Does Kirchhoff's Law Hold? Disagreeing with a Master 

Hello team RECTIFIER! Make sure to watch the next video on the topic: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Q9LuVBfwvzA.html

You can tell he's serious because he doesn't shock himself in this video.

"I couldn't be happier to be wrong and learn something new." -an important moral fiber rare these days.

Bad probing is almost always the number one source of error in electronics experiments. Kudos Mehdi

Can i just say that watching both this and your follow up video, i think the best lesson to be learned here is how to handle a disagreement like an adult. You found someone who had reached a conclusion that you disagreed with, and were still respectful of their findings and knowledge, while showing the reasoning that lead you to disagree. If more people could handle their disputes like this the world would be a happier place. Best wishes to you.

Very well done and diplomatic ;)

I am surprised that Dr. Lewin did not consider the mutual coupling of the coils with each other in his experiments. In his test moving the probing wires around should change his results. I could not find anything wrong with your analysis. Dr. Lewin seems to verify his hypothesis through the demonstrated experiment which appears to be flawed in how it is setup and yields an incorrect result. First step would be to correct the setup before we even discuss the issue at hand.

Teacher: The test isn't complicated The test:

If you don't understand anything, it's fine. He is not explaining it you, he is explaining it to Walter Lewin XD

"my mom thinks I'm mostly ok." 😂 r e l a t a b l e .

"My mom thinks I'm mostly ok." It's ok Mehdi. We're all in that boat together. Love you man. Keep up the great work!

Your regular, humour-filled videos with shocking situations that make you want to go Ohm, are nice and I love them, but this video was really refreshing. Seeing you explain a confusing topic and simplifying it down so those of us, not too familiar with electronics yet can understand...dude, I need more of this. I think that is a legitimate sign of intelligence.

I come to this video from time to time hoping I can understand all the concepts explained here a lot better. Out of all Mehdi's videos, this one does even more hard science than Mehdi usually does. That being said, I have learned quite a bit from this great dude, and I do appreciate the fact that he shocks himself a lot just for the laughs and to enhance the learning experience.

Interesting to see you challenging Dr Lewin. Science drama is so much better than typical RU-vid drama. And this is science drama _on_ RU-vid! A new paradigm!

What I got (reinforced) from this is that even the wire is a circuit component. Since the sense wire folds back on itself and follows about the same path back around, it induces nearly equal but opposite current from the wire that it's adjacent to, cancelling itself out. So you only read the effects of current through the opposite resistor. At least, that's what appears to be happening. He touched on that near the end when he drew in the hidden transformer.

4:48 "I have a coil or solenoid"... Me: This is going to explode. 4:57 "The resistor limit the current to 10-12 Amps"... Me: This is going to explode. 5:30 "Now I'll measure across these two points..." Me: This time for sure.

You were totally respectful and very educational with this video. The net result is more people learning about electronics, so I think this is a wonderful video.

I am really glad you did this video, not just cause I agree with you. It can be scary to challenge the findings of someone you respect but I think he would respect that challenge because we'll science.

From another Electrical Engineer- you got my vote👍

Oh, I worked in that field - years ago. The KVL is derived from "E = -grad( phi )" and the corresponding integration theorem. If there is an time varying magnetic field, the true electric field is "E = - grad(phi) - (dA/dt)" . I.e. the KVL holds in the electro-quasistatic approximation assumption, that dA/dt is approximately 0. The KVL is false otherwise.

And this is why science is based not on authority, but on peer review.

I like how respectful this video was towards one of the greatest minds in out current time. Its not bad to disagree with someone and politely explain why. This is a great science video with awesome explanation AND a great guide to social communication. Good for you EB!

bro curl(E)=-B_t (where B_t is partial derivative of B with respect to t) is a maxwell eq. it is always valid. while applying kvl u assume that E is grad of some scalar function, if a vector field is grad of a scalar func, then it must be curl free. however we know that curl(E)=-B_t, thus kvl is not always valid, which assume curl(E)=0.

Hmm...that is the basiscs of everthing: the ppotential difference as Voltage is only valid in a electrostatics, where the electric field is concervative. I think, this is tought in the very first lessons of every electrodynamic lecture.

