I Walter Lewin Demo/Paradox: Electromagnetic Induction Lecture 16

[tedward]

Only In the case of an electrostatic field, the voltage is equal to the potential difference. Due to the conservative nature of the static field, the voltage does not depend on the integration path between any two points. In the case of time-varying electromagnetic fields, voltage and potential difference are not the same. The potential difference between two points is unique, while the voltage and induced emf between two points depends on the integration path.

For Lewin's circuit paradox, two points in a circuit cannot be at different potentials just because the voltmeters are on different sides of the circuit. This is a probing problem. We can think of the voltmeter as measuring the voltage produced across the source impedance of the probe wire as the current flows through it, which is why the voltages on both sides of the voltmeter are different. So, stubbornness and arguments may be because everyone has a slightly different idea of definitions, conventions, and terminology.

Yes, the difference in convention is a big factor in all the disagreements. Part of the reason I revived this thread was to explore why otherwise very intelligent people have such heated disagreements on this - there has to be a resolution. It seems that anyone who understands that there are differing conventions should be able to recognize when one is being used vs another. That's why I advocate for sticking to the terms 'scalar potential' and 'path voltage' to keep from confusing them. Lewin only has a probing problem if he's trying to measure 'scalar potential' (static field only). If he's trying to measure 'path voltage' (the sum of induced field and any static field), he's doing it correctly and arrives at correct conclusions, i.e. path dependence. What drives me mad is when people don't know or understand the different conventions, and say Lewin is wrong, when they don't even understand what he's actually saying. When he says path voltage has a non-zero sum, he's simply stating Faraday's law, almost verbatim.

 

[tedward]

I can't see how that can be when he said Kirchoff is wrong. I thought we about had this resolved. I said in an earlier post that the setup did not match the schematic. Had the setup been represented correctly on paper then transformer secondaries would have been drawn in and he would not have been able to claim he was probing the same point with both voltmeters.

LOL I love how you confuse "I've already stated my opinion on this" with "I thought we about had this resolved".

 

[Averagesupernova]

@tedward watch the YouTuber electroboom. He has at least one video that does the same experiment but does it more thoroughly than Lewin. Admittedly he is a clown but he gets his points across very well. I also learned today that he is the engineer who Lewin refers to that said Lewin's experiment's results are due to bad probing. I really have nothing else to say about this. For you to come on here and say that you now realize we disagree about flux in a loop because I am wrong is nuts. I've told you many times here why I hold my position and I only get a reply from you that says: "But the loop is the flux!" And yes I realize that.
-
One last thing, I'm sure there are many other YouTube videos out there but I really hadn't bothered to look for them. I don't really find any of this that mysterious.

 

[tedward]

@tedward watch the YouTuber electroboom. He has at least one video that does the same experiment but does it more thoroughly than Lewin. Admittedly he is a clown but he gets his points across very well. I also learned today that he is the engineer who Lewin refers to that said Lewin's experiment's results are due to bad probing. I really have nothing else to say about this. For you to come on here and say that you now realize we disagree about flux in a loop because I am wrong is nuts. I've told you many times here why I hold my position and I only get a reply from you that says: "But the loop is the flux!" And yes I realize that.
-
One last thing, I'm sure there are many other YouTube videos out there but I really hadn't bothered to look for them. I don't really find any of this that mysterious.

I've watched electroboom. First he says Lewin is wrong, then he consults with Belcher (see his paper below) who breaks down exactly why Lewin gets his results, then he replicates Lewin's results, and still won't agree with Lewin. The guy is most certainly a clown, but even when he tries to be serious is logic is all over the place.

If you understand the two voltage conventions, and know what Lewin is doing, he is certainly right. If you use different convention and get zero, that's right too. Both parties should agree on the fundamental physics. It's people who don't understand the conventions and mix either analyses together that get the physics wrong.

