Is MIT Prof. Lewin wrong about Kirchhoff's law?

[Dale]

I meant time varying fields present in the circuit loop. Time varying fields on the interior of the inductor is modeled by circuit theory, w/o the need to consider fields.

That is a good way to put it (better than my number 3). If you had written this then I would not have objected.

The Lewin paper explicitly stated the field inside the circuit loop, not that on the interior of an inductor. Did you read the paper by Dr. Lewin?

Yes, I read it. In the paper, despite how he drew it, he is considering the field inside an inductor. The example in the video is better on that count.

As far as a cap having " no net charge", this is very semantical. "Charge" as used by the science community implies "differential". An "uncharged cap" has lots of charge, but zero difference. A "charged cap" has the same total absolute charge but is displaced forming a differential. If you define "net charge" as total charge on both plates, then of course there is no "net charge" in either case, energized or not. Whan I say "charge" in ref to a cap, I infer the differential quantity, not the absolute total which you define as "net charge".

Dr. Lewin is correct on all counts. He simply illustrated how non-conservative fields differ from conservative. You're trying to look for reasons to poke holes in his case by bringing in arbitrary arguments based on your own semantics.

It is not my own semantics, it is the standard meaning of the term "net charge". Your objection here is a little excessive.

In the final analysis Dr. Lewin states the following.

1) With conservative E fields, KVL holds, & the potential from a to b is independent of the path.

2) With non-conservative E fields, KVL does not hold, & the potential from a to b is dependent on the path.

Introducing hyperbole does not alter this basic tenet. Is there any issue with the above 2 statements?

Yes, they are wrong for the same reason as above. As written they would apply to the apply to the fields within the interior of an inductor and not only to fields in the circuit loop.

 

[Dale]

Here are my 2 cents. Maxwell's equations and the Lorentz force equation are the governing equations for classical electromagnetics and they describe all classical EM behavior. However, they are a pain to work with, so we have many approximations which are valid in certain cases: Coulomb's law, Biot-Savart, KVL, KCL, etc. All of these are approximations to Maxwell's equations that only apply in certain circumstances and you need to learn when they apply and when they do not apply along with the equations themselves. Once you learn their domain of applicability they are all very useful and correct approximations.

 

[Studiot]

Once you learn their domain of applicability they are all very useful ...

I agree 110% with this.

But that does not account for my example (post#32) where the only law from your list plus Faraday's law that applies is KVL.

None of the others will yield a correct, or indeed any, answer.

 

[cabraham]

That is a good way to put it (better than my number 3). If you had written this then I would not have objected.

Yes, I read it. In the paper, despite how he drew it, he is considering the field inside an inductor. The example in the video is better on that count.

It is not my own semantics, it is the standard meaning of the term "net charge". Your objection here is a little excessive.

Yes, they are wrong for the same reason as above. As written they would apply to the apply to the fields within the interior of an inductor and not only to fields in the circuit loop.

Faraday'a Law, FL always applies, under all conditions. KVL does not always apply. I think the disagreement is one of logic, not e/m theory. With conservative E fields, KVL always holds. What if the E field is non-conservative? The negative of always is not the same as never. With a non-con E field, KVL does not always hold. That does not mean KVL never holds.

The interior of an inductor is one case where KVL holds, but there are others. If a time varying E field is distributed in space, & I wish to compute Vab along various paths, can KVL hold? Of course. Two differing paths can enclose the same flux resulting in the same potential. Closing said loop on these paths results in zero potential around the loop, which makes KVL valid under said conditions.

If Dr. Lewin would have stated that KVL can never hold w/ time varying mag fields, I would have disagreed. He simply stated that KVL is valid conditionally, whereas FL is valid unconditionally. Scientific observation backs this claim.

Of course, if we add a generator to the loop representing the induced emf/mmf voltage/current, then KVL will hold. That is because we are accounting for induction in the circuit model. But in reality if we trace E around the loop, we get a non-zero value, which voids KVL. We can keep KVL intact only by adding a generator into the circuit model.

Dr. Lewin is among the world's most qualified instructors regarding this material. I'm a little surprised at the EEs (or non-EEs) in the industrial community who are bashing Dr. Lewin. Those who do make me wonder how much e/m field theory they've had. Nothing personal, but will the critics of Dr. Lewin please state explicitly the errors in Dr. Lewin's teachings? He's a prof at MIT, an institution world renowed. Who are these critics anyway? What are their credentials? I'm just wondering.

In his accompanying paper Dr. Lewin explains how the inductor interior fields are covered in circuit theory by v(t) = L*di(t)/dt. If you measure v(t) by integrating E*dl inside the conductor, you get a different answer. The E field is indeed non-con, leading to differing potentials across two points, depending on the integrating path.

I spent years designing inductors, xfmrs, RLC filters, SMPS, regenerative braking, motor drives, etc. I learned much about this topic beyond what I learned in e/m fields back in undergrad EE. But the undergrad EE curriculum was very good. I just needed to practice e/m, which I did.

If anyone wishes to address a specific topic, I'll do that. But bashing Dr. Lewin does not make you right. I'll discuss anything politely using science. Peace.