Hi, I'm a theoretical physicist. I don't think Prof. Lewin was completely wrong, but I don't think your reasoning is wrong either. I agree with your calculations, but I think you are not applying Kirchhoff's law as is usually understood from the physicist's point of view. One may argue that Prof. Lewin is also wrong for the same matter when he says that Kirchhoff's law is sometimes wrong. It is never wrong: it's just that it does not apply on certain systems. In the end the problem, as I perceive it, is a semantic and not a physics one. What I am certain, though, is that Lewin proved himself to act rude and arrogant in that comment box. Your objection was completely legit and he had no right to call you an uneducated.

I was working on this same experiment for a Book. And I couldn't find a Simple way of explaining this. You did it in just 15 minutes which is awesome. This is very well done and quite diplomatic I must say.

One of my subscribers just turned me onto your videos. Absolutely magnificent stuff your brilliant! Going through most of your videos now it's going to take me awhile, but I'm having a blast. Thanks for sharing

It's very brave of you to challenge someone like that. Keep it up

would it be possible for you to start a lecture series about circuit analysis? i believe you are the best teacher i know. theory combined with actual applications/experimentations is the best way to learn. i haven't been bored in any of your videos. you're so good! more voltage times current to you sir!

Always express you thaughts. Just because he wrote 15 science books doesn't mean he Is right, or that he Is smarter than you.

The first serious video in this channel 😂 A lot of love to Elctro Boooom

I am a law student who desperately wanted to study physics. I've searched for law stuffs, and RU-vid suggested me this. Thanks to RU-vid for realising my heartaches.

You are correct I have experienced different measurement around the loop while performing some practical in my university even my professor were stoked to see that, but I realized later that I had bad probing. Well explained Keep the videos coming and always express it good to see what other people think.

May I suggest an alternative test for probing this circuit: Rather than having the probe wires in the same plane as the resistor loop, instead have the wires perpendicular to the plane of the loop (parallel to the changing magnetic field). Thus, no EMF would be introduced into them until they are sufficiently far away to make the effects negligible.

Kvl is a simplified form of Maxwell's equation obtained by lumped matter discipline in which we assumed dphi/dt = 0 I.e zero change in flux.

This video illustrates why I subscribe to your channel. While the majority of your videos have an important entertainment value, they're based on scientific principles. I appreciate the level of critical thinking you are able to apply to the many scientific laws of electricity. Thank you for the work you put into your videos.

Great scientists admit when they are wrong and let everybody learn from their mistakes; those other scientists get their ego punctured.

Howwwwlyy Shhieeeett!! When I heard "2 different Voltages across the same 2 points", I questioned my life and all circuits that I ever made ^^ Now that I saw the great explaination it all came together for me. But I do agree with you. It does make a lot on sense when you think about it.

WoW ! - I feel like I'm watching two gods fighting each other on mount Olympus and I have a BSEE degree.....

I agree. I'm an OLD electronic tech/engineer and have seen this sort of thing come up as a problem in a industrial installation.

This and the follow-up part 2 video are my two very favorite videos of yours! Your passion is for the science itself...finding the truth...This is the same passion, Faraday, Maxwell, Feynman, and the other greats all shared...You're in good company! Thank you for this series and for the inks to the counter-arguments by Lewin...

This is a risk one encounters when delving outside of ones field of expertise. By ignoring the transformer created in his model, Lewin made a mistake that you clearly identify. Well done!

Studying electrical engineering and watching your videos is the best combination

I don't want to take sides but Dr. Lewin's reasoning is sound. KVL as we know it from (lumped) circuit theory can be derived from Maxwell's equations as a particular instance. If the magnetic flux enclosed by the circuit (contour for the path integral) is negligible then the voltage produced by it is negligible and we get the known KVL for voltage. This is much better explained in Harrington's "Time harmonic elmag fileds" with a nice summary in Table 1-1.

I will watch this in front of my family, so they will think I'm smart

Maybe he was trying to challenge some unknown genius to step forward and call him out??

