))

There is no major problem here. Frequently editors tie themselves in knots trying to synthesise meaning from contradictory sources: what is the definition when these sources disagree? The job of an encyclopedia editor is not to try and synthesise a definition, but if there is contradiction, report it (with sources). Notinasnaid 09:02, 1 May 2007 (UTC)

For reference, the intro used to use the definition: A magnetic field is that part of the electromagnetic field that exerts a force on a moving charge. I think that's preferable to the current intro, and doesn't contain any gross inaccuracies. (There are subtleties with spin, which I think are important enough to mention in the intro.) It basically delegates a lot to the electromagnetic field article, which I think is a Good Thing.

A stationary charged particle experiences a force in a changing magnetic field.

Right, because a changing magnetic field produces an electric field, and electric fields act on stationary charges. --Starwed 09:38, 1 May 2007 (UTC)

I think that is way too technical by itself. How about

A magnetic field is a field which has particular influences, originally named because it is found around a magnet, and the original influence known was the attraction of some metallic objects. Magnetic fields have now been found to occur naturally without magnets, as in Earth's magnetic field, and to be produced by an electric current.

In technology, magnetic fields have many applications, from compasses and refrigerator magnets, through electric motors and electromagnets to the linear particle accelerator (which can be used in medical treatment) and the maglev train (a train "levitated" by magnetism).

In physics, more formally, a magnetic field is that part of the electromagnetic field that exerts a force on a moving charge. This article deals mostly with the physics of magnetic fields.

Notinasnaid 10:03, 1 May 2007 (UTC)

I took some of your ideas, and tweaked it a bit:

"A magnetic field is a physical force field that acts on moving charges, electric currents, and other objects which are susceptible to its effects. The existence of the magnetic field was first discovered in the existence of effects of certain naturally occurring rocks which exerted forces on similar rocks and on some metals such as iron, which came to be known as magnets. Later, magnets revealed the existence of the Earth's magnetic field and led to the invention of the compass. It wasn't until the 19th century, however, that physicists first began to understand and quantify the effects of the magnetic field. In particular, the magnetic field was shown to also affect and be created by currents, and to have a strong and important relationship to the electric field."

"Magnetic fields have many applications in modern technology. These applications include compasses, refrigerator magnets, electric motors, electromagnets, maglev trains, magnetic resonance imaging (MRI), and particle accelerators of various designs. Magnetic fields play keys roles in many areas of science, particularly physics."

"In the SI unit system, the magnetic field has units of Tesla (T), where one Tesla is equal to one kilogram per second per Coulomb. As the Tesla is a large unit in practice, another common unit is the Gauss (G), which is used in the CGS system of units, where 10000 G is equal to one Tesla."

Let me know what you think. I tried to give a bit of historical perspective, which I also used to introduce some of the key effects of the MF. I reworded your applications section a bit, and added a short bit on units (maybe a lot of people come here for that, I don't know). DAG 21:11, 1 May 2007 (UTC)

Starwed, you agreed that a stationary charged particle experiences a force in a changing magnetic field. You then presumed to know the reason why and proceeded to restate the original fact using different words. You said that it is because a changing magnetic field produces an electric field, and electric fields act on stationary charges.

Well we know that an electric field is defined as a force per unit charge and so it obviously acts on stationary charges. You have effectively said that a stationary charged particle expereiences a force in a changing magnetic field because a changing magnetic field produces a force on a charged particle, and you have presumed to have given us all extra information that wasn't already in the originator's statement. You have agreed with a statement and then re-worded it in order to appear wiser than the person making the statement. (58.10.102.198 12:29, 1 May 2007 (UTC))

Introduction

Somebody put in a very novel but clumsy definition of the magnetic field as being an axis of all the possible directions that a force would act if a charged particle were to move perpendicularly to a magnetic field.

Magnetic field lines are demonstrated to first day high school pupils by sprinkling iron filings on a sheet of paper over a bar magnet. When unlike poles are attracting, the magnetic field lines are acting like lines of force directly connecting the two unlike poles. That is about as basic a concept as we will ever get of a magnetic field line. It is a line of force. More precisely it is a line of tension.

