I Walter Lewin Demo/Paradox: Electromagnetic Induction Lecture 16

[tedward]

THE TEST LEAD QUESTION

An important question that keeps coming up is whether or not a voltmeter measurement in a circuit with an induced emf, placed either across a resistor or a section of conducting wire, 'masks' the intended measurement because it is subject to the same induced field as the section being measured. It's a valid concern, provided there is actually something there to measure. The answer to this question depends only on your choice of voltage convention.

Certainly we don't have this problem when we measure a resistor in a regular DC circuit. A voltmeter is a just a resistor placed in parallel, so it's true voltage (and reading) is exactly the same as the measured resistor. But isn't it subject to the battery's emf as well? Of course it is. You can look at it either way - "measuring" the resistor's voltage, or reacting to the emf in exactly the same way as the resistor. It's the same thing said two different ways. Does it make a difference if we're talking about induced emf?

Let's say we're trying to measure the 'scalar potential' in a section of conducting wire in an induced-emf circuit, just wire around a solenoid with one lumped resistor. The scalar potential here is the integral of the Electrostatic field only:

$V_s = \int{\vec E_s \cdot\vec dl}$

In this case $E_s$ can be thought of as the negative of the induced field that would be present if it wasn't canceled out, or as it would appear in free space. Some people refer to this as the 'emf' in this section of the wire (a term I object to, but I digress).

I place my voltmeter in parallel with the wire section. The wire has a presumably non-zero scalar potential between the two points of measurement, and for the exact same reason my voltmeter leads have the same scalar potential as long as it closely follows the DUT. The voltmeter should read zero as the 'potentials' in the wires cancel each other out. It certainly does, so it seems like this argument works in this case. We now know that voltmeters can't measure scalar potential independently. (Keep in mind the scalar potential is just a mathematically derived quantity anyway, charges have no way of responding to it independently of induced field).

Now say we want to measure the 'path voltage' between two points on a wire. This the standard (in my opinion) definition of voltage that is measurable, and corresponds to the integral of the total E-field along a path:

$V = \int{\vec E \cdot\vec dl}$

This definition is the same as the voltage drop across a resistor from Ohm's law, and actually represents the work done on a test charge between two points along a given path. So let's hypothesize that there is an actual non-zero path voltage that doesn't disappear in steady-state. Well the same non-zero path voltage would occur in the lead wires, as the argument goes, so the zero reading (same one we got before) doesn't tell us anything.

Since the measurement itself is suspect, we have to simply find another way to determine what the path voltage should be, in order to determine if voltmeter measurements are valid. Luckily, as path voltage corresponds to net electric field, this is easy to do. Net electric field, the only field present that actually exerts a force on a charge, is the sum of induced field and electro-static field:

$E = E_i + E_s$

In the steady-state case (after charges have reached equilibrium, virtually instantly), there can be no net force on a free charge in a region with no (or negligible) resistance, or you would have arbitrarily large / infinite current. Since the net force on any free charge is zero, then the net electric field must be zero, since electric field determines the force felt by a charge according to:

$\vec F = q\vec E$

So we can rest assured that the net electric field in a section of conducting wire between resistors is zero. Since the definition of path voltage is the integral of electric field, this means that the voltage drop - the same voltage drop we use with Ohm's law, is zero, in perfect agreement with our voltmeter. This also means a voltmeter measurement across a resistor only measures the resistor's drop, and we don't need to worry about 'missing' the voltage in the wire, because there is none.

This makes perfect sense. If the (completely valid) argument is that voltmeters are not immune to physical effects of the circuit, then they must be affected by both induced electric field and static field, just like the section they are measuring. If these effects cancel out in a conducting wire - and they do - than they cancel out in the leads on a voltmeter, resolving the issue.

When does your voltmeter give incorrect readings? Whenever you have changing magnetic flux passing through your measurement loop, due to the induced emf, per Faraday's law.

CONCLUSION: You can't use a voltmeter to measure the mathematical concept of scalar potential (regardless of whether it cancels out in your measurement loop, or is simply non-physical). A voltmeter ONLY measures path voltage. If you're using the standard path voltage convention, (and there's no flux in your loop), you can trust your voltmeter.