This is a very good point, though several times before when I watched the video but didn't realize how important it is. The matter of this question is how to model the real physics system: we can model the magnetic field by inductances and transformers as electrical engineering, while physicists may look at PDEs and have less emphasis on lumped circuits. As for the probing, that's another vital lesson I have learnt, because I was lucky enough that I didn't burn the scope with ground circulation with two passive probe at a region of high di/dt, quite similar as here.

7:12 thats good one.

I fully agree that the model is missing an inductor. The ability for a wire to be able to have current induced from a changing magnetic field needs to be modelled in the circuit as an inductance. Just like the lumped element model for transmission lines.

You just invented Polite Roasting

Two truly good and decent men struggling to teach the next generation!.. they should be proud of each other!.. Im proud of you ElectroBOOM!

Hello sir, I’m not sure if I’ve understood your video but in my opinion what professor lewin is talking about is maxwell’s equations. One of maxwell’s equation says that in presence of changing magnetic fields, electric fields are no more conservative therefore the work you need to do to get from one point to another does depend on the path you take and potential difference is just the work you have to do divided by the charge you’re holding

Being an accomplished physicist does not preclude him from being wrong.

I love this about a person of science. Challenge even the most established idea. Your humble nature shows, and is really appreciated. Good vid, as you demonstrate how the exact positioning of sensory wires makes a massive difference.

The Wikipedia article on Kirchhoff's circuit laws explains this under Limitations: "The current law is dependent on the assumption that the net charge in any wire, junction or lumped component is constant. Whenever the electric field between parts of the circuit is non-negligible, such as when two wires are capacitively coupled, this may not be the case. This occurs in high-frequency AC circuits, where the lumped element model is no longer applicable. For example, in a transmission line, the charge density in the conductor will constantly be oscillating." "On the other hand, the voltage law relies on the fact that the action of time-varying magnetic fields are confined to individual components, such as inductors. In reality, the induced electric field produced by an inductor is not confined, but the leaked fields are often negligible."

Kirchhoff’ law is for static fields. Given this fact the argument is doomed as we already know we are in trouble. The voltage between 2 points does not make any physical sense if you have a time varying field. You can only measure voltage acting around a complete loop. So measurements depend on the path of the wires connecting the 2 points. Replacing the distributed induced e.m.f with a transformer is not valid. In reality there is an induced electric field acting on all the wire so replacing with a transformer does not model the physics correctly. Choosing a straight path between the points does not help anything. In short there are somethings which can not be modelled with a discrete circuit and this is one. To understand this properly you need to think in terms of fields. But as always very entertaining presentation.

Great discoveries are made by those who question the leaders of the field

Uh, if you get different readings, dependent an moving your scope/sense wires around, that might be the hint, that your sense wires and scope position are not just sensing wires, but part of the circuit you created.

i like this way of experimentally trying to prove someone wrong. It's a nice and a humble way to disagree with someone of such high caliber.

11:00 KVL states that, i*R1+i*R2=0 (i !=0) => R1=-R2, given that a resistor is a "passive lumped element" and this equation couses a "passive element rule violation" since one of the resistances is below zero. So in that case KVL does not hold and the induced voltage should be calculated by the "integral E dl" which means that there exist electric field change (voltage drop) through the loop wire which has 0 resistance we assume generally and that is a contradiction.

"My mom thinks I'm mostly OK" Words to live by brother.

I remember having a similar conversation with one of my instructors as well. He simply said, high tolerance applications, use Kirchhoff's Law. For low tolerance applications, use Faraday's Law. I doubt I would have caught this. This clears up a lot for me.

YES! I saw the transformer, too. The sense lines are part of the circuit! (I was just an ME, not an EE, although I am a licensed ham for what that's worth.)

Amazing video, and bad youtube algorithm, even tho i been watching your videos for ages (and subscribed) this good quality video was never in my feed... found it by mistake, and i was like “this must be new upload- just to see it’s 2 years old”

Dr. Lewin is displaying behavior far too common in the veterened engineering academics in that he clearly believes his knowledge and opinion is higher than anyone else. It is an unfortunate side effect of hubris in this field and I've personally experienced it in many professors. Simply in the way he responded to your comments, insisting that any argument is the result of no education and only his video and lectures can educate you, all the way to that last clip you showed where he reveals that every other author and professor disagree with him and yet they're the ones that are wrong? I recall a professor refusing to allow us to use Thevenin's equivalence when analyzing BJT circuits simply because she didn't like it. Every single online tutorial, university, and textbook insists on its use over 8 KVL equations but she didn't care because her opinion with gospel. Knowledge =/= education and that's incredibly important to keep in mind. You can have all the knowledge in the world but if you don't or can't question that knowledge then you're not well educated.