Claude

 

[Dale]

If Dr. Lewin would have stated that KVL can never hold w/ time varying mag fields, I would have disagreed. He simply stated that KVL is valid conditionally, whereas FL is valid unconditionally. Scientific observation backs this claim.

Sure, I agree, I have said as much at least twice in this thread. But the example Dr. Lewin presents in his notes is one where KVL holds.

 

[atyy]

Faraday'a Law, FL always applies, under all conditions. KVL does not always apply. I think the disagreement is one of logic, not e/m theory. With conservative E fields, KVL always holds. What if the E field is non-conservative? The negative of always is not the same as never. With a non-con E field, KVL does not always hold. That does not mean KVL never holds.

The interior of an inductor is one case where KVL holds, but there are others. If a time varying E field is distributed in space, & I wish to compute Vab along various paths, can KVL hold? Of course. Two differing paths can enclose the same flux resulting in the same potential. Closing said loop on these paths results in zero potential around the loop, which makes KVL valid under said conditions.

If Dr. Lewin would have stated that KVL can never hold w/ time varying mag fields, I would have disagreed. He simply stated that KVL is valid conditionally, whereas FL is valid unconditionally. Scientific observation backs this claim.

Of course, if we add a generator to the loop representing the induced emf/mmf voltage/current, then KVL will hold. That is because we are accounting for induction in the circuit model. But in reality if we trace E around the loop, we get a non-zero value, which voids KVL. We can keep KVL intact only by adding a generator into the circuit model.

Dr. Lewin is among the world's most qualified instructors regarding this material. I'm a little surprised at the EEs (or non-EEs) in the industrial community who are bashing Dr. Lewin. Those who do make me wonder how much e/m field theory they've had. Nothing personal, but will the critics of Dr. Lewin please state explicitly the errors in Dr. Lewin's teachings? He's a prof at MIT, an institution world renowed. Who are these critics anyway? What are their credentials? I'm just wondering.

In his accompanying paper Dr. Lewin explains how the inductor interior fields are covered in circuit theory by v(t) = L*di(t)/dt. If you measure v(t) by integrating E*dl inside the conductor, you get a different answer. The E field is indeed non-con, leading to differing potentials across two points, depending on the integrating path.

I spent years designing inductors, xfmrs, RLC filters, SMPS, regenerative braking, motor drives, etc. I learned much about this topic beyond what I learned in e/m fields back in undergrad EE. But the undergrad EE curriculum was very good. I just needed to practice e/m, which I did.

If anyone wishes to address a specific topic, I'll do that. But bashing Dr. Lewin does not make you right. I'll discuss anything politely using science. Peace.

Claude

How can anyone who walks around with a plastic banana in his shirt pocket be "among the world's most qualified instructors"?!

 

[stevenb]

Dr. Lewin is among the world's most qualified instructors regarding this material. I'm a little surprised at the EEs (or non-EEs) in the industrial community who are bashing Dr. Lewin.

I have to say that I am also disappointed to see what appears to be some out of place bashing of Prof. Lewin. Personally, I think he is an outstanding teacher and is dedicated to not only teaching the material well, but inspiring students to appreciate the beauty of electromagnetics and physics in general. I've watched every one of his lectures in this series (more than once) and can't see any major issues with anything he teaches. He stresses concepts and provides experimental demonstrations to solidify those concepts in the students mind. The one minor issue I have is in this one lecture where he chooses a definition of KVL that I feel is not the best one, but I don't view this as a big deal because he clearly defines his meaning. If this were a more advanced class, then I would expect him to give a more comprehensive overview of KVL along the lines of Kraus, but this is a freshman level class (many of the students not even targeting EE or physics) which is likely the first high level exposure these students have to the subject. The quality of this course, for the level it targets, and the quality and dedication of the Professor, are absolutely outstanding in every way.

 

[atyy]

I have to say that I am also disappointed to see what appears to be some out of place bashing of Prof. Lewin. Personally, I think he is an outstanding teacher and is dedicated to not only teaching the material well, but inspiring students to appreciate the beauty of electromagnetics and physics in general. I've watched every one of his lectures in this series (more than once) and can't see any major issues with anything he teaches. He stresses concepts and provides experimental demonstrations to solidify those concepts in the students mind. The one minor issue I have is in this one lecture where he chooses a definition of KVL that I feel is not the best one, but I don't view this as a big deal because he clearly defines his meaning. If this were a more advanced class, then I would expect him to give a more comprehensive overview of KVL along the lines of Kraus, but this is a freshman level class (many of the students not even targeting EE or physics) which is likely the first high level exposure these students have to the subject. The quality of this course, for the level it targets, and the quality and dedication of the Professor, are absolutely outstanding in every way.

Unfortunately, it was not truly exceptional, merely outstanding, because he failed to wear his banana!

BTW, is there any video where he is really wearing a banana - or is that an urban legend, like KVL?

 

[Dale]

But bashing Dr. Lewin does not make you right. I'll discuss anything politely using science.

I have to say that I am also disappointed to see what appears to be some out of place bashing of Prof. Lewin.

So which of my comments do you consider "bashing"?