You don't try to give an intuitive description of a line of force in terms of some specialized aspect of it, in this case the F = qvXB effect which is only one aspect of the magnetic field. That equation bears no relation to the force produced on a stationary charge by a changing magnetic field, or to paramagnetic attraction, or to diamagnetic repulsion, or to either ferromagnetic or electromagnetic attraction or repulsion.

Until such times as we agree on what a magnetic line of force actually is, then we will merely have to accept that it exists and describe it as it would be described to a high school physics student. (58.10.102.198 12:43, 1 May 2007 (UTC))

Any comments on my proposed opening (previous section, in italics)? Notinasnaid 12:48, 1 May 2007 (UTC)

OK. let's go over your proposal point for point.

A magnetic field is a field which has particular influences, originally named because it is found around a magnet,

This line involves repitition of both the words 'field' and 'magnet'. In the current introduction, it states something to the extent that a magnetic field is a force field that is detected by its effects. Why would you want to replace that?

and the original influence known was the attraction of some metallic objects.

OK, so you have mentioned paramagnetism and assumed that it was the first effect known to man. I'm not so sure about that. Anyhow, the effects of a magnetic field are (1) paramagnetic attraction, (2) diamgnetic repulsion, (3) electromagnetic induction which splits into the force acting on a moving charge at right angles to a magnetic field, and a force acting on a stationary charge in a changing magnetic field, (4) ferromagnetic and electromagnetic attraction and repulsion, (5) force on a moving charge that is not tied up with electromagnetic induction. The present introduction lists three of the important effects. What is wrong with it the way it is?

Magnetic fields have now been found to occur naturally without magnets, as in Earth's magnetic field,

Did the first magnets not occur naturally?

and to be produced by an electric current.

This would be implied in the existing introduction.

In technology, magnetic fields have many applications, from compasses and refrigerator magnets, through electric motors and electromagnets to the linear particle accelerator (which can be used in medical treatment) and the maglev train (a train "levitated" by magnetism). In physics, more formally, a magnetic field is that part of the electromagnetic field that exerts a force on a moving charge. This article deals mostly with the physics of magnetic fields.

That is material for a special section on applications. That is not introduction material.

Why not leave the introduction as it is. It is short, concise and covers the main points. (58.10.102.198 13:11, 1 May 2007 (UTC))

Thank you for your detailed reply. I see we are really debating something much more fundamental to Wikipedia, so I will start a new section, below. Notinasnaid 02:15, 2 May 2007 (UTC)

Too technical for a general audience

When I added the Wikipedia tag for "Too technical for a general audience" tag to the article, it led to a lot of very good discussion about definitions, which should continue. However, I feel it has largely avoided the real significance of this tag. At issue is not just whether the article is accurate (though this is vital), but whether it is accessible.

I'd recommend the linked Wikipedia:Make technical articles accessible in full, part of the Wikipedia Manual of Style, but I will also quote some of the key points.

• "Articles in Wikipedia should be accessible to the widest possible audience. For most articles, this means accessible to a general audience."
• "Consider the types of readers that may encounter a technical article...The general public, with no technical background... it should be clearly established what field of study the concept belongs to, and if it has any practical applications. "
• "Put the most accessible parts of the article up front. It's perfectly fine for later sections to be highly technical, if necessary. Those who are not interested in details will simply stop reading at some point. "
• "Add a concrete example"
• "Use jargon and acronyms judiciously"
• "Use analogies"
• "Do not 'dumb-down' the article in order to make it more accessible. Accessibility is intended to be an improvement to the article for the benefit of the less-knowledgeable readers (who may be the largest audience), without reducing the value to more technical readers."

I contend that the article fails most of this test, except avoiding dumbing down, by any measure. At the moment it approaches the subject purely as an exercise in (largely theoretical) physics, except for a small and underdeveloped "applications" subsection of "See also", some mention of compass needles (though they are never put in context), and a good (but technical) discussion of electric motors in "Rotating magnetic fields". The article does not even use the word "electromagnet".

I contend that to make this article accessible, it needs more material on applications, such as a complete subsection discussing applications in a non-technical way, probably first in the article after the lead sections (as this is likely to be the most accessible part). The technical aspects of these applications can later be referred to in context (as in the electric motors) section.