The reason you don't find it mysterious is that you are locked into a certain way of seeing things and refuse to consider other points of view. The fact that your fundamentals are severely lacking makes statements like "Lewin is just sad" laughable. Read my post. Understand what flux is really is. Discard your model, because it's not helping you make correct conclusions, regardless of convention.

https://web.mit.edu/8.02/www/Spring02/lectures/lecsup4-1.pdf

 

[tedward]

So it is not inconsistent with Ohm's law, because the current and power loss in a resistor is calculated in terms of the voltage , not potential difference.

But when it is different from the case of electrostatic field, we have to change the expression from j=c*Ec to j=c*(Ec+Ei), where j = current density, c = conductivity, Ec+Ei = total field

Right, I understand that there is a version of Ohm's law under the 'voltage is scalar potential' description, but the rule now has to be redefined to include induced effects. If you sum those two effects (path voltage), and call that the V in V = IR, you don't have to redefine the rule. We can certainly debate the usefulness of one convention or the other. What I don't understand, is that when I state clearly that I, or Lewin, is considering 'path voltage', you claim that voltmeters don't give the right measurement. Voltmeters measure the electric field between two points, whatever it is. If that's what you're after, your voltmeter works fine. If you are looking to measure scalar potential, a voltmeter will not help you unless you have a very contrived setup.

 

[Averagesupernova]

Voltmeters measure the voltage across the internal resistance of the meter. If the leads are in the flux field as they are in Lewin's, how is the voltmeter to know if the leads are part of what is intended to be measured or not? It can't. I have one more thing that may convince you that it is possible to arrange a loop, or actually a whole coil, in a solenoids field and not have it influenced at all. I have to dig out a book because the technology is obsolete enough that it's difficult to find on the net. Some older folks here will likely know what I plan to do. Be back here in 4 to 5 hours.

 

[tedward]

I have to pin you down on something and finally get an answer from you. In the active circuit, with at least one lumped resistor, pick a section of uninterrupted conducting wire. For the moment, forget voltage of any kind, static, induced, net, emf, whatever. My question to you is: What is the electric field in that section of the wire? Is it zero, or non-zero? And if non-zero, which direction does it point - with the current or against?

 

[Averagesupernova]

"The active circuit". What does that mean? You didn't specify enough to answer. If you mean in the @mabilde setup with the power on then every single mm of wire has an electric field between points if there is a resistor at at least one place. The closer to the resistance of the wire that the resistor gets, the smaller the field. Do I really have to answer the direction? For Pete's sake I'm the one who's been talking about Kirchoff always holding. So it has to cancel the field at the resistor. Going around in the circle keeping track of polarities add them up and they zero. That's for that specific case.

 

[tedward]

every single mm of wire has an electric field between points if there is a resistor at at least one place ... So it has to cancel the field at the resistor.

Wait, I'm confused by your answer. Let's try this again. Single loop circuit surrounding a solenoid at the center, or as Mabilde has it in the latter part of his video, just inside the solenoid as we've been discussing (it doesn't make a difference). The solenoid has AC current through it, inducing an emf on our loop, just like usual. Say there are two lumped resistors, who's resistance is orders of magnitude higher than the wire itself. Say the resistors are 1 k-ohm each. I'm going to assume the resistance of the wire itself is arbitrarily close to 0 compared to the lumped resistors. With some VERY rough dimension estimates from the video, my-back-of-the-envelope calculation for the resistance of the full copper loop (excluding lumped) resistors is about half a milli-ohm, or .0005 ohms. For the sake of the question, when I ask is the electric field zero, I mean is it arbitrarily close to zero when compared to field in the lumped resistor? I.e is it small enough to be neglected in most calculations? Or is it significantly non-zero, something on the order of the field in the resistors? And if significantly non-zero, does it point with current or against? I'm being pedantic but your answer was unclear.

