Talk:Faraday's law of induction

Note on Faraday's law
Ok, I am fairly new to physics and I dont understand everything about this article, but I have the impression that in chapter "Faraday's law", subchapter "Quantitative", the paragraph part " B·dA is a vector dot product (the infinitesimal amount of magnetic flux through the infinitesimal area element dA)" should probably rewritten in a way that would reflect the contribution of angle θ between the surface area and the direction of magnetic flux like " B·dA·cosθ is a vector dot product (the infinitesimal amount of magnetic flux through the infinitesimal area element dA multiplied by cosθ, where θ is the angle between the vertical to the area element dA and the direction of the magnetic field in that area", or at least imply that the concept of cosθ is integrated in the notion of surface element dA.

Could someone more expert than me take a look at it? 2A02:587:4511:2200:71DC:846:1E07:ADC (talk) 16:34, 5 July 2017 (UTC)


 * Bolded quantities are vectors, so B • dA conveys all of that already. Headbomb {t · c · p · b} 19:32, 5 July 2017 (UTC)


 * I had suspected something like that, but it's nice to clarify it for the non-experts. Anyway, thanks for the answer.  2A02:587:4511:2200:7DFB:B05C:1AC6:4256 (talk) 21:57, 5 July 2017 (UTC)
 * Yeah, clarification could happen. We might need to create template to explain the notation so that could be re-used in articles. Bouncing ball explains the notation (take a look at the article, to see if the notation is clear to you), since this is often encountered by people unused to seeing vectors. Faraday's law of induction isn't really an introduction topic, so you ought to be familiar with vectors by the time you encounter it. But it's good to think about people who would come with a trades background (e.g. car mechanics), rather than academic background. Headbomb {t · c · p · b} 01:20, 6 July 2017 (UTC)

Proof of Faraday's law
In the section entitled "Proof of Faraday's law" it is said that:
 * The four Maxwell's equations (including the Maxwell–Faraday equation), along with the Lorentz force law, are a sufficient foundation to derive everything in classical electromagnetism.[15][16] Therefore, it is possible to "prove" Faraday's law starting with these equations.[24][25]

Um, isn't this confusing? Maxwell's equations include Faraday's law. So, I don't think this couple of sentences make sense. In particular, as far was I can see, the "proof" of Faraday's law from the Lorentz force law only invokes Gauss's law, not the other three of Maxwell's equations (and certainly not Faraday's law!). Anyway, I think these sentences need to be fixed, but I thought I'd first ask other editors what they thing of this. Thank you. Attic Salt (talk) 14:03, 6 October 2018 (UTC)


 * You're getting confused by the fact that there are two related laws that are sometimes called by the same name. In this article we're calling one of them (∇×E=-∂B/∂t) "the Maxwell–Faraday equation" and the other one (EMF=-d(flux)/dt) "Faraday's law", but different people use different terminology, and in particular lots of people call the Maxwell-Faraday equation by the term "Faraday's law" (confusingly). Anyway, "The Maxwell–Faraday equation" (∇×E=-∂B/∂t) is one of the four Maxwell's equations. "Faraday's law" (EMF=-d(flux)/dt) is not. Does that help?


 * The article used to have a clearer explanation of this than it does right now... --Steve (talk) 21:01, 6 October 2018 (UTC)
 * , Thank you for this technical pointer. Attic Salt (talk) 22:00, 6 October 2018 (UTC)

Equation needs source
The following equation needs a citation
 * $$ \mathbf E_s (\mathbf r) \approx -\frac{1}{4\pi}\iiint_V \ \frac{(\frac{\partial \mathbf{B}} {\partial t}\,dV)\times\mathbf{\hat r'}}{|\mathbf r'|^2} $$

The folowing has been suggested as a citation : However, the equation does not appear in that page range. It has been suggested that the material in that page range justifies the equation. It appears that this is a case of SYN. Simple manipulation of mathematical formulas are allowed, but this cased appears to be too complicated. Further, I think that the equation, if it is correct, needs some qualifying remarks. The B field is generally unlimited in space, so the volume integral must be an integral over all space in the most common cases, the most common cases. If correct, it seems to have dubious value. Constant314 (talk) 21:54, 16 March 2019 (UTC)