I had been wondering about Dr. Lewin´s experiment since the first time I saw it. I watched it several times and had come to a similar conclusion. Since this is an air core transformer, any nearby wire is part of that transformer. Magnetic fields can have very complicated effects. Basically I´m glad you adressed this.

Hi, I think that what you are missing is that is not always possible to consider an inductance to modem the changing magnetic field. For example you could consider a magnet moving near your circuit. From a mathematical point of view maxwell’s law says that the integral of E in a closed loop (which in electrostatic is the ddp) is zero if and only if the flux of the magnetic field is constant through the surface enclosed by the loop. Anyway very interesting video thanks!

For those of you who think Lewin is wrong, I suggest you apply Faraday's law in empty space. A changing magnetic field will induce an electric field even in empty space and not just in wires. This electric field is non conservative. Do you still think the potential difference between any two points in space is uniquely determined?

As a medical student I have no idea what I'm doing here lol

Why do I watch this? I understand nothing.

Watching this video in 2024: Medhi's error happens at 8:28. He 3rd meter which he claims is 'across' the two points of the loop is actually a reading AROUND the loop. At 10:17 he claims that an open loop - which doesn't enclose the changing B field, will have 1/2 voltage induction outward, cancelled by half voltage induction back inward. That is completely false. Faradays law requires you to have a closed loop. He even says "they are in the same field". Wrong. They are not in ANY field. The B field change is only in a sub area in the centre of the loop - there is no B field at any portion of his C shape wiring at 10:25 which is why it measures zero.

I know nothing about this yet i enjoyed it thoroughly :)

It was an excellent demonstration of the importance of considering all the details in a scientific experiment. In the demonstration, the hypothesis is raised that the consecrated Kirchhoff's Law could be nonsense, depending on the side where the instrument that measures the same induced voltage is positioned - an obviously absurd hypothesis. If the measuring instrument (oscilloscope) is to the right or left of the same circuit, the voltage reading should be the same - but in the demonstration it did not occur. Thus, the hypothesis that the said Law would be flawed was proven. The layman certainly went unnoticed that in both measurements, right and left, the circuit was not the same. The circuit, in fact, is not only what the demonstrator draws, but also the wires, cables and the internal impedance of the oscilloscope should be considered. As it is electromagnetic induction, any opening between wires will have voltage induction by the variation of the magnetic flux that surrounds them. The measuring circuit, to be the same with the instrument on the right and left, should be what was drawn by the demonstrator at 12:04. Soon after, he shows in practice that he did not follow what he drew; leaving again a new half turn wire near to the experimental loop over the magnetic field generator. It was an excellent joke of illusion. Thus, the hypothesis of failure of Kirchhoff's Law can not be confirmed.

1:20 everyone. Imagine this world if just more people had Mehdi's scientific and philosophical humbleness

10:03 I love how he says " half-e-Vee" thats the Pinglish (Persian/English) translation of "half of V" . I love it because I do the same thing when I'm doing circuit analysis... add lots of farsi profanity.