Above all, the lead section needs to be rewritten. At the moment it is

In physics, a magnetic field is a force field that surrounds electric current circuits. A magnetic field can also be found in the vicinity of ferromagnetic materials such as iron. The existence of a magnetic field is ascertained by its effects. The most important of these effects are (1) Force on a moving electrically charged particle, (2) Force on a stationary charged particle when the magnetic field is changing, (3) Mutual force acting between two objects or electric current circuits that are surrounded by a magnetic field.

I realise technical details are under discussion, and this is more accessible to a "general technical audience" at about the level of first year college science course than it used to be. But words like "ferromagnetic" are an obstacle, and that's still about the simplest sentence.

I contend that it is perfectly possible to write an article that the average child of age 10 or more can take away some enlightenment about magnetic fields from. Enlightenment such as "magnetic fields are what you get around magnets" and "magnetic fields make a compass work". Maybe younger; I don't know at what age magnets are introduced to a typical curriculum.

I have therefore proposed (elsewhere) a form of words which begins by defining a magnetic field in terms of the its most familiar everyday form, continues to list a handful of everyday applications (not an exhaustive list), and then moves on to provide a strictly accurate definition in terms of physics. Recall that the lead section should say nothing not repeated and expanded later in the article. I proposed earlier in this post that the first section following be an expanded applications discussion. Then the rest of the current article.

Before getting bogged down in a discussion of the form of words, I would like to open the debate on the general principle: How can we make this article more accessible? What do people think of the general framework proposed? Does anyone contend that the article would be fatally damaged by providing an opening that could be understood by a 10 year old?

Comments please. Notinasnaid 02:58, 2 May 2007 (UTC)

While I agree to some extent, the simple fact is that not all articles on Wikipedia can be accessible to a general audience, nor should they be. However, this article should be, IMHO. More technical articles related to this subject can be written and linked to from this article. Do you agree or disagree with this approach, Notinasnaid? Alfred Centauri 03:23, 2 May 2007 (UTC)

I think the biggest problem with the article vis-a-vis a general audience has to do with Notinasnaid's point #3 (that is, with putting less technical things up front). The first thing (after the intro) a reader sees is basically an equation. Probably there should be a section or two on less technical or less mathematic material (similar perhaps to the Properties section half-way down the article). I'm not saying take out the technical material (though a good rewrite seems in order), but move it to the end, after more discussing the magnetic field more generally. And then, ease into it. DAG 03:35, 2 May 2007 (UTC)

Good point. Are you ready to start the editing? Alfred Centauri 03:42, 2 May 2007 (UTC)

Yes. We have to get the equations away from the first few sections. More emphasis needs to be placed on describing the pattern of a magnetic field and discussing all the observed effects. I can count (1) attraction between unlike poles (field lines connect directly) (2) repulsion between like poles (field lines spread outwards). (those first two effects are electromagnetism and ferromagnetism). Then there is (3) the alignment of a bar magnet in a magnetic field. (4) attraction of certain non-magnetized materials (paramagnetism) (5) Weak repulsion of other non-magnetized materials (diamgnetism). (6) force on a charged particle that is moving at right angles to a magnetic field (7) force on a stationary charged particle in a changing magnetic field.

Then we need to start doing sections on the mathematical formulations of these effects.

(a)Ampère's law (closed current loop causes magnetic field) (b)Biot-Savart law (defintion of B field commensurate with Ampère's law) (c)Faraday's law of electromagnetic induction (covered by aspects (6) and (7))

and finally how these equations come together into Maxwell's equations. (210.86.146.250 05:42, 2 May 2007 (UTC))

A naive question

Does all of the definition and mathematics in here apply purely to the magnetic field, or is any of it related to the electromagnetic field? Notinasnaid 19:34, 2 May 2007 (UTC)

Lorentz force on wire segment

I had to blink at this formula. The information is correct, I'm only nitpicking on the display. The formula is:

$F=Il\times B\,$

Which is correct. However, directly after the forumla, the section goes on to label each variable within the formula with:

F = forces, measured in newtons

I = current in wire, measured in amperes

B = magnetic field, measured in teslas

$\times$ = vector cross-product

l = length of wire, measured in metres

This text (and this effect should replicate above) is in Arial. The capital I ("eye") and lowercase l ("el") appear exactly the same (pixel-perfect for me) in both IE and Firefox. The letters are also not in order, so some knowledge (which, hopefully, could be picked up in the article) is needed to decipher which variable is being explained.