 * It seems to come from inverting ∇×E=∂B/∂t using the formula e.g. here. It's dubious in that the inversion is generally not unique, basically it "needs some qualifying remarks" just like you said. Even if it's true, I don't think it's sufficiently important to be worth writing down here. I agree, let's delete it. --Steve (talk) 00:30, 17 March 2019 (UTC)


 * It isn't dubious, it expresses the electric field as a function directly, instead of as part of an equation that needs solving. It is a suitable non-relativistic general solution which satisfies all the realistic boundary conditions.
 * For example, Steve showed in the moving magnet and conductor problem that the curls are equal, but it doesn't prove that the fields are equal. With this formula, that can be accomplished.
 * Please sign your comments by appending four tildes ~ at the end of your comment. Wikipedia will convert that into your user name.  Also use leading colons to indent your comments.Constant314 (talk) 20:48, 17 March 2019 (UTC)


 * Just to be clear, by dubious, I'm questioning the equation's value to the article. I also question its notability if it doesn't appear in any reliable source. With regard to qualifying remarks, B is often non-zero over all space, so the integral is over all space, yet there is no use of retarded time.  In the analogous integral for B as an integral of J, it is also an integral over all space, but J is usually limited to small volume much less than a wavelength, so that integral works without retarded time.  But, in any case, the equation needs to appear explicitly in a reliable source so insure both correctness and notability. Minor manipulation such as the source uses different symbols for the variables or has them in a different order is allowed. Constant314 (talk) 20:48, 17 March 2019 (UTC)


 * Yes, I mentioned "non-relativistic", so only applying to a small region of space. Faraday's law gives the bulk scalar quantity of the voltage, without all the fine details. The Maxwell-Faraday equation only provides the curl, and doesn't give readers much conception of the field where the curl is zero. With the electric field as a function, it gives readers a more complete understanding of the structure of the field, they can realize that the field assumes circular forms. Legit War Articles (talk) 11:20, 19 March 2019 (UTC)


 * Looks like I have answered my own objection. The equation in in Griffiths 4th edition on page 321.  However, he doesn't dwell on it.  It is just an intermediate eqution toward the derivation of Faraday's law in integral form.Constant314 (talk) 00:07, 20 March 2019 (UTC)

It is said Franz Ernst Neumann offers the mathematical formula of Faraday's law. If someone can offer a details what Franz Ernst Neumann did that will be wonderful.

Maxwell also did the derivation of Faraday's law in the paper 1855/1856 On Faraday's Lines of Force. If someone can following the thought of Maxwell but use today's mathematical symbols that will be wonderful. Imrecons (talk) 13:27, 25 October 2020 (UTC)

Silver plates experiment
The article states the flux changes dramatically when the current follows the red lines. But there is hardly an emf. Conclusion: the current doesn't follow the red lines. Madyno (talk) 18:56, 24 July 2022 (UTC)

Rule of left hand
Hi everyone, I'm reading through the section where a left-hand rule is given to compute emf. It states that, aligning the left hand fingers with the loop, the thumb indicates the normal to the surface. Then if the variation of flux is positive, the emf follows the fingers (and the opposite if the variation of flux is negative): ok. This first step, I believe, is misleading: the normal of a surface enclosed by a path is given by the right hand rule (https://en.wikipedia.org/wiki/Right-hand_rule) If we use the right hand rule to compute the normal then the direction of emf becomes opposite to the fingers, which is correct.

To keep using the left-hand rule in the text, I think it should be mentioned that the thumb is the direction opposite to the normal, thus embedding the sign "-" of Faraday's law. Then the rest of the text is correct. But the figure needs to be remade, as it still shows the normal aligning with the thumb. What do you think? OOTeSkew (talk) 09:41, 17 August 2022 (UTC)

Inconsistency in notation throughout the article
The first equation under "Faraday's law" (in "Mathematical statement") uses two integrals to describe integration over a surface. This is the only use of this notation throughout the article: Every other occurrence of integration over a surface uses a single integral sign. In my opinion, the double integral notation is better (as it is more explicit), but in either case the notation should be consistent. Proxagonal (talk) 08:40, 2 June 2023 (UTC)

"Two phenomena"
It depends on how you are modeling electromagnetic interactions. Faraday's experiments established that emf induced in a loop is attributable to the RELATIVE MOTION of the loop and the ambient magnetic flux, commonly represented by "field lines." That's one phenomenon, not two.

