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

[stevenb]

The second part where you repeat what Sarumonkee did, agree with my result in post #226. I put the theory and equivalent circuit and what experiment I did also. Take a look at my attachment and explanation why you see very little voltage on the probe. My theory is because the probe ground lead and the part of the wire form a loop that pick up the exact same voltage.

I'll go back and look. Maybe I'm misunderstanding, but aren't you saying exactly what I was saying in previous posts? That is, the scope probes complete the loop also and have an equal and opposite emf. I'm in agreement with you that the wire itself has emf. Am I understanding correctly, or did I miss the point you are making?

I will read through your posts more carefully when I get home.

Is there a misplaced decimal point in entry line 4 of the B column in Table1?

Yes, you are correct sir. Thanks for the correction.

 

[yungman]

I redraw and make it much shorter so hopefully is not too long drawn!

Please comment on this. this is only my theory and I am totally open up for debate. This is really really tricky. As I said, I have not come up with a way to get rid of the pesty probe loop.

 

[yungman]

I'll go back and look. Maybe I'm misunderstanding, but aren't you saying exactly what I was saying in previous posts? That is, the scope probes complete the loop also and have an equal and opposite emf. I'm in agreement with you that the wire itself has emf. Am I understanding correctly, or did I miss the point you are making?

I will read through your posts more carefully when I get home.



Yes, you are correct sir. Thanks for the correction.

Yes, I don't think we disagree on the observation of the experiment, it is the interpretation of the result. If you have a chance, loop the ground of the probe over like what I did and see.

This is really really tricky. And I emphasize, this is only my theory...Only! Feel free to disagree and we can debate on this.

 

[stevenb]

I redraw and make it much shorter so hopefully is not too long drawn!

Please comment on this. this is only my theory and I am totally open up for debate. This is really really tricky. As I said, I have not come up with a way to get rid of the pesty probe loop.

OK, I like what I'm seeing in this post. You are basically getting the right idea here. In your drawing you show loop1 and loop2 which both enclose the full flux. You mention that the 0.9V is correct if you look at loop2, which I agree. You also mention this is not actually voltage drop on R2, but I don't quite agree with this. You see there is also loop3 which is BKA'AB, which is the measurement loop that does not enclose any flux, but does include R2. So this 0.9V is the true potential across the resistor R2. This is one of the points I was trying to make previously. There is a key difference between emf and potential even though they are both voltage. You can measure emf caused by enclosed flux change. You can also measure potential on a wire or on a resistor. But, you can't use a voltmeter to measure the emf on the wire that is part of a measurement loop that does not enclose flux. This is an important distinction to make and explains why our measurements are not able to "see" the wire emf, even though I have no doubt it is there on sections, with a net of zero around loop3. I expect an electric field measurement would let you see this nonconservative field directly.

I agree with what you are doing with putting the probe ground over the top of the coil. Here you are capturing some of the flux, not all. So your observations and interpretations make sense here.

Your final question, I'm not sure I understand. This is definitely path dependent, but I'm not sure what "flux-circulating-dependent" means. I would say that it is "flux-enclosing-dependent", if that's what you mean. - speaking loosely. The issues of chosen path (note that closed paths are implied here), or the enclosing flux are essentially the same thing.

 

[yungman]

OK, I like what I'm seeing in this post. You are basically getting the right idea here. In your drawing you show loop1 and loop2 which both enclose the full flux. You mention that the 0.9V is correct if you look at loop2, which I agree. You also mention this is not actually voltage drop on R2, but I don't quite agree with this. You see there is also loop3 which is BKA'AB, which is the measurement loop that does not enclose any flux, but does include R2. So this 0.9V is the true potential across the resistor R2. This is one of the points I was trying to make previously. There is a key difference between emf and potential even though they are both voltage. You can measure emf caused by enclosed flux change. You can also measure potential on a wire or on a resistor. But, you can't use a voltmeter to measure the emf on the wire that is part of a measurement loop that does not enclose flux. This is an important distinction to make and explains why our measurements are not able to "see" the wire emf, even though I have no doubt it is there on sections, with a net of zero around loop3. I expect an electric field measurement would let you see this nonconservative field directly.