 

[Averagesupernova]

The voltage when measured correctly has to add up to the voltage across the resistor (s) if it is probed over various places around the loop. Are you serious? We are back to this? I thought this was settled. A transformer with multiple windings has to behave the same way so why not here?

 

[alan123hk]

I'm the one who's been talking about Kirchoff always holding.

As someone who graduated from electronic engineering and has been working in related work for decades, I never think that Kirchhoff's circuit laws are wrong. I think only improper application can lead to different results than the actual situation. I don't know if there have historically been different versions of Kirchhoff's circuit laws with slightly different definitions, since I haven't researched it myself. In short, I would build a suitable circuit model and then apply Kirchhoff's circuit laws from DC to high frequency, which for me would give me very useful results for solving practical problems. Of course, I have to evaluate the possible deviations between the calculated results of this circuit model and the reality, and I fully understand what I am doing.

 

[tedward]

Alright I deleted my last reply - sorry I had to read your answer in #128 several times to understand what you meant. But now that I think I understand what you mean, I want to push this question a bit, because it's important in finding out where we stand.

So you claim that the net electric field $E$ at all points in the conducting wire is non-zero, and points opposite the direction of the field in the resistors. I claim net electric field in the wire IS zero, because the electrostatic field $E_s$ form the charges built up at the resistors pushes back - the same exact thing that happens in conducting wire in DC circuits.

What you are describing sounds a lot like you're talking about $E_s$ only, which essentially means you're using the 'scalar potential' convention. If that's the case, than we're just talking about different voltage conventions and we might actually be able to reach a consensus on physics with a bit discussion of the different conventions.

But if you think the NET field, (the TOTAL field the charges actually feel) in the conducting wire is non-zero, than you have to explain how it is that current in a region with non-zero field and (effectively) zero resistance is not infinite/arbitrarily large.

 

[tedward]

As someone who graduated from electronic engineering and has been working in related work for decades, I never think that Kirchhoff's circuit laws are wrong. I think only improper application can lead to different results than the actual situation. I don't know if there have historically been different versions of Kirchhoff's circuit laws with slightly different definitions, since I haven't researched it myself. In short, I would build a suitable circuit model and then apply Kirchhoff's circuit laws from DC to high frequency, which for me would give me very useful results for solving practical problems. Of course, I have to evaluate the possible deviations between the calculated results of this circuit model and the reality, and I fully understand what I am doing.

I think we agree on this. In your convention of voltage, i.e. 'scalar potential', Kirchoff's law always holds, as electrostatic field is conservative. In the path voltage convention, (integral of net electric field), Kirchoff is no longer valid in induced circuits, as the net field includes the non-conservative induced field. (Though I think we still disagree on what a voltmeter can measure accurately).

Funny thing is, even with the path voltage convention that Lewin uses and I subscribe to, you CAN still use Kirchoff's laws if you choose a path that goes outside the transformer (in the multi-turn case). That's how most books define the voltage of a transformer or inductor and refer to it as Kirchoff's laws (though they're usually not explicit about it). The ambiguity only comes in when you force people to acknowledge the circuit path itself, which is what Lewin's circuit does. I think Lewin would still insist on calling this Faraday's law as he only uses the coiled path in the multi-turn transformer. That probably the only place I disagree with Lewin, but it's strictly semantics, not physics.

 

[Averagesupernova]

First things first. What is known as a goniometer is a special kind of transformer. I've snapped pix out of the 1985 ARRL handbook. I was surprised I didn't see it mentioned in other books I have. I am likely mistaken in mentioning it's obsolescence as I believe radar and other direction finding operations still use it. It was a common device on vectorscopes that analyzed the NTSC color signal. Now you may ask what any of that has to do with what we've been discussing. What can be done with one of these is drive each stationary coil 90° out of phase with each other. As the coils are placed, they do not interfere with each other. The rotating coil which is not shown in the pic will then align itself with the stationary coils so than when it is rotated the signal on it will be the vectorial sum of the signals in the other two coils. The rotating coil is free to rotate 360° plus. There are no stops. Is this not proof that coil placement affects coupling between said coils? Even to the point of zero coupling? If one of the stationary coils is not driven with a signal there will be no signal out of the rotating coil when it is aligned with the dead coil. It is not the exact same setup (sorry, no pie shaped conductors) but if you are able to understand the lowly goniometer then I have to assume you are able see how the pie shaped conductors work correctly.