Also, it seems a twee odd (and certainly doesn't help) that the variables are not labelled in the same order that they appear in the formula. They appear to be in no real order at all...

The text immediately below contains similar problems when discussing vectors with current and the segment. To clear it up, some possible solutions:

• Rearrange the variable explanations to match up with appearance in the formula.
• Could the formula be modified to use a capital L as opposed to a lowercase one? Anything wrong with this / would it be confused with other common uses? (such as L for rotational momentum?)
• Make the variable explanation monospace. This doesn't correct the paragraph afterwards discussing vectors, however.
• Is there an HTML entity for a cursive lowercase L?

I might "be bold" in a few days, but if anyone has any objections, now's the time to let the world know... ;-) (Ack, forgot to sign... these bots are fast!) Deathanatos 04:21, 3 May 2007 (UTC)

Ah hah! There is a unicode script L, which might also help: It's &#8467; and displays as ℓ. Kinda small... would it work? (It appears to be the character my physics equation sheet uses) Deathanatos 05:19, 3 May 2007 (UTC)

But of course the HTML entity doesn't display in IE (at least for me in IE6)... I'm such a spoiled FireFox user... Deathanatos 05:21, 3 May 2007 (UTC)

Electromagnetic Induction

The force that acts on a moving charged particle in a magnetic field is a component aspect of electromagnetic induction. It was not incorrect to have mentioned it in the introduction. However it is a specialized aspect of the magnetic field and it has now been side referenced. An introduction to an article entitled Magnetic Field should only give an overview of the general picture of the magnetic field. The general picture is that of solenoidal field lines in conjunction with the fact that like poles repel and unlike poles attract. (201.53.10.180 16:20, 14 May 2007 (UTC))

Cleanup of this page

I think the best approach to cleanup this article would be to move the discussion of B and H fields to the end of the article.

Lines of Force

I can't see what the problem was with the term 'Lines of Force'. The term 'Lines of Force' was good enough for Faraday. These lines of force pull magnets together and they push magnets apart. It seems to me rather clumsy to replace the term 'Lines of Force' with 'Lines of Alignment of the needle of a compass' as if to suggest that the alignment of a compass needle has got nothing to do with force. Whoever made that amendment seems to have forgotten that the torque that causes the alignment of a compass needle has got a force component to it. That force comes from the magnetic field lines. Magnetic field lines are 'Lines of Force' without any shadow of doubt about it. (81.129.175.154 09:16, 17 June 2007 (UTC))

This change was probably made because forces that magnetic fields exert do not have direction of $\mathbf {B}$ but direction of $\mathbf {v} \times \mathbf {B}$. --83.131.87.100 11:58, 18 June 2007 (UTC)

When two magnets are attracted together, the direction of the magnetic force is exactly along the magnetic field lines. That means that magnetic force is exactly in the direction of $\mathbf {B}$. You are getting confused with the force on a moving charged particle which is at right angles to $\mathbf {B}$ (81.129.175.154 19:56, 18 June 2007 (UTC))

Incorrect. When you place a magnet in uniform magnetic field, then THERE IS NO NET FORCE on it. (There is torque instead. And the direction of the torque DOES NOT coincide with the direction of the magnetic field either, but is perpendicular to it instead).

You are correct in saying that a magnetic field vector is an axial vector field.You are further correct in saying that a charged particle moving in a magnetic field will experience a force that is at right angles to the magnetic field. However you seem to be wilfully blind to the fact that two magnets pull together and that the force in this situation is directed exactly along the magnetic field lines. Magnetic force has got more aspects to it than just the

If you place two magnets parallel to each other, the net force each is experiencing is directed TOWARD another magnet (it is either attraction or repulsion - depending on poles' orientation). As you can see, the force is again directed NOT along magnetic field lines (which are parallel to magnets in this situation). So, magnetic field lines are NOT lines of force as you erroneousely claim. Why did you claim what you don't know? Can you please revert back your INCORRECT reverts? Sincerely Enormousdude 20:14, 20 June 2007 (UTC)

Place the north pole of a bar magnet near to the south pole of another bar magnet. The magnetic field lines will cross directly between these two poles. The two poles will pull together in the direction of these field lines. Your mention of there being no net force in a uniform magnetic field is actually a separate phenomenon that applies to the force on unmagnetized materials in an inhomogeneous magnetic field. It comes under the study of diamagnetism and paramagnetism.