1) He teaches correct physics
2) He describes KVL as "MISLEADING" and "DEAD WRONG" (emphasis in original)
3) He justifies his assertions using a strawman definition of KVL
4) The usual definition of KVL is correct under standard circuit theory conditions

What points have I made besides these, or which of these points is "bashing"?

 

[stevenb]

So which of my comments do you consider "bashing"?

1) He teaches correct physics
2) He describes KVL as "MISLEADING" and "DEAD WRONG" (emphasis in original)
3) He justifies his assertions using a strawman definition of KVL
4) The usual definition of KVL is correct under standard circuit theory conditions

What points have I made besides these, or which of these points is "bashing"?

Personally, I don't consider any of your comments bashing. I never felt you were speaking ill of him at all. There is a difference from having a technical disagreement and crossing the line to an insult. I can't say I noticed you cross that line.

There are other comments in this thread made by someone else that I do feel cross the line, but I really don't want to point to specific people and comments, because that is a job for moderators. But, I've been planning to make a general positive comment to counter the negative ones, and cabraham's comment opened the door to that, so I step in.

 

[yungman]

Faraday'a Law, FL always applies, under all conditions. KVL does not always apply. I think the disagreement is one of logic, not e/m theory. With conservative E fields, KVL always holds. What if the E field is non-conservative? The negative of always is not the same as never. With a non-con E field, KVL does not always hold. That does not mean KVL never holds.

The interior of an inductor is one case where KVL holds, but there are others. If a time varying E field is distributed in space, & I wish to compute Vab along various paths, can KVL hold? Of course. Two differing paths can enclose the same flux resulting in the same potential. Closing said loop on these paths results in zero potential around the loop, which makes KVL valid under said conditions.

If Dr. Lewin would have stated that KVL can never hold w/ time varying mag fields, I would have disagreed. He simply stated that KVL is valid conditionally, whereas FL is valid unconditionally. Scientific observation backs this claim.

Of course, if we add a generator to the loop representing the induced emf/mmf voltage/current, then KVL will hold. That is because we are accounting for induction in the circuit model. But in reality if we trace E around the loop, we get a non-zero value, which voids KVL. We can keep KVL intact only by adding a generator into the circuit model.

Dr. Lewin is among the world's most qualified instructors regarding this material. I'm a little surprised at the EEs (or non-EEs) in the industrial community who are bashing Dr. Lewin. Those who do make me wonder how much e/m field theory they've had. Nothing personal, but will the critics of Dr. Lewin please state explicitly the errors in Dr. Lewin's teachings? He's a prof at MIT, an institution world renowed. Who are these critics anyway? What are their credentials? I'm just wondering.

In his accompanying paper Dr. Lewin explains how the inductor interior fields are covered in circuit theory by v(t) = L*di(t)/dt. If you measure v(t) by integrating E*dl inside the conductor, you get a different answer. The E field is indeed non-con, leading to differing potentials across two points, depending on the integrating path.

I spent years designing inductors, xfmrs, RLC filters, SMPS, regenerative braking, motor drives, etc. I learned much about this topic beyond what I learned in e/m fields back in undergrad EE. But the undergrad EE curriculum was very good. I just needed to practice e/m, which I did.

If anyone wishes to address a specific topic, I'll do that. But bashing Dr. Lewin does not make you right. I'll discuss anything politely using science. Peace.

Claude

As I pointed out over and over again that his assertion the KVL was not correct with his so call experiment that was fraud. No if and buts about it. When you start out wrong, there is absolutely no point of talking about all his equation and theory. I am sure his equation and the non conservative nature were correct, but all meant nothing when the reasoning on attacking KVL is fraud. You cannot just over look the fraud of his experiment and keep moving into his derivation. I am not even trying to defend KVL, it could have problem in other cases, BUT not from his fraud experiment, and to me that is everything.

I am particularly hard on him because of his arrogance on calling people wrong when he was actually the stupid one that he did not understand the first thing about electronics. This is not even hard to spot for anyone with REAL life experience designing switching power supply. Just because he was a good lecturer do not gave him the right to blast others and particular to that degree of arrogance and stupidity. You said you designed transformer, you should know exactly what I am talking about. If you jack up the frequency you get more efficiency until the point the core loss become obvious. We use around 100KHz and we got really good result. We managed to wind a transformer with about 30V to 30V 15KV isolation for the 24V to 24V DC to DC converter and we use fiber optic to serve as feedback from HV side down to ground level to close the control loop. The transformer core was only about 1.5"X1.5" size so we can only put less than 10 turns ( I don't remember exactly). We got over 100W up onto 12KV. In his case, I take that he did not have a core ( air core), saturation is not even a problem, you got the power to pump in the create the magnetic field, you can really crank out some voltage. I am not a transformer expert, my engineer was and we talked a lot about this.

I know most of you don’t want to engage me on this because I kept talking about the experiment instead of all the theory that you are interested. Unless you can prove me wrong, this whole talk are all based on some fraud observation. I can assure you that I can produce more than 1V with just one turn as I said over and over again in the DC to DC converters we designed. He just miss the whole transformer effect on his experiment.

 

[sarumonkee]

@yungman: Thanks. The point I would like to point out is, the wire has little effect compared to the resistors, and this is why though we have 1 volt around the loop, this 1 volt is mostly on the resistors.