Concerning the electric field. Electric fields are not treated too heavily in most textbooks I am familiar with. If there is a potential difference between two points, then there is an electric field. The explanation of what happens in a completed circuit is drawn out and overly complicated for what we need to do here. You can watch several videos on YouTube and at least one will say as much as who cares.
-
I suppose if I don't understand the electric field as well as you or Lewin or whoever maybe I don't have any business discussing this. And I don't care. I can say the same thing about you not understanding how the significance of how conductors are oriented in a magnetic field determines the current induced in them or not in them.

 

[tedward]

First off, apologies for my post (that I deleted). I thought you were deliberately ducking the question to avoid getting pinned down until I re-read your reply a few times. But I do want to follow up on the voltage convention question, I have a thought experiment in mind I'll post tomorrow.

Re: the goniometer: this looks super interesting and I'll take a look when I can.

On the electric field - simplest way to think about it is just voltage spread over small distance, or a voltage gradient, so volts/meter. You can get a voltage difference by adding up the field along a length. Yes it's probably not something you have to pay too much attention to or that comes up a lot practically, say in household electronics or power systems and such. Engineers and physicists tend to think in these terms when we're modeling problems like this. It's especially true when there's so much confusion about voltage terminology, we need to get under the hood and discuss what happens inside a wire and look at the forces felt by the 'lowly electron' - it helps get to the root of the problem. What seems very abstract to one is actually very concrete to another I guess.

To your last point - that's a fair, honest take, and yes it seems we have very different backgrounds in terms of how we learned what we learned. I'm guessing yours is very practical, mine was very theoretical. I suspect you can run circles around me in terms of real electronics. I'm really more of a math guy with an ME degree who enjoys physics, but not a ton of practical electronics background. I tutor high school and college students, math and physics, so my mind is very math/theory oriented and that's how I approach problems, with mathematical models. On a very theoretically oriented problem like this that seems like the best approach (to me).

What's got me so fixated on this problem is just trying to figure out how professionals in different fields can disagree so vehemently, when there should be some kind a of a consensus. We should be able to at least figure out exactly where we disagree and why. And it should probably be explainable in basic terms. Anyway happy to keep a friendly discussion going forward - but if you call my ideas BS or ridiculous, I'm gonna push back ;)

 

[Averagesupernova]

The best I've seen yet.

 

[tedward]

Lol I've watched this, and his other videos on the subject, and find myself yelling at the screen. He's a good teacher as far as I can tell but falls into the same traps as so many others on this problem (in my view). Maybe we can pick apart some of his points later. I'm done for now.

 

[Averagesupernova]

He's a good teacher as far as I can tell but falls into the same traps as so many others on this problem (in my view).

I would be curious to what those are. I'm sure we've discussed some if not all of them here. Any new ones?

 

[tedward]

Probably the same ones, but he at least walks through his analysis clearly, so we can say 'this part right here doesn't make sense and here's why' without getting lost. His analysis lines up with Mabilde, and they both cite the same paper by Kirk McDonald - physicist at Princeton (iirc) - as the basis of their analysis. But the funny thing is - and I have a post coming - McDonald's analysis actually agrees completely with Lewin's. They don't disagree on physics. He just uses a different voltage convention - scalar potential. So this 'should' just be a difference of conventions and semantics.

 

[tedward]

Obviously, the potential difference generated by the charge measured by the voltmeter now moves from the two points a-b to the two points c-d, which should be roughly equal to the arc length between points c and d multiplied by the induced electric field.