You cited another scenario in which a bar magnet will align in a magnetic field. Yes indeed a torque is involved in this scenario but every torque has a force, and the forces in this scenario are in the direction of the magnetic field lines, even if the torque is perpendicular. Torque and force are related to each other through a vector cross product.(81.129.175.154 12:21, 21 June 2007 (UTC))

Incorrect again. Looks like you never took e/m class. To begin with, there are NO magnetic poles. Neither inside a bar magnet, nor anywhere else. It would be enough to point to the second Maxwell's equation (Gauss's law for magnetism) which shows that you are dead wrong about magnetic poles and stop discussion right there. But it seems that you are not familiar with those equations.

To explain this to you in more obvious terms, take a disk-like Nd magnet (say, like a quarter in shape). Tell then, where is its north pole and where is its south pole if the magnet happens to be very thin (say, like a quarter)? And what happens when two such magnets are at some distance from each other (say, a few diameters away)? Magnets still strongly attract or repel each other depending on orientation, but where are the poles? Another example - a circular current loop. Where is its north pole and where is its south pole? Place two loops at some distance from each other - and again similar to disk magnets they would attract or repel (plus mutual torques, of course) - yet there are NO POLES! What then attracts to what?

Take a ball Nd magnet. Where are its poles? Finally, take a bar magnet and break it into two halves. Do you know that you will NOT get two separate poles as you probably expect - instead, you will get two bar magnets with two poles each!. Where are then two SEPARATE poles? And where did NEW poles came from?

What do you mean by saying "Your mention of there being no net force in a uniform magnetic field is actually a separate phenomenon that applies to the force on unmagnetized materials in an inhomogeneous magnetic field. It comes under the study of diamagnetism and paramagnetism..." ? This is nonsense. Permanent magnet in uniform magnetic field has nothing to do with unmagnetized materials (permanent magnet IS magnetized by definition) nor with paramegnetism nor diamegnetism. Look up any e/m textbook. Paramagnetizm is a phenomenon of realignment of atomic magnetic moments in external magnetic field (just as a current loop is experiencing torque in external field, atomic magnetic moments do the same). Diamagnetism is inducing magnetic moments by external magnetic field in a substance atoms of which have zero own magnetic moments. Then according to Lenz law induced moments are directed opposite to the source field - thus resulting in net force on the diamagnetic directed opposite to the gradient of magnetic field (=repulsion from stronger field regions). One example of perfect diamagnetic is a superconductor.

As you can see, a permanent magnet in uniform magnetic field has nothing to do with paramagnetizm, diamagnetizm or behaviour of nonmagnetized materials.

You know, not only permanent magnets and current loops have magnetic field, but also some so called elementary particles do. For example, electron has magnetic field - and thus magnetic moment, proton has magnetic field, neutron, etc. So, two electrons or neutrons interact with each other in a similar way two bar magnets do (if to neglect quantum effects here). But where are poles in an electron? In a neutron? Electron is considered elementary particle - meaning it has no internal structure. So, if it had poles then the two poles must sit right in the same place - and thus must cancel completely each other out resulting in zero net force AND in zero net torque on an electron in external magnetic field. But this is NOT the case. Electron in external magnetic field does experience both torque (which results in its precession and in different magnetic potential energy depending on its orientation) and does experience net force (which resulted in sorting of spin up and spin down Ag atoms in historic Stern-Gerlah experiment).

So, where are those imaginary magnetic poles you like so much?

And if there are no poles, then what force (on poles) you are talking about? If there is no force (on non existing poles) - then when you claim that magnetic field represent lines of force - then lines of WHICH force are you talking about?

Sincerely, Enormousdude 19:45, 22 June 2007 (UTC)

I'm talking about the force that pulls two magnets together. It's directed along the $\mathbf {B}$ lines. (86.145.135.204 16:59, 23 June 2007 (UTC))

It is NOT. Place two magnets parallel to each other. Say, place two 1" long bar magnets at 2" distance from each other in parallel say by north poles up. The magnetic field of each one in the location of another magnet is directed DOWN then. Yet the force left magnet is experiencing is directed to the LEFT, and the right one - to the RIGHT (not UP as you claim).