Explaining the path dependency of the voltmeter indications in the Lewin experiment isn't a trivial matter. To do so requires us to consider the role of electric fields in establishing uniform current flow along the closed secondary loop. In Lewin's experiment both conservative (irrotational) and non-conservative (solenoidal) electric fields act concurrently together along the secondary loop path. This is not arbitrary but occurs out of physical necessity. The induced solenoidal electric field is the primary agent of current flow. The conservative (quasi-electrostatic) electric field arises naturally in response so as to moderate uniform current flow everywhere along the secondary circuit path. This concept probably isn't on the radar for most of us, nor is it normally an issue in typical circuit measurements. We expect that a voltage observation made under low-to-medium frequency conditions is independent of the measurement path topology. When we connect a voltmeter across the secondary terminals of a 50-60 Hz transformer we would normally be confident that irrespective of how we position the voltmeter, we can trust our measurement. We aren't concerned with the conditions along the secondary winding itself. At higher (radio) frequencies we might exercise more caution with our "voltmeter" setup. Under low-to-medium frequency conditions the external electric field in the space between the transformer terminals determines the voltmeter indication. This external field is conservative. The voltage indicated at the open secondary terminals appears as a potential difference (PD) whose value we equate with the underlying emf. In the Lewin experiment we are actually considering what happens along the single turn secondary winding proper. There is no unique terminal pair where emf may be observed. As Dr Lewin notes, there will be a negligible resultant electric field along the interconnecting conductors which comprise most of the secondary loop. The greater part of the induced loop emf will be concentrated across the discrete resistor bodies with little appearing elsewhere. There is negligible resultant electric field along any inductive element winding carrying electric current - time-varying or otherwise . In the Lewin experiment there is a clear dilemma with respect to Kirchhoff's loop rule - the algebraic summation of voltage drops encountered in a unidirectional traversal of the closed secondary circuit loop is not zero. One needs to reflect on the meaning of terms like voltage and potential difference. It's worth noting that in electrical engineering terminology there is an accepted distinction made between voltage (electric tension) and potential difference - as may be found in the International Electrotechnical Commission (IEC) glossary of definitions. Some experts argue that if we consider only the conservative electric field components encountered in a traversal of the Lewin secondary circuit then Kirchhoff's loop rule does apply - since only scalar PDs are included. This latter view allows one to always validate KVL, irrespective of whether or not there are non-conservative induced electric fields present. This approach of "ignoring" the induced electric field component along the the secondary circuit loop might seem a misdirection. It's not clear why this is done other than stating that KVL applies only to conservative fields. As mentioned earlier, the electromagnetically induced electric field is the prime agent of current flow in the secondary circuit - the conservative electric field is not. The latter arises from the redistribution of surface charge density gradients along the circuit path in response to the physical imperative for both charge neutrality and compliance with Ohm's Law within the conducting medium. The view that Ohm's doesn't apply is inconsistent with explanations typically found in standard texts on Electromagnetic theory. David Griffiths text "Introduction to Electrodynamics" is a useful source in that regard.

Dear Mehdi Mercury, I am (was) an electrical freshmen. After watching all your videos over the weekend, I decided to switch to Business & Management because I can no longer solder or plug in something to the outlet without imagining sparks.

Mehdi is soo near to 2M...

As an electrical engineer, I would agree with Dr. Lewin. The electric field becomes nonconservative in the presence of time-varying magnetic fields (Faraday's law). In other words, the Curl of E is non-zero. We can only define scaler potential for a field when the curl of it, is zero. Therefore, the concept of potential in the presence of a time-varying magnetic field (curl of E is nonzero) doesn't even make sense.

Your "noise" measurements are the inductance of the two wires in parallel and EMF induced into the circuit and the untwisted portions of your lead. Reason why it differs is they are in different positions one time closer, another time farther away, or other times not totally parallel with each other. In order for you to get an accurate reading you should use shielded leads from point to point or have your untwisted leads, 90 degrees from the measurement point. And if you really want to get picky, the probe itself will affect your measurement as it becomes part of the circuit. Because, depending on the frequency and voltages being measured, you can introduce capacitance or attenuation. I see what the professor is saying... when a circuit is being effected by EMF due to the circuit component characters, wire and connection resistance, until the EMF finally peaks, the circuit will behave and measure differently in different spots and will not equal zero. Depending on the placement of the EMF and the measuring devices you can get, either a positive or negative peak. You can see it in your noise measurement, those ripples are the varying voltages until the circuit stabilizes. Due to each component characteristics and connecting wire length the circuit at times, the total voltages will not equal zero. In addition, EMF waves are formed in the circuit which can be out of phase until the circuit "catches" up. And you also have angular velocity, field flux, stray field and cross lines to account for until the field stabilizes. Plus, just arbitrarily setting the circuit over the coil doesn't allow for accurate readings... When the law was written, they did not understand I-V characteristics, nor could they measure it or the circuit accurately. Plus you are measuring with a single scope... measure it will multiple scopes and compare the timeline of the voltages measured in the circuit and you will see.