Hey Hikaru, I think the wire is important as if we look at the impedance of an inductor (which totally exists, (at least Yungman and I know exists), we have s*L. The s is proportional to frequency, and a step function (switch turning on), has some high frequency components in it. This means the inductance of the line could act like a pretty big impedance at higher frequencies.

I want Prof. Lewin to show two more volt meters, one going from both probes of the first two meters on the "D" "node" and another between the "A" "node" points. I put "node" in quotes because I believe his circuit model is flawed, as Yungman has stated (missing inductance).

 

[Phrak]

How much voltage you measure across an inductor depends upon how you route the probe wires. Does this help confuse things?

 

[sarumonkee]

How much voltage you measure across an inductor depends upon how you route the probe wires. Does this help confuse things?

Well, it doesn't actually apply in this situation, I think. Maybe specify a little more if I missed you point please. The voltmeter (an O-scope in this case) has a huge resistance, probably in the range of 10MΩ), so the current in the voltmeter probe wires will be small. This means the volt meter probe wires hopefully won't pick up too much EMI compared to his circuit of wire and resistors.

 

[kifu]

Hi, I didn't manage to see trough all the posts written here, I appology for that. Just wanted to offer intuitive explanation. Walter H. G. Lewin have been explaining the experiments through calculations and he admitted it is not intuitive at all. But I think one can expain it, assuming there is additional loop of wire in series with one voltmeter/oscilloscope.

http://img573.imageshack.us/i/fvsk.png/

I think third diagram is equivalent of the first one, but not the last one.

If you've hooked up both oscilloscopes on one side of the circuit you would have identical readings.

 

[Phrak]

I think, DaleSpam has lent clarity to all this, and he would be worth re-reading. Apply Faraday's law with Maxwell's correction and you should have a classically indisputable form of Kirchhoff's voltage law.

Now, I don't know what situation you are referring to. There are a lot of posts!

Take an inductor with a small number of turns like one turn around a high permeability material, to make things evident. How many rounds your meter probes make through the core determines the voltage measured.

 

[sarumonkee]

I think, DaleSpam has lent clarity to all this, and he would be worth re-reading. Apply Faraday's law with Maxwell's correction and you should have a classically indisputable form of Kirchhoff's laws.

Now, I don't know what situation you are referring to. There are a lot of posts!

Take an inductor with a small number of turns like one turn around a high permeability material, to make things evident. How many rounds your meter probes make through the core determines the voltage measured.

Are you referring to a current measurement? The point of Prof. Lewin's experiment was not about voltmeter measuring errors, it was to supposedly show measuring across different points of two "nodes" can give you different voltages. I don't think they were actually "nodes" as inductance was not included.

 

[atyy]

Are you referring to a current measurement? The point of Prof. Lewin's experiment was not about voltmeter measuring errors, it was to supposedly show measuring across different points of two "nodes" can give you different voltages. I don't think they were actually "nodes" as inductance was not included.

So you want to know if the voltmeters were connected at exactly the same two points?

 

[sarumonkee]

@atyy: Yes, that's what I want to know. He didn't really go into detail about his setup, and from the look of the video, the probes were separated by about 4" on both sides of the circuit of wire and resistors. From my experience, that kind of layout can lead to some inductances that matter in switching situations.

If the probes were actually touching each other, I rescind all my previous comments, and will probably go read an E&M book from cover to cover.

 

[stevenb]

So you want to know if the voltmeters were connected at exactly the same two points?

I hope that is not the point of his confusion because it's clear that the scopes are effectively tied to the same point, and such a small inductance is irrelevant on these time scales. You can take the same voltmeter or scope, pick it up, move it to the other side and the reading will change. You could swap the meters and their reading would also swap.

If the OP is in doubt of this, then he needs to do his own experiments and re-study Faraday's Law. This is all straightforward stuff. The meter probes themselves form an additional loop that is closed through the meter's internal resistance. The fact that the resistance is very high and the current in the probe wires is low has no affect on Faraday's Law. When the meter is moved, the loops change their encirclements of the internal flux change.

This is exactly the thing that makes the experiment non-intuitive to the uneducated and the educated alike.

 

[stevenb]

If the probes were actually touching each other, I rescind all my previous comments, and will probably go read an E&M book from cover to cover.

OK, this is the issue then. Definitely restudy Faraday's Law, but more importantly do your own experiments. You need to see it to believe it. These experiments are really fun actually. You don't really need to do his exact experiment to get a feel for Faraday's law. You can wire up a large coil and drive it with triangle waves of current. Then make loops and take measurements.

The funny thing is that you can do these experiments and show them to your friends, and many will still think it's a trick of some type.

 

[atyy]

@sarumonkee: I see. Lewin's experiment was just for a lecture, not to convince a skeptic, so yes, his experiment was not done totally properly. However, if his errors were significant, his results should be different from what his calculations predict using Faraday's law in the big loop as the major effect (he predicts that the ratio of the voltmeter readings should be related to the ratio of the resistances). I haven't watched enough to know whether he got what he predicted.