View attachment 322084​

The distance between the associated thick red and blue lines is approximately zero. I've separated them slightly for easier viewing.

I'm trying to figure out exactly what you're saying here. We agree that the induced field between a and b is canceled out by the static field generated by the accumulated charge distribution, so the net e-field between a and b is zero. The voltmeter leads (the sections parallel to ab) are subject to these exact same effects (in the same respective amounts), so the net field in the voltmeter leads is also zero. Therefore, using the path voltage convention of integral of electric field, the zero reading on the voltmeter is accurate - it reports precisely the sum of the net electric field between ab which is zero.

If we use the scalar potential convention of voltage, we leave out the induced field, and only include the static potential which is associated with different points wire. I don't see how the static potential would 'redistribute' to c-d, wouldn't the potential values match exactly to the blue wire section? Though I'm not sure how it matters anyway.

Either way, if the scalar potential values are 'stuck' on the wires so to speak, the voltmeter won't measure them - this is your argument that the voltmeter leads 'double' or 'mask' the scalar potential. I accept that argument as long as we're talking about scalar potential. Voltmeters can't measure scalar potential in general because they can't separate the two effects - induced fields and static fields sum up vectorially and can't physically by 'untangled' unless you use Mabilde's setup. Maybe that's a way to think about it - voltmeters measure scalar potential when you intentionally 'subtract out' the flux in your loop as he does. But you use a flux-free loop you measure the path voltage.

What I don't understand is why you seem to claim that the voltmeter won't measure the 'path voltage' correctly (as I claim). Since the net e-field in any of the the wires is zero already, there is nothing to cancel out. As long as there is no flux in the voltmeter loop, voltmeters always measure path voltage. Maybe I'm missing your argument from the diagram, if so please help me out here.

 

[Averagesupernova]

Maybe that's a way to think about it - voltmeters measure scalar potential when you intentionally 'subtract out' the flux in your loop as he does. But you use a flux-free loop you measure the path voltage.

I'm going to answer this from my perspective even though I'm not the one the question was directed at.
-
Subtracting out the flux as you say is not what @mabilde is doing since his test leads are never anything but radially positioned. There is never anything formed on the radial leads to subtract out. So those are your 'flux free loop".
-
I suspect your opinion is that the "flux free loop" is outside the coil. It is actually not flux free in the Lewin setup. We on the same wavelength here?

 

[tedward]

Yeah we're definitely not on the same wavelength, and It's because we're using that word - flux - completely differently. We've been talking past eachother most of this time, because our mental models of how 'flux' works don't agree as far as I can tell.

Check out Lewin's video - yes it's the same one with the Super Demo. But everything he teaches about magnetic flux and Faraday's law before that is completely standard theory, absolutely no controversy at all.
Watch from about 5:00 to 35:00.

Whenever he's talking about flux, he's talking about the total amount of magnetic field that penetrates the imaginary surface formed by the a loop. So if you lay a piece of flat plastic wrap around a loop and tape it to the edges, that's the surface we're talking about (He does this with a plastic bag but he's making the point that the shape of the surface doesn't matter, just think of it is flat for convenience)

It's the rate-of-change of this flux that CREATES the emf - the sum of the induced electric field AROUND the circuit loop. You can now measure the total emf in ANY loop just by seeing how much magnetic flux passes through the loop's area (really it's how fast this flux changes).

When you say 'flux', what I think you mean is this induced emf / induced electric field in a particular section of wire. I think you're picturing magnetic filed lines that point out radially from the solenoid out to the wire (which is definitely not the case), and it's why you speak about 'flux' on a wire. You will hear people (like RSD Academy in his video) talk about 'emf' in a wire section, which makes a bit more sense but is still very ambiguous and I don't like the term. The proper definition of emf is the TOTAL amount of induced electric field around a loop, regardless of how the field is distributed around the loop.