 

[Averagesupernova]

@tedward I've read through your last post and I want to take some time to absorb what you've said and implied. I'll try to have a reply later today.

 

[Averagesupernova]

I still keep coming back to the same thing. The measurements @mabilde makes from the center are correct. I've explained how I think this is possible. I used the rubbing of violin strings vs cutting through as an analogy. You didn't buy it.
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You've implied that magnetic fields do not act on a wire, they act on a loop. Well, that's a bit of a BS thing to say considering we cannot measure it unless we form a loop. So it's pointless to introduce such ridiculous statements. Flux cutting through any tiny small portion of the wire will cause induction.
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Unless I have misunderstood, you have also implied that a loop outside of the solenoid is immune to the changing flux. This is false. It can be proven by sorting voltmeter leads together and orienting them around on the outside.
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Now for some specifics. You claim that the pie shaped affair inside the solenoid is just a pickup loop. That is an understandable position, but wrong. My position is that the pie shaped wires are not cut by the flux due the orientation with the field. I back this up by pointing out if it were just forming a pickup loop it would not read zero in the case of a shorted loop. Your position on that argument is that it is just canceling. That argument is not valid since the current in the pie shaped loop will be in the same direction as the large loop. There was talk about the pie shaped loop being a simulation of the real loop. This is an understandable thing to buy into until we disconnect the pie from the main loop and and give it its own stand alone arc at which time it will read the same as when the pie was directly connected to the main loop when the main loop was not shorted.
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We need to come to an agreement about how the conductors behave in the B field while moving in various ways relative to said field. I have my doubts if we will.
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I'm also not certain you have agreed that a shorted secondary ring in this setup can not have any voltage measured anywhere on it when the probes are placed correctly.
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All that being said, I think your last post is simply a more confusing way of saying all of the things you've already said previously in this thread.
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If anywhere in this post I have misunderstood your position on something I am sorry and invite you to clarify. Although I doubt I have misunderstood anything.

 

[alan123hk]

The test method used by @mabilde is undoubtedly correct. Single-turn transformers and multi-turn transformer work exactly the same. There is a scalar potential difference between any two points on the transformer winding wires. This not limited to the open circuit output of the two endpoints, there is a potential difference between any two tap outputs on any segment of the winding.

My personal idea is that there is no such thing of "simulate measurement", unless you manipulated it intentionally and improperly, or it was just simulated on the computer. It is important that the measurements are valid and accurate. If we insist that we are measuring something that doesn't actually exist, it's an invalid and inaccurate measurement. That is, if you say that this scalar field and potential generated by electric charges simply does not exist in electromagnetic devices.

But if that doesn't exist, how does that explain the countless secondary multi-tap output transformers people use every day. I think they're all using the scalar potential part (at least approximately) of the transformer. That potential difference is not only measurable, but also provide stable stream of energy. In addition, the magnitude of the potential difference is exactly equal to the EMF of the corresponding winding.

https://pressbooks.bccampus.ca/singlephasetransformers/chapter/multi-tap-transformers/

 

[tedward]

I'm pretty sure I understand your point. If so, this is (here at least) a discussion of convention and terminology, basically semantics. From our other discussions, WE at least (I believe) agree on the fundamental physics: what magnetic flux is, what Faraday's law says, how the various components of electric field combine, etc. We seem to disagree mostly on 'voltage' convention, i.e. what's a useful measurement and what's not, and what to include when analyzing a circuit.

I'm not an EE, so it's interesting to me to learn how EE's treat things differently from physicists. My background is ME, so my electrical background goes up to phsyics for engineers and circuit analysis, plus what other else I've learned/taught myself over the years (I've also been tutoring math and physics for well over 20 years, hence my continued interest in learning physics and making sure my understanding is rock solid). So I'm certainly willing to learn and/or give some ground on semantics.