Anyway, I agree with stevenb - go and do the experiment yourself - unless some kind soul or Lewin himself would be so kind as to redo it and post it here.

 

[hikaru1221]

I look at the wire as a Voltage source induced by the magnetic field. If you consider the voltage source in the loop, KVL held.

I'm not arguing with you about KVL. It's about what you are trying to say, that his experiment & his explanation are all a fraud. Would you kindly show me quantitatively that the transformer effect has that gravity to refute Prof. Lewin's explanation?

If I hold a PP3 battery in my hand there is EMF, but no magnetic flux and therefore Faraday's Law is not applicable.

There is, of course, no circuit at this stage either.

If I now connect two identical batteries ( or carefully adjusted power supplies) in opposition in a circuit, perhaps including resistance, there is still no magnetic flux as there is no current.
Kirchoff's law can be applied to this situation as we can sum the opposing EMFs meaningfully.

Sorry, I didn't see your post when I posted.
When Faraday deduced his empirical law, he did experiments with closed loops. The Faraday's law we have referred to so far is also in his integral form. This is why we cannot apply Faraday's law for an open circuit, because the law only applies to closed circuit. But KVL is also not applicable.
Now for your example of 2 oppositely-connected batteries, both Faraday's law and KVL apply:
_ KVL: $$- e + e + e_{B}= IR$$ where $$e_B$$ is the emf due to the magnetic flux change, which is zero.
_ Faraday's law: $$- e + e + IR = \oint Edl = -d\phi/dt = 0$$

Hey Hikaru, I think the wire is important as if we look at the impedance of an inductor (which totally exists, (at least Yungman and I know exists), we have s*L. The s is proportional to frequency, and a step function (switch turning on), has some high frequency components in it. This means the inductance of the line could act like a pretty big impedance at higher frequencies.

I want Prof. Lewin to show two more volt meters, one going from both probes of the first two meters on the "D" "node" and another between the "A" "node" points. I put "node" in quotes because I believe his circuit model is flawed, as Yungman has stated (missing inductance).

This is why I asked for a qualitative explanation. Inductance exists everywhere. It's just that whether it's significant enough.

 

[yungman]

How much voltage you measure across an inductor depends upon how you route the probe wires. Does this help confuse things?

There is always a way, without thinking deeply, one can run a second set of wire closely tie to the original wire loop and serve as the loop to pickup what ever voltage generated by the magnetic field and do a common cancellation. Yes it would involve some thinking, but it is absolutely doable. I am less interested in making the experiment than to challenge the experiment. Point is there is a way to cancel the magnetic effect on the probe that hook onto the two end of the wire and I am sure it is not hard, nothing more than breadboard a differential amp or play with the meter connections.

 

[yungman]

Well, it doesn't actually apply in this situation, I think. Maybe specify a little more if I missed you point please. The voltmeter (an O-scope in this case) has a huge resistance, probably in the range of 10MΩ), so the current in the voltmeter probe wires will be small. This means the volt meter probe wires hopefully won't pick up too much EMI compared to his circuit of wire and resistors.

If you have the two probs of the meter connect one onto one end of the wire loop, you form a secondary loop which is from say probe E to one end of the wire, then to probe F which connect to the meter and back to probe E through whatever internal resistance of the meter. That can pickup the magnetic field from the setup. It become a one turn transformer also!

As I say, using the technique of common mode cancellation would be an easy to solve this problem.

Another simpler way that might or might not be good enough, use a twist pair to connect the meter. One side of the twisted pair solder to one end of the wire loop in the setup, the other wire twist onto the wire from where the first twisted wire solder on, follow the wire of the setup to the other end before soldering on the the wire loop. What I am doing is to minimumize the loop area of the probe. The smaller the loop area, the less magnetic flux pass through, the error might be small enough to be acceptable. But the common mode cancellation is the way to go if you want accurate measurement.

 

[yungman]

I'm not arguing with you about KVL. It's about what you are trying to say, that his experiment & his explanation are all a fraud. Would you kindly show me quantitatively that the transformer effect has that gravity to refute Prof. Lewin's explanation?

I don't know what quantitively to show, it is a simple one turn secondary winding transformer! Say he generate the magnetic field with a source ( solenoid or what not), the one turn loop just pickup the magnetic field to generate the current. The professor did say he just monitor the voltage across the resistors and adjust the strength of the mag field to get the right voltage across the resistors. All you have to do is to consider the secondary winding of the transformer ( in this case is the wire loop that connect the two resistors ). In this case, I think the secondary ( loop wire ) generate exactly 1V to drive 1mA through the two resistors and the result observation shown in his experiment.

Concept is nothing more than a simple transformer. I cannot do any math here because I don't know his setup, which govern the coupling between the primary ( magnetic field generator ) and the secondary ( the wire with resistors).

As I said, in transformer, we can get about 6V per turn, get 1V on the wire loop in his setup is not even close to pushing anything.