One contribution to the electromagnetic force per charge on a particle is the gradient of a scalar--but that will produce no emf when integrated around a loop. The rest is due to the relative motion of the particle and the ambient magnetic flux, the so-called "cutting" of field lines. Feynman's exceptions to Faraday's Law are attributable to the motion, or lack thereof, of the conductor across magnetic field lines. Motion relative to magnetic flux is the underlying principle.

From the next section: "In the general case, explanation of the motional emf appearance by action of the magnetic force on the charges in the moving wire or in the circuit changing its area is unsatisfactory. As a matter of fact, the charges in the wire or in the circuit could be completely absent, will then the electromagnetic induction effect disappear in this case?"

Answer: The emf is the integral, around the loop, of the force PER CHARGE. Of course if the charge is zero then the force is zero, but this is as true for an electric force as for a motional magnetic one. If the absence of charges or a circuit would make emf disappear in the former case, it would in the latter case as well. If there is anything unsatisfactory about understanding motional emf on the basis of magnetic forces, the case has not been made here.

"From the physical point of view, it is better to speak not about the induction emf, but about the induced electric field strength..."

I see no real basis for this assertion.

"If the circuit area is changing in case of the constant magnetic field, then some part of the circuit is inevitably moving, and the electric field emerges in this part of the circuit in the comoving reference frame K’ as a result of the Lorentz transformation of the magnetic field, present in the stationary reference frame K, which passes through the circuit."

True, but if different segments of the circuit are moving with different velocities (which must be the case if the area is changing) then the frame-dependent voltages induced in each segment can't be added up to give the total emf. Faraday's law provides the emf in a single frame.

"In the reference frame K, it looks like appearance of emf of the induction, the gradient of which in the form of , taken along the circuit, seems to generate the field ."

Looks like? Seems to? LTFGD (talk) 01:35, 5 June 2023 (UTC)