Obviously transformers work, including the multi-tap variety. My model for this is just an externally controlled magnetic field through a coiled wire / single loop (with low/negligible resistance) connected to a circuit with a high resistance load, so I'm not really thinking too much about the primary. You can certainly take a voltmeter, measure the terminals (or wherever the tap points are), and get the 'voltage' output. If you put a black box around the transformer, you couldn't differentiate it from an 'ideal' AC voltage source (the AC version of a battery, if that's a thing).

One way to think about this output voltage is simply considering the electric field, through space, connecting the terminals on a path outside the coils, as Feynman does for an inductor in his published lectures. With this view, if I analyzed a circuit loop though this path, I would consider this an $\int E \, dl$ voltage, or path voltage, and Kirchoff's law applies. You could fairly call this (As Feynman does) a potential difference, as the field is locally conservative outside the coils. If I analyzed a complete circuit loop through the coils themselves, I wold simply call this the emf of the circuit (as Lewin prefers to), as there is a changing flux penetrating the surface the loop bounds (my rotini pasta) per Faraday's law.

In our discussions of the single loop transformer (the various versions of the Lewin circuit), in a section of conducting wire (with at least one lumped resistor in the circuit) there is always an electrostatic field to cancel the induced field, resulting in zero net E-field. Since the scalar potential is $\int E_s \, dl$ and the induced voltage is $\int E_i \, dl$, it seems the terminology of 'scalar potential' is equivalent to 'induced voltage', at least within a negative sign. So I don't necessarily see a conflict here, what I call emf you might call scalar potential. As I think on it now, this is related to much of the confusion.

From a concrete physics perspective, and to avoid all sources of potential (no pun intended) confusion, I've taken an absolutist perspective, and have been trying to only consider what I would consider 'real', or physically measurable quantities. This means I exclusively use 'path voltage', or $\int E \, dl$ where E is the net electric field. I treat the net field as the only field that is physically 'present', as it is the only field that is responsible for exerting a net force, or doing actual work, on charge, without considering any other field. It's the only thing that charges 'feel'. If a charge is in a section of conducting wire, and induced field is balanced by static field pushing back, it feels zero force, and no work is done on it as it moves. The induced field that would be there in free space is no longer there, canceled by the force of electrostatic charge. So whichever term you use for it, scalar potential, induced voltage, or emf, it has no independent effect. That is my guiding star.

Hope that clears up my view. I'm also very curious what you think of the test lead question post. (more on Mabilde's setup in a separate post).

 

[tedward]

The test method used by @mabilde is undoubtedly correct...

My personal idea is that there is no such thing of "simulate measurement", unless you manipulated it intentionally and improperly, or it was just simulated on the computer.

I get your point about 'simulating' a measurement. If I want to measure loss of energy due to friction of an object moving on a surface, I can measure the kinetic energy at two points and subtract them - even if I can't measure the heat dissipated in the air directly - and report it as friction loss. So part of my issue might be philosophical, but a lot of it is certainly about intent. Again choice of convention plays a big role here.

Mabilde is an EE professor (iirc), and likely subscribes to the convention (which is as far as I can tell unique to that field) that 'voltage' refers to 'scalar potential' only - though he never states this. He references Kirk McDonald's paper in his analysis, which defines scalar potential strictly as the electrostatic potential between points of accumulated charge at the ends of the resistors. Defined this way, this potential certainly adds up to zero around the loop, as the electrostatic field, on it's own, is conservative. This is apparently what he's trying to measure around the circuit.

As I laid out in my last post, the scalar potential between two points, at least in a section of conducting wire, corresponds to the induced voltage that would be felt between two points in free space. But we're not in free space anymore, this is conducting wire with a lumped resistance in the active circuit, so the net E-field here is in fact zero. The induced voltage / scalar potential in this region now ONLY exists as math, because charge cannot respond to it independently (all the electric field is concentrated in the resistors). But fine, let's pretend it's there. We're essentially asking what would the induced voltage be in this the section of the wire, either in free space or before the fields had reached an equilibrium.