BTW, after I think more about it, the inductance effect is not that important, I actually did a calculation with 24 gauge wire and calculate the inductance, it amount to only a few ohms at 1 giga hz. It is really the transformer effect that when a magnetic field pass through the loop, current generated, but it is consider as a voltage source. The professor just adjust the mag field the get 1V out of the loop to show the class. Below is the calculation of the inductance and the impedence:

I did some digging. say the wire is 24 gauge, the diameter is 2.032X10ee-4 m. Assume is copper $\sigma=64.516X10^6\Omega^{-1}m^{-1}$.

$$L= \frac {l}{\sigma \pi r^2} \frac{r}{4\pi f}\sqrt{\pi f \mu_0 \sigma}$$

$$\Rightarrow Z_L= j 2\pi f L \;=\; \frac {l}{2\sigma \pi r^2} \sqrt{\pi f \mu_0 \sigma} \;=\; \frac{l\sqrt{\mu_0} \sqrt{f}} {2r\sqrt{\pi\sigma}}$$

For 1 meter:

$$Z_L\;=\; \frac{\sqrt{4\pi X 10^{-7}} \sqrt{f}} {2X2.032X10^{-4} \sqrt{3.14X 64.516X10^6}} \;=\; 1.94X10^{-4} \sqrt f$$

So you see the impedence at reasonable freq is very low to be a factor in this experiment.

 

[Studiot]

Hikaru, thank you for being the only respondant to have the courage to post and answer to my question.


So did Farady state his law in 'Integral Form'


I think that what is happening here is that a non original form of Faraday's Law is being compared with a non original form of KVL. By non original I mean extended in the light of more modern knowledge.

 

[stevenb]

But the common mode cancellation is the way to go if you want accurate measurement.

This experiment has little to do with needing to make accurate measurements. The voltage readings from each meter are different by almost a factor of ten. You don't need much accuracy to show that there is a difference in the readings.

You are complaining about the routing of the meter leads, but this is exactly the point of the experiment. With nonconservative fields, voltage can't be defined without reference to a defined path. The meter placement and clearly shown lead paths define the measurement.

You're basically missing the whole point and making accusations needlessly.

 

[sarumonkee]

I hope that is not the point of his confusion because it's clear that the scopes are effectively tied to the same point, and such a small inductance is irrelevant on these time scales. You can take the same voltmeter or scope, pick it up, move it to the other side and the reading will change. You could swap the meters and their reading would also swap.

@ stevenb: look at the video part 2 at around 5:23. Freeze the video and look at his setup. The probes are NOT "effectively" connected to the same point. There is about 4-6" of wire on the secondary loop with the resistors on it. That means inductance to me. Your claim of moving the scope to the other side befuddles me, because the ENTIRE point of prof. Lewins lecture is not about the how to measure this system, but that across each resistor, a different voltage occurs, which I agree with.

Think of it this way: If 1mA amp is induced in the system, OF COURSE (as he puts it) there will be a -0.1V drop on the 100 Ω res, and 0.9V drop on the 900 Ω res. Now, if we simplify the system by saying "node A" is actually "effectively" the same point, we know have 1 V drop across "node D", a supposedly 0 Ω line (by Lewin's model). That means Lewin also denies that Ohm's Law applies in this situation, because that would mean infinite energy.

Ohm's law is hard to dispute, because this is more of a definition than a theory. Therefore, I contend we have a breakdown of his model.

Conversely, since you (stevenb) seem to be very sure of your answer (I am not 100% sure of mine, that's why I asked the question, and would like to learn), can you tell me how the energy got into the system from the main coil to his resistor circuit? Does it not involve inductance? I don't know of any case where you can couple energy like this without some kind of coupled inductor setup.

 

[atyy]

Does it not involve inductance? I don't know of any case where you can couple energy like this without some kind of coupled inductor setup.

Yes, it involves inductance, of the central big loop. That is the point.

But the same point is that that inductance will cause the voltmeters to read differently, even if they are connected to exactly the same two points.

There is some error due to the voltmeters not connected to exactly the same two points, and those little bits of resistance and inductance in principle count - but they are much smaller that the inductance of the central big loop.

 

[stevenb]

The probes are NOT "effectively" connected to the same point. There is about 4-6" of wire on the secondary loop with the resistors on it. That means inductance to me.

My point is that this 4-6 inch length of wire has such small resistance and inductance that the probes ARE effectively connected to the same point. That was the intent of my inserting the word "effectively". As you know, we often take different positions along a wire to imply the same nodal point. You are correct to point out that this can sometimes lead to erroneous measurements. I'm sure that if you do a careful enough measurement you could identify the effects of both resistance and inductance of the wire. But, in physics and engineering we try to develop the art of estimating orders of magnitude and understanding what effects are significant and which are not. The Prof. has set up an experiment that creates such a large disparity (0.1 V versus 0.9 V) that the gross behavior he wants to identify won't be masked out by these smaller effects.

Your claim of moving the scope to the other side befuddles me, because the ENTIRE point of prof. Lewins lecture is not about the how to measure this system, but that across each resistor, a different voltage occurs, which I agree with.

I didn't mean to create confusion. My main motive in mentioning the moving of the meter (how's that for an unintended alliteration! ) is to stress the point that the connection point of the meter at the nodes is not critical in this experiment. What matters is the location of the meter and the routing of the leads.