I agree with what you are doing with putting the probe ground over the top of the coil. Here you are capturing some of the flux, not all. So your observations and interpretations make sense here.

Your final question, I'm not sure I understand. This is definitely path dependent, but I'm not sure what "flux-circulating-dependent" means. I would say that it is "flux-enclosing-dependent", if that's what you mean. - speaking loosely. The issues of chosen path (note that closed paths are implied here), or the enclosing flux are essentially the same thing.

Yes, that is exactly what I meant. The question is you call it path or flux. I call in path independent, but you have to consider the flux. Question is how do you want to call it. To me. it is all about the flux enclosed. If you agree with the flux enclose, then we are more in agreement.

But still how do you read what the professor claimed? Path or flux?

I don't know! I say flux!

Regarding to reading of the voltage, you will find whether you consider R2 or loop2, they always equal. I know what I claimed was kind of outragous, but if you think in the point of view of the loop, it should make sense. You know, that sounds like is another potato or patarto thing again!


Final question, so which way is right? We did put a lot of stake into this!

1) Path independent, depend on the flux? Which is what I put my name on.

2) Path dependent, taking into consideration of the flux? How do you define path dependent?

We need a referee!

 

[yungman]

I keep thinking about the measuring method and about the path dependent. My problem with all the argument is this:

Just because we have not yet found a way to do measurement without getting the loop induced emf onto the probe do not mean the is not a potential different between point B and D, or point C and D. We are stipulating that we don't measure the emf because of the probes' ground lead. But let say for a second that We come up with a way to break the loop on the probe so we avoid the induced emf onto the probe, we should actually see the potential difference between point D and C like what Sarumonkee. So the issue is not that KVL don't work here, the issue is we have to find a way to get rid of the measuring instrument induced error. If we can succeed in getting rid of the measurment error, we can apply KVL on this closed loop with resistors.

There got to be a way to do accurate measurement and we should see the induced emf on the wire. I am trying to come up with a way to do the measurement, so far no luck yet.

I attached a priminary schematic drawing of a circuit to measure the voltage between point B and D of the loop. I use two section of preamp that use isolated supply and produce a differential output. The two pair of differential output is then sum together. I use differential outputs because any induced emf will become common mode and rejected by the differential amp in the following stage. As I said, this is priminary, but there got to be a way to get rid of the error of measurement. Our think about this more tomorrow.

 

[stevenb]

If we can succeed in getting rid of the measurment error, ...

I disagree with the interpretation here. I submit that we have successfully removed most of the measurement error with the experiments we've done. The issue of not being able to measure emf on a section of wire is a constraint forced by Faraday's Law. No matter how you arrange the system, you will induce an equal emf on the meter wires (whether O-scope, voltmeter or opamps) as is on the wire you are trying to measure. The net emf on this newly created measurement loop (which has no enclosed flux, ideally) is zero. You can't fight with Faraday's Law. It's just always true. As I mentioned above, I think that, in principle, you could use an electric field measurement probe to scan the electric field over the section of wire you are interested in. Then, you could mathematically integrate the field and call this a measurement of wire emf. However, this is an entirely different experiment outside the scope of what Prof. Lewin was talking about.

By the way, I made some corrections and additions to my previous document, which is now at Rev. B.

 

[Studiot]

There is a key difference between emf and potential even though they are both voltage.

Let us look at this another way.

Take a system comprising a single point charge, located anywhere, but conveniently at the origin.

It is basic that there is an electric field surrounding this charge with equal potentials on succesive concentric spherical shells. Thus potential varies with distance from the charge.
For the purposes of this discussion the details of the variation are immaterial.

Take two points, A and B at different distances from the charge.
There will exist a potential difference between A and B. Let us choose A and B so that this is 1.5 volts.

The system rules allow us to add or subtract any mass or move it within the system, but not to add charge or permanent magnets.

1) It is impossible to extract energy (do work) without introducing further charge.

2) It is impossible to generate magnetic effects without introducing further charge (or permanent magnets)

So what happens if we introduce a resistor with one end at A and the other at B ?
Is there a current in the resistor?
What is the potential difference between its ends?

Now compare this with a second system where we remove the charge and place the terminals of a battery with a 1.5 volt EMF at A and B.