You can't measure this quantity with a direct voltmeter measurement, simply based on the argument that has been raised repeatedly: that voltmeter leads cancel the thing you're trying to measure, since scalar potential, as it's defined, can exist in conducting wire. But one way to do it is to set up your voltmeter leads so that it feels the exact same amount of flux - and therefore emf - that correspond radially to this very symmetric circuit. This subtracts the portion of the emf through the loop from his measurement, giving him a non-zero number that of course changes with the angle of his pie-slice: both area of he slice and the arc-length are proportional to area.

Now if he's trying to measure this abstract quantity, and he describes his intent, his process, and how he intends to measure it, I have no problem. But consider what he states he's measuring. I'll have to watch the video again, but as I recall he never mentions the words scalar potential (tell me if I'm wrong), only 'voltage'. He certainly never discusses different voltage conventions (scalar potential vs. path voltage). So he's assuming everyone watching subscribes to the same definition that he's been trained, as apparently EE's are, to use. So, by using his set up, he sure makes it look like he's measuring something real in this copper ring - that charges actually gain/lose energy as they move across this conducting wire, even though absolutely no work is done on them as there is precisely zero net field there. He then proceeds to show, that the energy gained in the conducting wire is lost in the resistors. This is only true from the scalar potential convention, not from the common understanding of voltage (the true net work done on a charge per coulomb), as the net work done on a charge around the loop by the electric field is most definitely not zero.

Now consider his audience, which includes anyone who watches youtube who's interested in physics: certainly high schoolers, college students, teachers and other academics, and the casual science buff. They're convinced, as they saw with their own eyes, that there is a measurable difference in voltage / energy between two points of zero resistance conducintg wire. So of course, when they do a voltage sum, thinking they're using the more common path voltage convention, they have to take this into account, and the loop sum must be zero!! But most of the audience is not familiar with the technical differences in convention, and most assume we're talking about the standard type of voltage - the type that Lewin is using. So Lewin must be wrong!!

In reality, the emf provided by the flux term is ALREADY TAKEN INTO ACCOUNT in the resistors, and factoring in the scalar potential in the copper ring just subtracts this sum to get zero. So without understanding this strict convention, the audience has been forced to accept scalar potential as a convention unwittingly. What do they learn? That an induced emf circuit works exactly like a DC battery circuit, and the sum of the 'voltages' around the loop is zero. Therefore Lewin is simply confused, and path independence (a fundamental physical idea) is nonsense.

 

[alan123hk]

I'm also very curious what you think of the test lead question post.

The thick blue line outside is a section of the ring circuit, and the thick red line is the lead wire of the voltmeter pressed into a T shape. Both are conductors, so charges accumulate on their surfaces to cancel the induced electric field. Since the induced electric fields inside them are almost equal, the potentials generated by the accumulated charges on their surfaces are also almost exactly equal.

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.

Also, of course I admit that Farady's law is the basis of everything and is the king, because it is always correct.

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

 

[Averagesupernova]

@tedward you really need to lose the assumption that is acceptable to include whatever is induced into the voltmeter leads that causes changing voltage readings based on position. This path dependency view is nonsense. By coming to an agreement on how the leads can be positioned so the they are not contributing to the reading and then placing them there shows that everything make sense. It is my view that @mabilde has done this. There are other ways of doing this but in the single loop scenario I believe he has chosen the best method.
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Real electrical engineers always work with the simplest accepted laws (which admittedly are often shortcuts of something more complex) to obtain the desired end result.
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One of the most arrogant people I ever met once told me that when something is not making sense the first thing that should happen is to ask yourself what you are doing wrong. I was rather impressed with a statement like that coming from such an arrogant individual. He obviously applied that to himself. It's a trait many people would do well to adopt. Had Lewin done this, or whoever came up with this prior to him, I wonder where we would be.

 

[hutchphd]

One of the most arrogant people I ever met once told me that when something is not making sense the first thing that should happen is to ask yourself what you are doing wrong. I was rather impressed with a statement like that coming from such an arrogant individual. He obviously applied that to himself. It's a trait many people would do well to adopt.

I agree with your friend absolutely.
The point (I believe?) you are missing is that Prof. Lewin was perfectly aware of what he was doing. He was not confused by the result. Nor should be anyone else who understands Maxwell's Equations.