 

[tedward]

Subtracting out the flux as you say is not what @mabilde is doing since his test leads are never anything but radially positioned. There is never anything formed on the radial leads to subtract out. So those are your 'flux free loop".

Terminology aside though, I think I do understand your argument. And the argument makes sense IF you adopt the viewpoint that the 'voltage' in that section of conducting wire is real, and that's where we see things differently. Let me see if I can describe the situation from both points of view. Just to be clear, I'm talking about the section of the copper ring uninterrupted by resistors, but there are large, lumped resistors elsewhere in the ring.

We both agree that there is no induced field / emf (what you've been calling flux) in the voltmeter leads, as they are placed radially at right angles to the induced electric field, which points around the circle. You regard the 'emf' in the wire section (the pie crust so to speak) as real, and that's what Mabilde is measuring. I've been making the point that he's simply measuring the changing magnetic flux through his measurement loop (the loop being the entire wedge shaped area leads and wire section). If you're a proponent that the emf in the wire is real, you should be saying of "Of course he's measuring the flux in his loop, that is equivalent to the induced emf in the wire section - they're the same thing!" I believe this is what @alan123hk has been saying - it's a real measurement, not a 'simulation' as I've suggested.

In other words we SHOULD agree that there is flux through his measurement loop. You would argue this is equivalent to the real emf he's measuring in the wire, I say there's nothing there. Partly this comes down to voltage convention.

My conception of voltage - path voltage - corresponds to electric field. You cannot have a voltage without electric field, as voltage by definition is the summation of electric field over length. Or think of electric field as a voltage difference spread over a length. But you can't have one without the other. You yourself said if there's voltage difference across two points, there's an electric field between them. That's the path voltage convention.

Now, the electric field in the wire section is in fact zero. This point is not a matter of convention. This is because the induced 'emf' from the solenoid pushes charge around until they build up at the resistors, and that charge pushes back, building up until an equilibrium is reached. This is the exact same thing that happens with electric field in a wire between resistors in a DC circuit - the only difference is we're replacing the battery's emf with induced emf. You CANNOT have a non-zero e-field in conducting wire, or you would get arbitrarily large / infinite current. This is why I claim there is no voltage in the wire section. I'm NOT ignoring the induced emf, I'm simply saying that the field associated with it has been redistributed to just the resistors only after the charges reposition themselves.

The other voltage convention, scalar potential, which @alan123hk and Kirk McDonald use, ONLY considers the voltage from the static charges. It literally ignores induced emf (BECAUSE it is non-conservative) and measures the reaction of the charges TO the induced emf. So now you can 'assign' voltage to regions where there is no NET electric field, only the static field produced by the charges built up at the resistors. This is what McDonald does in his paper (that both Mabilde and RSD Academy cite) - he has 'potentials' in regions where he acknowledges there is no electric field. The sum of the 'voltages' under this convention add to zero.

Obviously I don't like this convention, but both sides do agree (or at least should) on the physics itself. In his paper, McDonald clearly states that the sum of ELECTRIC FIELD is NON-ZERO around the loop, and also acknowledges that some people (a.k.a. Lewin and most physicists) use the NET field to define voltage as I have. So if they actually understand McDonald's paper (I'm not sure if they do), I don't understand why Mabilde or RSD would say Lewin is wrong, rather than saying that his physics is right but he's using a different convention.

Now I don't know what convention you're using - I have a feeling you've taken a "voltage is voltage" view without worrying about the particulars, and you think you agree with Mabilde. But you have told me you think the net electric field in the conducting wire is non-zero, which would contradict physics. If I could, I would love to pin down @mabilde and/or RSD Acadamy and ask what they think the net electric field is in the conducting wires, all voltage terminology / conventions aside (same question I was asking you). If they say zero, then there is no conflict in physics, just convention. If they say non-zero, then I would question their understanding of physics.