Is there a current in the resistor?
What is the potential difference between the ends of the resistor?
Can we extract energy from the system?
Can we generate magnetic effects without adding further charges or magnets to the system?

 

[yungman]

I disagree with the interpretation here. I submit that we have successfully removed most of the measurement error with the experiments we've done. The issue of not being able to measure emf on a section of wire is a constraint forced by Faraday's Law. No matter how you arrange the system, you will induce an equal emf on the meter wires (whether O-scope, voltmeter or opamps) as is on the wire you are trying to measure.
So the point is to find a way which I am working on it slowly. The circuit I propose in the attachment of #246. is an attempt to use common mode rejection to eliminate the induce emf. I don't think it will work that well, but I believe there is a way and I am working on it.

The net emf on this newly created measurement loop (which has no enclosed flux, ideally) is zero. You can't fight with Faraday's Law.
You are looking at what you called the loop 3, but if you look at the loop 2 in my drawing, it contain all the flux.

It's just always true. As I mentioned above, I think that, in principle, you could use an electric field measurement probe to scan the electric field over the section of wire you are interested in. Then, you could mathematically integrate the field and call this a measurement of wire emf. However, this is an entirely different experiment outside the scope of what Prof. Lewin was talking about.

By the way, I made some corrections and additions to my previous document, which is now at Rev. B.

What if I can find a way to measure the wire?

 

[yungman]

Let us look at this another way.

Take a system comprising a single point charge, located anywhere, but conveniently at the origin.

It is basic that there is an electric field surrounding this charge with equal potentials on succesive concentric spherical shells. Thus potential varies with distance from the charge.
For the purposes of this discussion the details of the variation are immaterial.

Take two points, A and B at different distances from the charge.
There will exist a potential difference between A and B. Let us choose A and B so that this is 1.5 volts.

The system rules allow us to add or subtract any mass or move it within the system, but not to add charge or permanent magnets.

1) It is impossible to extract energy (do work) without introducing further charge.

2) It is impossible to generate magnetic effects without introducing further charge (or permanent magnets)

So what happens if we introduce a resistor with one end at A and the other at B ?
Is there a current in the resistor?NO.
What is the potential difference between its ends?
NO.
Now compare this with a second system where we remove the charge and place the terminals of a battery with a 1.5 volt EMF at A and B.

Is there a current in the resistor?Yes.
What is the potential difference between the ends of the resistor?
Can we extract energy from the system?Yes.
Can we generate magnetic effects without adding further charges or magnets to the system? Yes.

What are these have anything to do with the experiment? Please don't be criptic, explain to me.

 

[Studiot]

What are these have anything to do with the experiment?

The difference between EMF and Potential has been mentioned several times and you did ask for an explanation, in an an earlier post.

This is my way of trying to highlight that difference.

The difference is essentialy that a potential cannot introduce energy not already in the system, whereas an EMF can.

 

[stevenb]

What if I can find a way to measure the wire?

Then you will have taught me something new. I love to learn new things, so if you do find a way, please tell me how you do it, and I will try to verify experimentally also.

 

[stevenb]

I'd like to provide a diagram that makes the measurement error sources clearer. The diagram shows the incorrect way someone might setup the experiment on a first try. This diagram is particularly helpful to reveal the problems caused by a dual-trace scope with common grounds. No one seems to be doubting this issue now that we've identified it, but there may be some people that don't fully visualize the cause of the problem. I think this diagram will be helpful for visualization, and note that I certainly needed to draw it out myself to see the ground loops from the dual trace scope.

For fun, I also included a subtle pardox type of question that is related to this. I just throw it out there as a puzzle for others to chew on, if they enjoy such things.

 

[yungman]

Then you will have taught me something new. I love to learn new things, so if you do find a way, please tell me how you do it, and I will try to verify experimentally also.

I am just saying that, still got ways to go. I started using common mode and did the design shown, something just don't look right and I don't think that is going to do it. If you have time, take a look, I think the measuring loop still there even I use differential drivers and recievers. Don't take the value of those resistors seriously, I just put in 5K because it just come to my mind! But you'll see where I am going.

If it is easy, someone must have come up with something long time ago!

 

[yungman]

The difference between EMF and Potential has been mentioned several times and you did ask for an explanation, in an an earlier post.