 * This is why we stick to paraphrasing reliable sources. Of course, that can produce incorrect results also.  The Feynman Lectures are a special problem.  Feynman was teaching, not creating a textbook.  We know that sometimes he would intentionally state an incorrect conclusion as a didactic artifice.  Of course, he would correct it later, but you have to read carefully and be sure that you are using the correct statement and not the provocative statement. Constant314 (talk) 01:56, 5 June 2023 (UTC)
 * I'm not sure who the "we" and the "you" are in your response. It looks like the Wikipedia entry is using the "provocative" statement, whether or not Feynman may have taken it back later. LTFGD (talk) 12:45, 5 June 2023 (UTC)
 * We and you are being used rhetorically. Yes, I think that statement was intended as a make-you-think statement rather than the literal truth. Feynman writes $$ \frac F q = E + v \times B $$ and calls it two phenomena which is odd because E and B are just two parts of the electromagnetic field which is one phenomenon.  I don't know where he fixes it, probably when he discusses relativity.  Some people, like me, who have read The Feynman Lectures extensively can find examples of intentionally incorrect statements.  That is a problem when using statements from The Feynman Lectures out of context.  The rest of the context may be in another chapter.  It would be reasonable to request additional citations. Constant314 (talk) 14:21, 5 June 2023 (UTC)
 * I added the dubious template Constant314 (talk) 14:30, 5 June 2023 (UTC)
 * I little self-disclosure: Recently I came across an article in American Journal of Physics that was casting shade on Faraday's Law (or the "flux rule") and contained a significant error. I couldn't get a corrective note published even after the reviewer conceded my point. There seems to be some sort of consensus that Faraday's Law is wrong or defective and we need to go back to relying on Maxwell's equations directly, and even if an error is identified it shouldn't be published for fear of disrupting that narrative. So I started looking around and found another paper, in European Journal of Physics Education, doubting that "cutting field lines" could account for certain voltage measurements, when it patently does cause those results. Now I'm thinking writing a more extensive paper for the second journal and have been looking through the literature. Eventually I became curious as to what I'd find on Wikipedia. If I do write the longer paper, I might adopt some of the wording to include as a revision here. Thanks for the response. LTFGD (talk) 19:09, 5 June 2023 (UTC)
 * Modern physics has banished "lines of flux" as being non-physical. You cannot have motion with respect to lines of flux.  In the equation $$ \frac F q = E + v \times B $$, v, the velocity is the velocity measured with respect to the observer's frame of reference.  Likewise, F, E, and B are as measured in the observer's frame of reference.  Most especially, v is not velocity with respect to the magnetic field. Constant314 (talk) 19:43, 5 June 2023 (UTC)
 * Pure assertion, and false on its face. Lines of flux are simply a way of representing the directed flux density, i.e., magnetic field, relative to which a particle patently can have a velocity. You can enter a region of flux, you can exit. Or, given a moving magnet, the flux can move past you. It can move into a loop and out of the loop again. Start on one side of a bar magnet, move to the other side. Did you not cross, i.e., have motion relative to, magnetic flux? Or move the magnet, so that all the flux was on one side of you and now it's all on the other side. Did the flux not move? Give me a reputable modern (i.e., living) reference for your statement that field lines have been banished from modern physics and I'll be happy to take it up with the author. LTFGD (talk) 02:02, 6 June 2023 (UTC)
 * Not my problem, but "We have something like this in the electromagnetic field. For we may picture the field to ourselves as consisting of lines of force. If we wish to interpret these lines of force to ourselves as something material in the ordinary sense, we are tempted to interpret the dynamic processes as motions of these lines of force, such that each separate line of force is tracked through the course of time. It is well known, however, that this way of regarding the electromagnetic field leads to contradictions." -- Einstein, 1920 Constant314 (talk) 03:18, 6 June 2023 (UTC)
 * "...something material in the ordinary sense..." Nobody (except possibly Faraday in his later years) is saying that. Field lines are a representation of magnetic flux density, relative to which one can obviously have a velocity. Your problem is being able to back up your assertions. Among academics, the invitation to offer a reference is generally understood to mean book, author, page or journal paper, author, page. Or if you just poked around on the web until you found something likable, you could at least include the link. It's a free country and you're under no obligation, but the Wiki article obviously needs some repair, which I may get around to offering. LTFGD (talk) 14:08, 6 June 2023 (UTC)
 * The physical existence of lines of flux and motion relative to them has been banished for over a century. It is hard to find references that say, "Oh by the way, we don't consider lines of flux to be physical anymore.  You cannot have velocity with respect to the field."  References simply don't spend much effort on non-facts.  So, yes, I grabbed something that was easy to find from a long time ago, because it was settled a long time ago.  Here you see Einstein using that as an established fact, in 1920, to explain something else.  Everybody got it back then, because it was relatively new.  If you read the rest of that resource, you will see that Einstein explains that motion only exists between objects and not between objects and immaterial things such as fields.  Thus, you can have motion between the coil and the magnet, but not between the coil and the field.  You may think that it is the same thing, but it is not.
 * Let me turn it around and ask you to find a reliable reference (a real, widely used, physics textbook) that says the velocity in question is the velocity relative to the field and not the velocity observed by the observer. This could save you a lot of embarrassment.  Please avoid engineering texts because those mostly use 19th century physics (which is still quite useful). Constant314 (talk) 00:45, 7 June 2023 (UTC)
 * Where do I see Einstein saying such & such in 1920?. If I read the rest of what resource? What's the reference for what Einstein said?
 * You are apparently ignoring what I wrote. I am not claiming the physical existence of field lines. They are a representation of magnetic flux, or flux density (which is B). Get it? A representation. As I explained, you can move into and through and out the other side of a region of magnetic field, i.e., you can move relative to the field. Or, you can pick up a magnet and move it so that flux enters one side of a loop and comes out the other side, i.e., in this frame the flux/field has a velocity across the loop. The point is patently obvious. I don't need a reference for that--I am the reference because I know the physics and taught it at the college level for over 40 years. I am not relying on what others say, because I am fully able to argue the issue on its merits. Emf is accounted for in all cases by relative motion of charges and magnetic fields. If some dogma to the contrary has developed, that is a matter first of all to be taken up in the journals.
 * If you would (could?) address arguments on their merits, rather than just keep making assertions about what others say (spiced finally with a snide and irrelevant comment about engineering texts), a fruitful discussion might be possible. Otherwise, we're done. When the time comes, I'll offer the needed amendments to this article. LTFGD (talk) 02:58, 7 June 2023 (UTC)

Sorry, I had intended to include the link Unfortunately, Einstein spoke in German and that is a translation.