 

[alan123hk]

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.

 

[hutchphd]

For Lewin's circuit paradox,

It is neither a paradox nor a surprise to Prof Lewin. Jeez.

 

[alan123hk]

It is neither a paradox nor a surprise to Prof Lewin.

I sincerely believe this.
(I mean I belive that Prof. Lewin was perfectly aware of what he was doing. He was certainly not confused by the result.)

 

[hutchphd]

You are then sincerely mistaken.

 

[alan123hk]

Right - this is the new definition of Ohm's law that accommodates scalar potential. But the good old V = IR that everyone actually uses and is measured by a voltmeter is the path voltage, Int(E.dl).

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

 

[Averagesupernova]

The point (I believe?) you are missing is that Prof. Lewin was perfectly aware of what he was doing. He was not confused by the result.

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.

 

[hutchphd]

He said that Kirchhoff was wrong when blindly used in the situation he presented. Not "Kirchhoff" (the man) but "Kirchhoff" (the Law) when carelessly applied. Lewin was not confused about either Kirchhoff's circuit law nor Faraday's Law .

 

[Averagesupernova]

He said that Kirchhoff was wrong when blindly used in the situation he presented. Not "Kirchhoff" (the man) but "Kirchhoff" (the Law) when carelessly applied. Lewin was not confused about either Kirchhoff's circuit law nor Faraday's Law .

That's a stretch. Taking that approach and to put it the way he did and not explain what's really going on is irresponsible. Especially for someone in his position.

 

[hutchphd]

He was teaching the sophomore EM course at MIT. He explains it in great detail in previous and subsequent lecturees. I do not understand the vitriol it engenders: none is appropriate. He did not ascribe it to voodoo.
He was warning his students not to blindly apply Kirchhoff by using a vivid and effective lecture demo. More power to him.

 

[Averagesupernova]

Fine, whatever. I can't say I've ever fallen into the blindly following Kirchoff trap or whatever. I still think it's a silly thing to do. I could say the same thing about ohm. Incandescent bulbs don't follow ohms law when it is misapplied. E * I doesn't give us Watts when we misapply and ignore current being out of phase with volts.

 

[tedward]

I still keep coming back to the same thing. The measurements @mabilde makes from the center are correct. I've explained how I think this is possible. I used the rubbing of violin strings vs cutting through as an analogy. You didn't buy it.

Flux cutting through any tiny small portion of the wire will cause induction.

So now that you've collected all our disagreements in one place, It's easy to see where the common thread lies that runs through all of this. At first I wondered why you were ignoring or disagreeing with any argument that dealt with flux passing through a loop. It's painfully obvious now (from your description) that you simply do not understand what magnetic flux is, or how it affects a circuit. I don't know if you're a high-schooler, an electrical engineer, or have a Ph.D. I don't care. Whatever model or rule-of-thumb you've learned, and however you learned it, it is wrong. It does not help the discussion to ignore your clear misunderstanding that you have laid out above for anyone to see. If you want to speak intelligently on these topics, you have to know the fundamentals first. Now that I can clearly see where the fence between our yards lies, it's probably a waste of time discussing further. But this is a physics forum where people come to learn/discus physics, and the teacher in me wants you to learn this correctly, so that something fruitful comes from this discussion. You can open an A.P. Physics textbook, watch Lewin's fantastic lectures, or even watch some Kahn Academy videos. But learn it right. I don't care if we agree on the Lewin 'paradox' anymore, I just want you to (re)learn the basics for your own benefit. I'll break it down for you (or anyone else who wants to learn) here and respond to some of your other points separately.

THE SOLENOID'S FIELD

First let's get our picture right. In our solenoid, current through the windings generates a magnetic field. The field points vertically (oscillating up and down) along the axis, is uniform, and only exists inside the solenoid volume. I'm using the common assumption of an infinitely tall solenoid to avoid worrying about the return path flux, which is a practical consideration but not relevant to the ideal case. The point is that there is no flux between the solenoid and the loop circuit, even if there is considerable distance from the solenoid to the loop wire.