I think his point is that the voltage across each resistor is not well defined without a simultaneous definition of path for the measurement. It's clear that current times resistance (potential) is different on both resistors. However, if you try to measure that potential, you will get different readings of voltage depending on the path. The measurement that actually correctly indicates the potential is the one where the leads and meter do not encircle the flux change. Imagine if you were doing an experiment and did not know the flux change was there. You would start pulling your hair out because the voltage reading would change drastically when you move the leads. Of course, this can happen (and often does happen) in real modern circuit measurements, particularly when designing and testing switching power supplies.

Think of it this way: If 1mA amp is induced in the system, OF COURSE (as he puts it) there will be a -0.1V drop on the 100 Ω res, and 0.9V drop on the 900 Ω res. Now, if we simplify the system by saying "node A" is actually "effectively" the same point, we know have 1 V drop across "node D", a supposedly 0 Ω line (by Lewin's model). That means Lewin also denies that Ohm's Law applies in this situation, because that would mean infinite energy.

I'm not sure I'm understanding you here, but it seems to me that you are not grasping the concept of nonconservative fields, and the fact that both resistors can tie to the same nodes with different potentials. This seems counter-intuitive because we are trained to expect the potential across two nodes to be the same, but in this case they are not the same. The model of a 0 ohm connection, even if unrealistic, is perfectly acceptable as an approximation in this case. It helps reveal the physics, just as we often ignore friction to help teach physics principles in mechanics problems.

Ohm's law is hard to dispute, because this is more of a definition than a theory. Therefore, I contend we have a breakdown of his model.

Anyone can break down anyone else's model because no model is perfect. The only question is whether his model is good enough. I believe that it is because when I check his detailed analysis and explanation it agrees with his scope readings. I'm also giving him and his helpers the benefit of any doubt and assuming they are smart enough to check out all these things you are worried about. This is all stuff that is well known by people with experience. I don't see any red flags or smoking guns and the end result makes sense once you think about it.

Conversely, since you (stevenb) seem to be very sure of your answer (I am not 100% sure of mine, that's why I asked the question, and would like to learn), can you tell me how the energy got into the system from the main coil to his resistor circuit? Does it not involve inductance? I don't know of any case where you can couple energy like this without some kind of coupled inductor setup.

The energy conversion is through induction, as described by Faraday's Law. Whether you think of this as an inductor, a transformer or a generator is not the main issue. But, this inductance effect (if you like to call it that) is unrelated to the parasitic inductance of the wire itself. The small inductance and resistance of the wire just don't enter into the physics in a significant way, in this experiment and analysis. For this reason you can swap the locations where the two scopes tie into the nodes. You can also move the connection points anywhere along this few inch length you are concerned about. You can also physically pick up one meter and move it to the other meter's location and then both meters would read about the same.

 

[atyy]

Impressive.

Want to try assonance next?

 

[yungman]

This experiment has little to do with needing to make accurate measurements. The voltage readings from each meter are different by almost a factor of ten. You don't need much accuracy to show that there is a difference in the readings.

You are complaining about the routing of the meter leads, but this is exactly the point of the experiment. With nonconservative fields, voltage can't be defined without reference to a defined path. The meter placement and clearly shown lead paths define the measurement.

You're basically missing the whole point and making accusations needlessly.

I think you are missing the point of the transformer effect and I hope you see from the professor's drawing the wires and the two resistors form a loop. I never challenge the measurement of the two resistors, I challenge the fact he ignore the measurement of the wires. There is voltage develop across the two end of the wire due to the transformer effect because it is a loop. I hope you understand transformer even if it is a single turn loop like in this case. If you have a way to measure the voltage across the wires that connect the two resistors, you will find you voltage.

I have no easy way to draw a schematic here, maybe it is too confusing to describe in words. I claim the wires that connect the two resistors serve as the secondary winding of a transformer and generate 1V that create the 0.1 and 0.9V on those two resistors. And that is what the professor missed.

There is nothing wrong with his non conservative stuff, he just miss the voltage source from the transformer. You read through my long description about how we can generate about 6V per single turn of the transformer? Measuring at different points of the 4" to 6" wire like you described is like tapping at different position of the transformer winding!

 

[yungman]

My point is that this 4-6 inch length of wire has such small resistance and inductance that the probes ARE effectively connected to the same point. That was the intent of my inserting the work "effectively". As you know, we often take different positions along a wire to imply the same nodal point. You are correct to point out that this can sometimes lead to erroneous measurements. I'm sure that if you do a careful enough measurement you could identify the effects of both resistance and inductance of the wire. But, in physics and engineering we try to develop the art of estimating orders of magnitude and understanding what effects are significant and which are not. The Prof. has set up an experiment that creates such a large disparity (0.1 V versus 0.9 V) that the gross behavior he wants to identify won't be masked out by these smaller effects.
Inductance is very small, but the transformer effect is big. You ever seen transformer that have two output taps only half turn apart on the winding? I did, I worked in a company called Aydin Energy Div. in 1979 that wind huge custom transformers for enectrical companies, the winder was joking and told what is this about two taps within half a turn and showed me.

4 to 6" of line is not short, if it is on a mini transformer, 6" is 5 to 6 turns on the winding, that is a lot of volts! You look at the turn, not the length.