Einstein is the best I can do as far as sources to refute your mistaken belief that velocity is with respect to the field, which is why I urge you to try find a reference that says explicitly that velocity is with respect to the field. And from The Feynman Lectures (this time, I think he means it). Skip down to section 15-4 and read what he says about real fields. To paraphrase: fields are nothing but numbers that do nothing expect provide a computational convenience. And I mean it about the engineering texts. They use pre-relativity physics for the most part. Anyway, I have had my say. Cheers. Constant314 (talk) 04:42, 7 June 2023 (UTC)


 * I said I was done, but I forgot this simple analogy. Put your leg on a bed with your toe pointed up. Throw a blanket over your toe.  The blanket now has a lump.  Move your foot laterally.  The position of the lump moves, but the fabric does not.  In this analogy, your foot is the magnet, the fabric is the field.  The height of the lump is the value of the field (a scalar field in this case).  Motion with respect to your foot is not the same as motion with respect to the fabric.  It is an imperfect analogy, because the fabric is made of material stuff.  You can have motion with respect to the fabric. Constant314 (talk) 14:41, 7 June 2023 (UTC)
 * Einstein's speech is one in which he is pushing the idea of an ether in general relativity. Talk about ideas that have been banished! (whether justly so, I offer no comment here.) But again, as mentioned two or three times earlier, I am not claiming that magnetic field lines are "something material in the ordinary sense." That dispenses with the Einstein quote.
 * Feynman 15-4? I don't see anything to the effect that you can't have a velocity relative to the field. He says you can't put your hand out and feel B, but you certainly could if your hand contained sufficient ferromagnetic material. His main point in "B versus A" seems to be that the "reality" of the field resides in our ability to use it to calculate or explain things without resorting to action at a distance. Fair enough. We could in principle calculate ourselves to death using (retarded) action at a distance, but instead we make use of representations. And a perfectly fine representation, as I noted at the outset, is magnetic field (or flux, or flux density, or field lines), with force on a charged particle being ascribed to the relative motion between it and the field. But again, you are not addressing my arguments on their merits but making reference to dicta which do not themselves even address those arguments.
 * I don't need an analogy, because my argument addressed the actual situation. But, your analogy only makes my point. The foot would be a moving magnet. The lump is the field, and it moves. A cat, seeing the moving lump, could chase it, thereby having motion relative to the lump. The fabric would be some sort of ether, which is superfluous to the discussion.
 * I'm a little disappointed you didn't trot out the old "infinitely long solenoid" for which B outside is zero even though emf is induced by changing the current. (Hint: B outside is not zero while the current is changing.) Or even the toroid, which is more interesting but still explainable. But, since you seem unwilling to make arguments, I see no reason to rebut them here. All the best. LTFGD (talk) 15:35, 7 June 2023 (UTC)
 * I am not trying to prove anything. You seem to want to challenge some articles in journals and it is an Occom's razor situation: you should challenge your assumptions.  I'm just trying to point to the path of the next level of understanding.  Good luck with your efforts. <b style="color: #4400bb;">Constant314</b> (talk) 20:41, 7 June 2023 (UTC)
 * Got it. You don't have any serious arguments, even in defense of your own Wiki contribution, but you imagine yourself in a position to point my way to higher understanding. LTFGD (talk) 14:48, 8 June 2023 (UTC)
 * I guess I just cannot stop. Consider this, an observer in a large cardboard box has a moving charged particle in his box.  He can measure the velocity of the particles and all the fields local to the particle in his frame of reference.  The B field is caused by a moving magnet that is outside the box that he cannot see and is unaware of.  What does he used for velocity in the equation $$ F = q ( E + v \times B)     $$? <b style="color: #4400bb;">Constant314</b> (talk) 15:36, 8 June 2023 (UTC)