MAGNETIC FLUX

What is magnetic flux? It's the amount of magnetic field, summed over a defined area, that passes through that area. The calculus version is written like this: $$\Phi_B = \iint \vec B \cdot d\vec A $$
In a simple situation like ours, it reduces to a simple formula: $$\Phi_B = BA_s$$ where $B$ is the magnitude of the field in the solenoid, and $A_s$ is the cross section area of the solenoid only, regardless of the size of our circuit. We only include the solenoid area as there is no magnetic outside the solenoid to contribute to the sum.

FARADAY'S LAW

How does it affect the circuit? Faraday's law (applied to our situation) basically says two things. First, if the flux through the solenoid changes in time, it creates an electric field in space that surrounds it, always encircling the solenoid in one direction. It also says that that the circulation of this electric field, meaning the total sum of the field on any circular path around the solenoid, equals the time rate-of-change of this magnetic flux: $$\oint \vec E \cdot d\vec L = -\frac {d \Phi_B}{dt} $$ In space, you can picture the electric field as clockwise arrows circling the solenoid, where the field strength decreases with radius but the total sum of any circular (or any path) is always the same. This is an important point - the electric field strength decreases with distance, but the total circulation is the same no matter the radius. And that circulation is always non-zero, as long as there is a changing flux. That's what non-conservative means. The negative sign is just there as a nod to Lenz' law, which says the direction of the induced field opposes changes in the flux.

EMF

When our circuit loop is placed around the solenoid, this electric field interacts with free charge in the loop, pushing charge around and creating a current. Inside the circuit, we now refer to the circulation of the field an electromotive force, or emf. $$emf = \oint \vec E \cdot d\vec L $$ This emf is a property of the entire loop itself, and is also called the induced voltage of the circuit. It's important to remember that emf is not some new mysterious physical quantity. It's just the sum of the induced electric field over the length of the loop. The ONLY manifestation of induction here is via electric field.

As consequence of Faraday's law, we can also say that any closed path that has NO flux penetrating it, has zero emf. This is really handy when analyzing voltmeter loops to make sure that they are unaffected by unwanted magnetic flux. In fact, you can apply Faraday's law to the entire circuit loop, smaller loops in a network, loops that other have other loops inside them, paths through free space, or any combination of circuit and free path. It always works.

Now let's talk about your model for a second. You have spoken several times of your 'violin string bowing' picture. The best I can tell is you got this from an induction generator picture (like the video you linked to), which involves a fixed field and moving conductor. In this case, there is no electric field directly responsible for moving charge - it is simply the magnetic force (one part of the Lorentz force): $$F_B = q \vec v \times \vec B$$ Interestingly, this different physical phenomenon gives rise to exact same equation - Faraday's law. The Feynman lecture I linked to (did you bother reading it?) discusses this ambiguity.

So how do I know your model is wrong? Because the magnetic flux, as we said, only exists in the solenoid. It does not have to come in contact with the loop. The loop could theoretically be at any distance, with no magnetic field of consequence in between. So this bowing picture with flux interacting with the loop, on it's face, falls flat. Now I don't want to confuse the issue, but the purist in me needs to mention that the way the induced electric field is created in the first place is via an electromagnetic wave, assuming the flux is oscillating like an AC source. The 'M' in this EM wave plays no part in our analysis, as it does not contribute to flux or do work on any charge in our circuit. And if the flux in the solenoid is increasing linearly, as many examples treat it, there is no magnetic field at the loop at all.

Obviously, in Mabilde's setup, he does put his copper ring as close as possible to the solenoid. This is to avoid the practical issue of the returning path of the solenoid field (comes out the 'pipe' at the top and turns around to re-enter at the bottom) which has much weaker field strength but could certainly affect measurement loops.

So now you should be caught up. That's what we mean by flux. We do not speak of flux 'cutting through wires', that is meaningless. Certainly induced electric fields have a physical effect on wire sections, either alone or part of a circuit, but I'll address that in another post as well as some of your other points.

 

[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.
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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.