 

[Averagesupernova]

We both agree that there is no induced field / emf (what you've been calling flux) in the voltmeter leads

I have not been calling that flux. I can't reply back at the moment but I will post more.

 

[Averagesupernova]

Ok. Let's try again. The flux, lines of force, whatever you want to call them, I know what they are, I have for many years, didn't think I'd have to post a pic to show it.

Ok. The dotted lines coming out of the right side of the coil (N) that curve around and go back into the left side I call flux. As the current increases, more of these lines are present and they 'bloom' outward away from the coil and inward towards the center of the bore inside the coil. Every line that is outside the coil must also be crammed into the inside of the coil. As the current in the coil decreases the opposite happens. I'm sure you agree with this. It's very obvious that a single loop of wire wrapped around the coil inside or outside will get 'cut' by these lines. The closer to the coil it is placed, the tighter the coupling will be.
-
Now flip that whole thing so we are looking down at it as the experiments we have been discussing have been displayed. No change really, just a more familiar perspective.
-
The infamous radial leads in the @mabilde experiment NEVER are cut by the flux. They are in the field but the flux lines while going in and out are not cutting them at right angles like they are the loop arc. So, the pie angle is certainly represented by the voltage measured here. Slide the contacts so the angle gets bigger and the voltage increases. Slide them all the way around so they are in contact with the single resistor and you get the same voltage as if you had twisted pair voltmeter leads coming from the resistor on the outside of the loop. This is one way that proves only the arc voltage is being measured and it isn't that a pickup loop is being formed by the pie shape.
-
The second way that proves this in the @mabilde experiment he used a shorted loop instead of the resistor. No voltage was ever read no matter where he positioned the pie shaped leads. There's no reason to believe that there was any kind of canceling effect occurring here. The fact that the pie shaped leads didn't give a reading here should prove that the radial leads are immune to contributing to a reading one way or the other. Measuring from the center is the ONLY way to measure a voltage between points on the ring accurately.

 

[alan123hk]

I don't see how the static potential would 'redistribute' to c-d, wouldn't the potential values match exactly to the blue wire section?

$\text {Because}~~PD_{ab}=PD_{ac}+PD_{cd}+PD_{db} ~ ,~ PD{cd} = PD_{ab}- PD_{ac}-PD_{db}$
$\text{where PD = Potential Difference}$
$Since ~~PD_{ab}, PD_{ac},PD_{db}~~ \text {are known,}~ PD{cd}~~ \text {can be determined.}$

Though I'm not sure how it matters anyway

Since the electric field in the space outside the ring circuit is composed of the induced electric field and the electric field generated by the charge, if you want to predict, calculate and simulate the total electric field in the external space, you must know the electrostatic potential generated by the charge, and then you can calculate the electrostatic field from this electrostatic potential. If you only care the physical phenomenon inside the loop wire and the series resister, capacitor, and inductor, you may not need to pay attention to this electrostatic potential.

Voltmeters can't measure scalar potential in general because they can't separate the two effects

As mentioned earlier, the voltmeter is not completely unable to measure this electrostatic potential, sometimes it can be measured directly, such as the output of the transformer we usually use, and the setting of Mabilde. As for the total electric field in the outer space of the ring circuit, I think we can try to measure it with some advanced non-contact techniques like Scanning Electron Microscope (SEM)

https://cmrf.research.uiowa.edu/scanning-electron-microscopy
https://www.x-mol.net/paper/article/1234209940452691968

 

[tedward]

Ok. Let's try again. The flux, lines of force, whatever you want to call them, I know what they are, I have for many years, didn't think I'd have to post a pic to show it.