I didn't mean to create confusion. My main motive in mentioning the moving of the meter (how's that for an unintended alliteration! ) is to stress the point that the connection point of the meter at the nodes is not critical in this experiment. What matters is the location of the meter and the routing of the leads.

I think his point is that the voltage across each resistor is not well defined without a simultaneous definition of path for the measurement. It's clear that current times resistance (potential) is different on both resistors. However, if you try to measure that potential, you will get different readings of voltage depending on the path. The measurement that actually correctly indicates the potential is the one where the leads and meter do not encircle the flux change. Imagine if you were doing an experiment and did not know the flux change was there. You would start pulling your hair out because the voltage reading would change drastically when you move the leads. Of course, this can happen (and often does happen) in real modern circuit measurements, particularly when designing and testing switching power supplies.



I'm not sure I'm understanding you here, but it seems to me that you are not grasping the concept of nonconservative fields, and the fact that both resistors can tie to the same nodes with different potentials. This seems counter-intuitive because we are trained to expect the potential across two nodes to be the same, but in this case they are not the same. The model of a 0 ohm connection, even if unrealistic, is perfectly acceptable as an approximation in this case. It helps reveal the physics, just as we often ignore friction to help teach physics principles in mechanics problems.



Anyone can break down anyone else's model because no model is perfect. The only question is whether his model is good enough. I believe that it is because when I check his detailed analysis and explanation it agrees with his scope readings. I'm also giving him and his helpers the benefit of any doubt and assuming they are smart enough to check out all these things you are worried about. This is all stuff that is well known by people with experience. I don't see any red flags or smoking guns and the end result makes sense once you think about it.



The energy conversion is through induction, as described by Faraday's Law. Whether you think of this as an inductor, a transformer or a generator is not the main issue. But, this inductance effect (if you like to call it that) is unrelated to the parasitic inductance of the wire itself. The small inductance and resistance of the wire just don't enter into the physics in a significant way, in this experiment and analysis. For this reason you can swap the locations where the two scopes tie into the nodes. You can also move the connection points anywhere along this few inch length you are concerned about. You can also physically pick up one meter and move it to the other meter's location and then both meters would read about the same.

......

 

[stevenb]

I think you are missing the point of the transformer effect ...

... I claim the wires that connect the two resistors serve as the secondary winding of a transformer and generate 1V that create the 0.1 and 0.9V on those two resistors. And that is what the professor missed ... he just miss the voltage source from the transformer.

... You read through my long description about how we can generate about 6V per single turn of the transformer? Measuring at different points of the 4" to 6" wire like you described is like tapping at different position of the transformer winding!

I'm not sure why you would say that I and the Professor have missed the "transformer effect". This effect is the source of the EMF that drives current in the loop. The main difference between this situation and a real transformer is that one does not usually put two large resistors in the loop winding of a transformer. Certainly the transformers you took measurements on were not built like this. But, this is a side issue.

The professor goes through a process of setting up the problem. First he describes the case with a 1 V battery in the loop, and then he erases the battery cell and uses changing flux in the center of the loop to replace the 1 V EMF. How can you say "he just miss the voltage source of the transformer"? He didn't miss it at all.

Faraday's Law in integral form just tells you that the 1V EMF exists somewhere in the loop. It doesn't specify where it is in the loop. Typically, a transformer is tapped to change the number of loops is the circuit, not to somehow tap a section of one loop. The details of what happens when tapping one loop need to be considered more carefully, as has been done in the provided analysis. In this case we know where the potential drops are (we can measure them with a meter that does not encircle the flux change) and we see that it adds up to 1V around the main loop. There is very little potential drop across the wires themselves. The transformer EMF in the main loop is 1V, so all is well with Faraday's Law. Also, all is well with the classical definition of KVL (given by Maxwell). Obviously, the version KVL that says the sum of potential drops is zero is violated, which makes the professor jump up and down and denounce his physics books for spouting bad physics.

In doing the proper measurement for potential on each resistor, you trace a path (through the meter and the resistor) that does not encircle the flux change and this tells you which resistor potential you are actually measuring. FL and KVL (both versions of KVL, mind you) work here. The Professor also reveals that if you consider the path through the other resistor, you see an apparent contradiction. You end up tracing a loop through the other resistor that encircles the flux change and you are not really measuring the potential on that resistor. Faraday's Law still works through that other path, and the classical definition of KVL also works, but the other definition of KVL fails yet again.

Since the professor is not actually acknowledging the classical definition of KVL, we can just ignore that aspect, and conclude that everything he is saying is correct. The results do not depend (other than small parasitic changes) on where you tap the node along the wire, but they do depend on how you route the leads of the meter. If we had the experiment in front of us, there would be a very simple way to prove this. Simply move the exact point where you tie into the nodes and see if the measurements change. It is my contention that they will not change very significantly. Anyone who doubts this should just do the experiment and convince themselves. Do you really think the people who set up this experiment would go through all this trouble, and then not verify this straightforward thing? You really think MIT people can miss a factor of ten in this way? That's hardly proof, but experiments are proof. I've done similar experiments in the past as part of my work. I can't ask anyone to accept my word, and if others don't want to accept the professor's capability, then just do the experiment.