Serious question: how is it possible that such a fundamental question doesn't yet have a solution that the scientific community agrees on? It looks very weird that nobody has encountered, and explained this before with some sort of peer review or it's just Lewin getting it wrong?

8:53 Dr. Lewin ended up not being a nice guy

Not only Dr Lewin, many physicists are of the same opinion.. Numerous books on electromagnetism have this problem and solution is different voltages..

I connect a voltmeter between two points on a circuit and think "I'm measuring the voltage between those two points". I'm not thinking clearly. The voltmeter is indicating a response to the total electric field which exists along the path occupied by the voltmeter and its test leads - i.e. between the points being probed. There may be both conservative Coulomb electric field components and non-conservative solenoidal field components which comprise the total electric field along that particular measurement path. In the case where there are definitely only Coulomb field components (e.g. in simple DC circuits) we can justifiably claim what the voltmeter indicates may be interpreted as the voltage difference or potential difference (PD) between the two points being probed. If there are induced solenoidal field components present along the measurement path, what we think we measure and what we actually "measure" may differ. This is what the Lewin experiment demonstrates quite clearly. Voltmeter indications in the Lewin experiment are ambiguous. Even if we closely align the measurement path with the actual path via the circuit between the probed points, the paradox remains unresolved - at least in the Lewin experiment case. There are always at least two possible paths between the probed points on a circuit. In more complex circuits the electric field conditions along the range of possible paths between the probed points will vary. Where solenoidal fields are likely present we might try to circumvent any ambiguity by judiciously choosing a measurement path between the probed points which we assert includes only Coulomb fields. This may not always be practicable. We can measure the PD across the terminals of an inductor but we can only surmise what electric field conditions exist along the inductor winding & which give rise to that PD. It is physically possible to arrange the measurement path to probe what is claimed be the Coulomb field (scalar) PD between the two points on the Lewin experiment. However we are simply choosing another measurement path which is after all, one of a number (an infinity?) of possibilities - the majority of which give different results. Surely it's the electric field conditions along the circuit path itself that are important - irrespective of whether there is ambiguity in the voltmeter observations.

Why don't you churn out a thesis paper on this?

A schooling in Metrology101. Step1: Check stray inductance, capacitance & noise. Step2: Marry me and give me scope.

Very well described! I work with small signals from microphones and phono cartridges and your video explains extremely well what happens in low inductance and low resistance loops and induced currents. Well done!

Hi there, I am an elektronic technician (one step below an engineer ;-) and I know the video from Lewin. Lewin is wrong! He has forgotton that in a loop with an changing magetic fiel the loop themself exactly each part of the loop is a part of the voltage source of the loop. You could cut the complete loop into infinite small parts of the whole source containing d Volts. If you summarize all the small parts of the loop which are induce voltage and summarise them, then you get sum of the voltage on the resistors and kirchhoffs law is working. The fail of Lewin is that he does not recognise, that each infinite small part of the loop is a part of the (magnetic induced) souce d U with its own " d internal resistance".

Medhi, I love your channel. I'm sorry to say both of you are arguing past each other... I'm a physicist who plays an EE at work so let me see if I can offer my 2 cents... The secondary of the transformer you refer to is an effective lumped element representation of the mutual inductance between the solenoid and the loop with the resistors. There is a secondary for the sense wire loop as well. However, the lumped element approach isn't general. The mutual inductance has to be calculated for a particular geometry, not a circuit, using you guessed it... Faraday's law. So you can only model the secondary if you have already solved the emf for the system. Lumped element then can be generalized for the flux profile so you can change the waveform, which makes it a powerful approach for circuit analysis, and makes the EE masters happy because they can just treat it like a circuit element and do normal AC analysis. See the appendix of Clayton Paul's book Intro to EMC for a fully worked example of this exact treatment. Now give me a damn oscope please.

As someone uneducated in the field, I came to the same conclusion before you finished talking. I would love to learn why you would be wrong as I currently don't see it. Your arguments make perfect sense to me. The probe wires are part of this experiment when it is setup like this.