 * If he doesn't have access to the full picture, he might inquire of someone who does. (Any representation that you would use for explanation and/or calculation requires access to sufficient information.) If the field is sufficiently uniform, our blinded observer could not detect the relative motion but would of course observe a uniform electric field in addition to the magnetic field. He would not know from limited data whether the perceived E was due to relative motion or due to a pair of invisible parallel charged plates. Of course, the uniform fields would not give rise to any emf around a loop. If, however, the B field is not uniform, as long as the observer has a time-dependent record of B at each location in his region, he could observe the motion of the array of B values (the flux density) move through the region and I suppose infer the velocity from that. By the way, no one is denying the existence of frame-dependent E or the validity of Maxwell's equations. There is more than one way to represent a situation. Motion relative to B is a very useful way of understanding and calculating induced emf as well as electromagnetic force-per-charge not stemming from the gradient of a potential. LTFGD (talk) 16:51, 8 June 2023 (UTC)
 * Now go back to Feynman's definition of a real field: "A real field is then a set of numbers we specify in such a way that what happens at a point depends only on the numbers at that point. You don't need to know the velocity of a magnet outside the box to compute what is going on inside the box if you have measured E and B inside the box. <b style="color: #4400bb;">Constant314</b> (talk) 22:14, 8 June 2023 (UTC)
 * Of course you can measure what happens in the box without knowing what's happening outside. And of course the observer in the box CAN ascribe the force on the particle to the combined effect of an electric and magnetic field. The interesting question here is how to understand and even calculate what's happening inside based on what's happening outside, which you already said was a magnet moving past. So there were no parallel capacitor plates, and the E field inferred by the informationally crippled observer in the box is not the gradient of a potential.
 * Of course you can calculate that E from knowing B in the rest frame of the magnet, then Lorentz transforming the field tensor to the frame of the lab/box. (Keeping in mind that relativistically, this B is not the same as B in the lab that causes the qvxB force on the particle.) What will you get for the force?
 * What you will get (in addition to the original qvxB force from the motion of the particle) is a (negative) qvxB force where THIS v is the velocity of the field through the lab and B is the magnetic field in the lab frame. (I can demonstrate that but won't try to do so here in this format). It is easy to see therefore that the entire force on the particle CAN (doesn't have to be) understood in terms of relative motion of the particle and the magnetic field (as long as there is not an electric field that is the gradient of a potential). The line integral of this force (per charge) around a closed loop is the emf around that loop, and it is easy to see that this will be equal to the rate of change of flux through the loop.
 * Thus, induced emf can be ascribed entirely to motion relative to the magnetic field (represented by field lines). One phenomenon. Not two different phenomena. That was my original point. The only thing left out of the above analysis is the case where the field lines are moving because the field itself is changing. For example, if the current is increasing, the B it causes will increase, causing field lines to move in closer together. There's no way for a charged particle to know whether the motion of the field lines is due to motion of a magnet or a changing field strength.
 * If our magnet is moving relativistically, then the component of B perpendicular to this motion (which is all that matters) is increased by the factor gamma from its value in the rest frame of the magnet. This is easily understood by Lorentz contraction compressing flux into a smaller area. Non relativistically (for the benefit of those benighted engineers and intro physics students), the method described here is a vast simplification because no transformation of field tensors is required and gamma equals 1 to close approximation.
 * I've carried on much longer than I intended, but it's not wasted time because all of this has to be articulated anyway in a journal paper, not to mention answering the inevitable concerns of reviewers. So, thanks. Any other questions? LTFGD (talk) 01:57, 9 June 2023 (UTC)
 * Good luck with your efforts. <b style="color: #4400bb;">Constant314</b> (talk) 13:10, 9 June 2023 (UTC)
 * P.S. I use the line cutting model a lot. It may be 19th century physics, but it is still very useful. <b style="color: #4400bb;">Constant314</b> (talk) 21:15, 9 June 2023 (UTC)
 * Thanks for your help. LTFGD (talk) 22:56, 9 June 2023 (UTC)