Please, also address the questions of my reply to you above - about magnetic poles of thin disk-like magnet, magnetic poles of a circular loop of current and magnetic poles of say electron. Also, explain me why second Maxwell equation (Gauss law for magnetic field) states that density of magnetic poles is zero?

Sincerely, Enormousdude 20:45, 23 June 2007 (UTC)

Enormousdude, you are in a state of denial. Magnetic force is more than just $\mathbf {v} \times \mathbf {B}$. There is another aspect of magnetic force that acts in the direction of magnetic field lines, and it is not the $\mathbf {v} \times \mathbf {B}$ force. This other aspect of magnetic force can cause a change in kinetic energy as can be witnessed when two bar magnets are accelerated together, whereas the $\mathbf {v} \times \mathbf {B}$ force never changes the kinetic energy of a charged particle. You have overlooked this other aspect of magnetism and now you are trying to deny that it exists. You are denying the most basic aspect of magnetism. You are denying Faraday's lines of force that pull two magnets together. You are deliberately turning a blind eye to this most basic of scenarios and trying to divert attention away to alternative scenarios. Every child knows that two magnets pull together, and every high school pupil knows that the force of attraction is directed along the magnetic field lines.(86.145.135.204 22:16, 23 June 2007 (UTC))

Wow, what a bunch of nonsense! Did you ever take physics class? Magnetic force is indeed MORE that $\mathbf {v} \times \mathbf {B}$ - it is actually $q\mathbf {v} \times \mathbf {B}$. Thare are NO "aspects" of magnetic field which "act" in the direction of magnetic field lines. Do I have to explain you how (and why) magnets attract to each other? Or you can read it in e/m textbook yourself, saving mutual waste of time? A permanent magnet consists of a bunch of atomic magnetic moments (magnetic dipoles). Energy of a magnetic moment μ in the external magnetic field B (of, say, another permanent magnet nearby) is equal to: U = -(μB). Force the dipole μ is experiencing in this magnetic field B can be expressed via gradient of potential energy (by definition of work): F = -grad U = grad (μB). You may see that the force is NOT directed along magnetic field lines but along the GRADIENT of magnetic field. On the axis of a cylindrical permanent magnet magnetized along its axis gradient is directed along the axis of the magnet - that is why two cylindrical permanent magnets PLACED COAXIALLY attract or repel along their axis. Non-coaxial arrangement resilts in a force between them NOT directed along either axis or magnetic field line direction, BUT always along the direction of gradient of magnetic field. The same result is obtained if to consider a permanent magnet as a loop of surface current (similar to a solenoid) and integrate Lorentz force its current elements are experiencing in the magnetic field of another magnet.

So, why do you keep insisting on the existence of 2 century old incorrect concept of "Faraday's lines of force" stretching between poles of a magnet - while here are NO magnetic monopoles, and while magnetic field lines are NOT lines of force?

How to explain you that there are no magnetic poles (which is evident from both definition of magnetic field and from second Maxwell's equation)? Consider thin disk-like magnet magnetized in axial direction. Very thin - like a quarter. Where is its north pole and where is its south pole? How close they are to each other if the magnet is really very thin? Or consider a single loop of current. Say, 10 A current is circulating in a 3 cm diameter circular wire. This loop behaves in external magnetic field the same way a permanent magnet in the shape of disk does. Answer please, where is north pole and where is south pole in this loop?

Also consider usual cylindrical bar magnet magnetized along its axis. Let's say, magnet is oriented up-down, with the north pole up. What is the direction of the magnetic field directly above the north pole? Obviousely up. What is the direction of the magnetic field directly BELOW north pole (=inside the magnet)? If the north pole is a monopole, then the answer is obvious - B is directed down (=from north monopole on top of magnet to the south monopole on the bottom of the bar magnet). However, if you make a small hole in the actual magnet directly under its north pole and insert a magnetic probe into the hole, you find that actual magnetic field is directed in the OPPOSITE direction: it is directed not down but UP!

Thus there are no magnetic monopoles, and claiming that magnetic field is a force field directed from north pole to south pole is incorrect.

Because you can't answer any of my questions above, I just safely assume that you don't know the answer to any of them simply because you are ignorant about electromagnetism as well as about physics in general. Why do you edit the article then?

So, don't correct what you PERSONALLY don't understand or don't know. Leave it to physicists. If you want to understand what magnetic field is and how two permanent magnets interact, take a physics class - then things may become a little more clear to you.