View attachment 322284View attachment 322285
Ok. The dotted lines coming out of the right side of the coil (N) that curve around and go back into the left side I call flux. As the current increases, more of these lines are present and they 'bloom' outward away from the coil and inward towards the center of the bore inside the coil. Every line that is outside the coil must also be crammed into the inside of the coil. As the current in the coil decreases the opposite happens. I'm sure you agree with this. It's very obvious that a single loop of wire wrapped around the coil inside or outside will get 'cut' by these lines. The closer to the coil it is placed, the tighter the coupling will be.
-
Now flip that whole thing so we are looking down at it as the experiments we have been discussing have been displayed. No change really, just a more familiar perspective.
-
The infamous radial leads in the @mabilde experiment NEVER are cut by the flux. They are in the field but the flux lines while going in and out are not cutting them at right angles like they are the loop arc. So, the pie angle is certainly represented by the voltage measured here. Slide the contacts so the angle gets bigger and the voltage increases. Slide them all the way around so they are in contact with the single resistor and you get the same voltage as if you had twisted pair voltmeter leads coming from the resistor on the outside of the loop. This is one way that proves only the arc voltage is being measured and it isn't that a pickup loop is being formed by the pie shape.
-
The second way that proves this in the @mabilde experiment he used a shorted loop instead of the resistor. No voltage was ever read no matter where he positioned the pie shaped leads. There's no reason to believe that there was any kind of canceling effect occurring here. The fact that the pie shaped leads didn't give a reading here should prove that the radial leads are immune to contributing to a reading one way or the other. Measuring from the center is the ONLY way to measure a voltage between points on the ring accurately.

I'm trying to see what you're seeing but I can't. Yeah, those look like correct pictures of a magnetic field of a solenoid. But for the life of me I can't understand what this notion of 'cutting' is. Violin bowing again? So It's the magnetic field lines themselves 'cutting' across the wire that generate the emf? You make no mention of the induced electric field in the loop, where's that? I'm sorry, you're whole conception of this problem is different from mine, we're not going to agree on anything. I tried.

 

[Averagesupernova]

Ok I'll post it again and try to explain it.

https://www.pengky.cn/zz-generator-...lternator-principle/alternator-principle.html
-
The wire loop of the rotor only generates when it is CUTTING through the flux lines. Notice when when the sine wave goes through zero the wire that forms the rotor is not cutting the flux. The voltage generated is based on the sine of the angle of the rotor at a particular instant.
-
It doesn't matter what is causing the cutting action. Growing and shrinking flux is just as effective as actual mechanical motion between the wire and the flux .
-
This has all been said to death here, there's really no more I can say.

 

[TSny]

As the current increases, more of these lines are present and they 'bloom' outward away from the coil and inward towards the center of the bore inside the coil. Every line that is outside the coil must also be crammed into the inside of the coil. As the current in the coil decreases the opposite happens. I'm sure you agree with this. It's very obvious that a single loop of wire wrapped around the coil inside or outside will get 'cut' by these lines. The closer to the coil it is placed, the tighter the coupling will be.
-----
The infamous radial leads in the @mabilde experiment NEVER are cut by the flux. They are in the field but the flux lines while going in and out are not cutting them at right angles like they are the loop arc.

I'm also trying to visualize this. Is it something like the following?

Suppose the magnetic field of the coil is coming out of the page inside the coil:

If the current in the coil increases, then the number of field lines increase. I think you saying that the field lines also move ("bloom outward") as the current increases, and the movement is radially outward.

Consider a pie-shaped loop inside the field region:

I interpret your description as saying that no voltage is generated in the straight sections because the field lines move parallel to these sections. The field lines do not "cut across" the straight sections. However, the field lines do cut across the arc section. So, you are arguing that voltage is generated only in the arc.

Is this at least somewhat along your line of thinking?

 

[Averagesupernova]

@TSny I could have been more clear. The lines bloom out on the outside of the coil. But they bloom IN towards the center of the bore on the inside of the coil. I'm not sure if the phrase bloom in is the wisest choice of words. Lol. The fact is that all of the flux lines originate AT the wires. Current increases and they move away from the wires.