Sir induced emf is path depending as it dipends of fulx linkages on the conductor ..... If the length of the conductor is more then flux linkages on the conductor will be more if one side of the coil experience more flux linkages than the other side then the voltages at the both sides will be different... And taking distributed parameters of the conductor(resistance).. we can say that voltage at the two points will be different....you are taking lumped parameters thats why contradictions are happening

First, Kirchoff's loop rule (your KVL) is NOT due to conservation of energy; it is due to the fact that the electric force is conservative and can be written as the gradient of a potential energy function. Alternately and equivalently, it is due to the fact that the electric field can be written as the gradient of an electric potential (voltage) function. Second, loops containing changing magnetic flux are NOT lumped components. The induced electric potential (voltage) is DISTRIBUTED equally and uniformly along the path (wire) of the loop. This is why many turns of wire generate higher and higher potential differences. Third, the circuit containing the oscilloscope must also be considered -- rather like the two loops in your twisted pair. In the first case the oscilloscope's loop canceled one half of the resistor circle's potential difference and in the second case the oscilloscope's loop canceled the opposite half of the circle's potential difference. Fourth, the magnetic flux is the magnetic field strength TIMES THE ENCLOSED AREA; positive sign for right hand rule and negative sign for left hand rule relationship between the loop and the field. It doesn't matter whether your oscilloscope leads retrace half of the loop each or not. You can attach them exactly at the resistor/cut as long as the resulting loop contains no flux. Let one of the leads retrace the circle before entering the oscilloscope's twisted pair and you will observe negligible pulses. The physical principles and definitions are absolute; however, interpretation within complex applications are subject to point of view. Which interpretation is "correct" is also subjective. Begin with Maxwell's equations (del X E = -dB/dt in this case) and then integrate E dot dL along the loop to get the potential difference around the loop due to the changing magnetic flux.

I find it a little disconcerting that a professor at a leading university who is well accomplished in his field proposes a radical change to a commonly accepted theory and then doesnt want to argue it because he is tired of arguing. Extraordinary claims require extraordinary evidence. It is a basic tennant of science imo. You dont get to make a great claim and then refuse to have the conversation and thereby win by default.

From Maxwells equations, the electric field E = minus grad V minus derivative of magnetic vector potential A. Obviously, mathematically, the sum of grad V around a loop is zero (~V2-V1+V1-V2). The question is, does the voltmeter measure grad V or E or something else in portions where A matters. It clearly doesn’t measure grad V, because the result depends on how you position its leads. The magnetic field affects the leads of the voltmeter and induces an additional E, thus current, inside them, which depends on how you position its leads in this magnetic field. The additional E is given by the rate of change of the total magnetic flux (magnetic field times area) through the closed loop formed by the meter leads connected to some circuit element. So, even if your leads follow the wires of the circuit, when you flip their position perfectly, grad V changes sign, while the additional E doesn’t flip sign. So, to eliminate it, the loop of your meter leads have to be parallel to the magnetic field (zero flux).

ElectroBOOM is mistaken in claiming there is a standing voltage along the conductor segments which form the majority of the Lewin secondary loop. Richard Feynman pointed out that even in the presence of time-varying magnetic fields a good conductor carrying an electric current has a negligible resultant longitudinal electric field. The voltage drop between two points along the same conductor equates to the line integral of the resultant longitudinal electric field encountered in a traversal of the conductor between the same two points. The voltage drop along a good conductor must therefore also be negligible. This is the case even if there is an induced electric field component along the conductor which arises together with the time-varying magnetic field. For the resultant longitudinal electric field to be negligible in that circumstance, the induced electric field component along the conductor must somehow be countered by another electric field component. This counter electric field can only arise from a electrostatic charge density variation established along the conductor surface. Hence the distinction between non-conservative induced electric fields and conservative electrostatic (charge based) electric fields.

Line integral of e.dl=0 is the statement of kirchhoff voltage law so according to that only conservative electric fields only obey this law we will take the approximation that inductors and solenoids will obey KVL so professor was right

I completely agree, im a janitor and i got shocked once so i know my stuff.

Richard Feynman would be proud of you for disagreeing with a master

This is the next big beef in the EE field . First was tesla vs Edison now it’s kirchoff vs faraday

I remember my teacher trying to explain Kirchhoffs law to me. Good times.