Sincerely, Enormousdude 20:11, 27 June 2007 (UTC)

There are no magnetic forces in direction of magnetic field, all of those forces are perpendicular to direction of magnetic field, so not even any net force can be in direction of magnetic field. There is one thing about magnetic field that deserves more attention than it usually does: vector of magnetic field is axial vector. This means that plane perpendicular to it's direction is one with direct physical meaning, and not it's direction itself. --83.131.92.177 17:24, 23 June 2007 (UTC)

You are correct in saying that a magnetic field vector is an axial vector field. You are also correct in saying that a moving charged particle in a magnetic field experiences a force that is at right angles to the magnetic field. That is one aspect of magnetism. But you seem to be keen to overlook another aspect of magnetism. You seem to want to turn a blind eye to the fact that two magnets pull together, and that the force involved is exactly in the direction of the magnetic field lines. (86.145.135.204 20:22, 23 June 2007 (UTC))

Incorrect. See my reply with explanations (on various levels) of how permanent magnets actually interact, and some questions to you (about magnetic poles of a disk-like magnet, a loop, an electron, anout magnetic field direction inside permanent magnet, etc) which will help you to understand that the force is NOT directed along magnetic field lines, (but along the gradient of magnetic field instead). Enormousdude 20:20, 27 June 2007 (UTC)

Should we remove the line "Another intuitive way to view \mathbf{B} is as a bundle of lines of force that pull two unlike magnetic poles together" from the definition section. I am no expert on magnetism so I can't tell from this discussion what to do, and whether it is correct or not. Nicolharper 23:49, 27 June 2007 (UTC)

Why would you want to deny the most fundamental aspect of magnetism? Magnets do pull together. Every child knows that. Whoever worded that line about "a bundle of lines of force" might have worded it better, but from what I can see it is absolutely correct in principle. What about re-wording it to ---- Ah wait a minute! I see now. He was specifically talking about the definition of $\mathbf {B}$ which is the magnetic field vector $\mathbf {H}$ multiplied by the magnetic permeability. Yes, $\mathbf {B}$ is a weighted version of $\mathbf {H}$ and so it is effectively a bundle of $\mathbf {H}$ lines. Quite frankly, I would just leave it in. (81.158.161.160 11:41, 28 June 2007 (UTC))

Origins of the Magnetic Field

I removed the section that claims that the magnetic field is an electric field as viewed by an observer in a moving reference frame. When I look at magnetic field lines around a bar magnet, I cannot imagine which rest frame I would need to be in in order for these field lines to become electric field lines. (81.158.161.160 20:26, 27 June 2007 (UTC))

Read any physics textbook - there is no magnetic field in the co-moving with charge frame (and don't forget that electrons have not only electric charge which creates electric field but also spin which is quantum mechanical motion - so electric field of electron is already in some motion). Moving electric field is what magnetic field is (to be more accurate - RELATIVISTIC component of moving electric field). Enormousdude 19:30, 28 June 2007 (UTC)

If the supposed fact that a magnetic field is the relativistic component of an electric field is well documented in the physics literature, that doesn't mean that this fact needs to be added to the introductory paragraph in the magnetic field article. There have already been complaints that the article is too technical for the average reader. So why the insistence on adding this obscure and higly controversial piece of relativity into the introduction? (81.158.161.160 12:20, 28 June 2007 (UTC))

Hold on, the only reason magnetic field exists is special relativity (Loretz transformations). Not many people understand that (apparently including you, by the way). There is NO magnetic field in classic (Galilean) transformation of Coulomb force from co-moving with the source electric charge to non-moving reference frame of observer. None. Nada. Zero. So, if you remove it then a reader will be lost as to understand the origin of magnetic field. (Is this your intention - to promote personal ignorance to Wikipedia readers?) There are plenty of phenomena in nature which are difficult for "average reader" to understand because they require proper education of the reader. For instance, understanding of origin of conservation laws require knowledge of mathematical symmetries, of least action principle and of Emmy Noether theorem. So, should we simply state that conservation laws are just the way nature works, or should we point to their origin? If a Wikipedia project is to accurately explain things and phenomena (as encyclopedias suppose to do), then we should. Sincerely, Enormousdude 19:30, 28 June 2007 (UTC)

Enormousdude, Maxwell was able to explain the magnetic field before relativity was ever thought of. The vXB force was in Maxwell's fourth equation. We don't need a Lorentz transformation to get the vXB force. Besides that, no amount of relativity can explain the other magnetic force that acts along the magnetic field lines. Magnetism was well understood in terms of Ampère's law and Faraday's law, well before Einstein or Lorentz came on the scenes. A magnetic field occurs around a closed electric circuit. It has got absolutely nothing to do with the Lorentz transformation. (81.158.161.160 20:56, 28 June 2007 (UTC))

Um, sorry, no. Care to provide a reference for the idea that a magnetic field has nothing to do with Lorentz transformation, cuz I got plenty of sources that say otherwise. I think you're misunderstanding Maxwell's equations a bit; the vXB comes from the Lorentz force law. Maxwell's equations do a lot, but they say nothing about the force on charged particles due to those fields. However, prior to Einstein, the Lorentz force law was based only on observation. You cannot discuss magnetic fields without a discussion of how the magnetic force naturally comes out of the Lorentz transformation of the Coulomb force, with a vector field crossed into the velocity exactly identical to the magnetic field described by Maxwell's equations. Special relativity basically says why a magnetic field has to exist given an electric field. There is no force along the field lines, as ED has already explained above; the attraction between to bar magnets is due to a non-uniform magnetic field. If you're really interested, I highly recommend Jackson's "Introduction to Electrodynamics" for an exhaustive explanation of EM phenomena. Unless you've taken university courses in E/M then most of what you know of electromagnetism is likely a simplified analogy to avoid heavy math that leads to faulty understanding when taken too far. So either provide a reference for some of these claims (forces along magnetic field lines) or else this falls into the WP:OR especially when we can cite physics textbooks that state otherwise. --FyzixFighter 05:05, 29 June 2007 (UTC)

No reference is needed to show that a magnetic force exists along magnetic field lines. First form high school pupils learn that with iron filings. Look at the field lines joining two attracting magnets. The attractive force is along those lines. You are in denial of this most basic fact because you know that this aspect of magnetism definitely cannot be explained by the Lorentz transformation. (81.158.161.160 10:30, 29 June 2007 (UTC))

Revision to intro

Sorry for the double post, but I just decided to be bold and changed the intro - the old intro was somewhat misleading and simplified to the point of absurdity (let's keep it "as simple as possible, but not more so"). It also already threw enough technical jargon around (axial vector, solenoidal) so the non-technical argument for not including SR in the intro doesn't hold water. I tried to model it after the the intro over at electric field. I think (or rather I hope) that I've avoided some of this "lines of force" disagreement by getting down to what the field describes, specifically in terms of the Lorentz force law. I also tried to address the "lines" question by using Faraday's original formulation (magnetic dipoles align themselves along these lines), since this is how most readers have been introduced to the concept, but leaving the more detailed explanation for later in the article. Also, certainly the full derivation of the magnetic field with SR does not belong in the intro, but it must be mentioned succinctly in the intro as this is a fundamental concept and is addressed later in the article. --FyzixFighter 06:42, 29 June 2007 (UTC)

New Edits

FyzixFighter, Regarding your points above, your wording in the introduction is better in some respects. You have said 'According to relativity----'. That is a better way of introducing that point. As regards Lines of Force, Faraday introduced the term, and so likewise I have added in that Faraday called the magnetic field 'Lines of Force'.

Check out equation (D) of Maxwell's original eight equations. Equation (D) is the Lorentz force if ever there was a Lorentz force. Lorentz only reintroduced the vXB component after Heaviside removed it in 1884.

I would agree with you that I see no need to specify that B is an axial vector field. I actually removed that yesterday, but somebody restored it.

Also, very importantly, vXB is not the entire picture of magnetism.The attractive force that acts in the direction along magnetic field lines, does not arise from vXB. Neither does the magnetic force that is involved in diamagnetism or paramagnetism. There seems to be too much attention focused exclusively on the vXB force in the definition and introduction. I tried to neutralise that a bit.

On another point, you said that there are no references to say that magnetism can be explained without the Lorentz transformation. What about if I were to mention Maxwell's equations?

On another point, try and see if you can fit solenoidal field lines around a point source. Ampère's law tells us that we need a closed circuit. (81.158.161.160 09:53, 29 June 2007 (UTC))