This is my way of trying to highlight that difference.

The difference is essentialy that a potential cannot introduce energy not already in the system, whereas an EMF can.

So potential difference is just that, the difference in voltage. EMF is one that can provide energy. Am I getting this?

What is your opinion on we me and Stevenb did so far. It has been between only the two of us so far. Put in some of your opinion so we can think about it.

So far as you see, we have not been able to measure the EMF( right?) of the wire from B to D. I am working on a method to do the measurement. Are we going anywhere?

 

[Studiot]

So potential difference is just that, the difference in voltage. EMF is one that can provide energy. Am I getting this?

Yes that's about it.

But, remember that the process is not symmetrical.
A system can dissipate energy ( eg a resistor can heat up).

This is how Kirchoff's laws are satisfied at anyone instant, although the balance numbers may be different from instant to instant if the system cannot replenish its dissipating energy.

This is the basis for my version after Kirchoff himself of his laws.

What is your opinion on we me and Stevenb did so far. It has been between only the two of us so far. Put in some of your opinion so we can think about it.

So far as you see, we have not been able to measure the EMF( right?) of the wire from B to D. I am working on a method to do the measurement. Are we going anywhere?

Steve is quite capable of stating his own case quite lucidly, and of teaching us both a thing or two, along with anyone else who care to listen.

You two have both done these experiments, I have not, so that floor is yours.

One thing they definitely reinforce is the importance of correct experimental technique, and the reason why often promising experiments 'go wrong'.

go well

 

[stevenb]

A final report on all completed experiments is probably about 2 weeks away because of holidays, sick wife and work schedule.

I just wanted to fulfill my promise and give a final version of the report, at the promised time. I think we've discussed all the important points in this report, but this is a final version with corrections and completed diagrams etc.

 

[yungman]

Right now is kind of boil down to the definition of path dependent. Anyone have a clear definition of path dependent? Our measurement is subject to the way we measure due to the flux enclosed. I want to know whether this is consider path dependent. I am still not convince this is path dependent yet. To me, it is still the difficulty of measuring rather than it is path dependent. Can someone comment on this? I want to hear in absolute on this, somehow everyone left and only Steven and me still going at it.

I have been busy in other things and have not have a chance to try any new way of measuring yet. I'll post my finding in the near future.

 

[scoutfai]

Does this interesting debate ends already?
The title of this discussion is "Is MIT Prof. Lewin wrong about Kirchoff's Law?", so the nutshell answer to this question is?

 

[stevenb]

Does this interesting debate ends already?
The title of this discussion is "Is MIT Prof. Lewin wrong about Kirchoff's Law?", so the nutshell answer to this question is?

Who is the final judge? In a forum we have no judges. The OP disappeared before all arguments and evidence were presented. It would have been interesting to know his final opinion, but it's clear that a student at his level is not qualified to judge objectively.

Yungman is still off thinking about how to circumvent Faraday's Law, and never conceded.

What is your opinion based on the evidence presented on both sides? Who is right? Is it the well known Professor with a lifetime of experience, or an anonymous student who raises the question and then leaves?

Hopefully my position is clear, and I do believe that I provided convincing evidence to support Prof. Lewin's position.

 

[asdofindia]

MIT OCW is a source of hope and inspiration for a lot of people (at least me) around the world.
Even if he's bluffing like Einstein, I wouldn't mind.

The answer to the original question: "If you've understood everything about Kirchoff's rule, Physics won."

 

[yungman]

Who is the final judge? In a forum we have no judges. The OP disappeared before all arguments and evidence were presented. It would have been interesting to know his final opinion, but it's clear that a student at his level is not qualified to judge objectively.

Yungman is still off thinking about how to circumvent Faraday's Law, and never conceded.

What is your opinion based on the evidence presented on both sides? Who is right? Is it the well known Professor with a lifetime of experience, or an anonymous student who raises the question and then leaves?

Hopefully my position is clear, and I do believe that I provided convincing evidence to support Prof. Lewin's position.

I have to be honest, I have not work on this since the whole thing seems to boil down to the meaning of "path independent". I might be able to do something if I use a ground plane underneath the coil and see whether I can destroy the so call "path". But does that really mean a much. I am not here to challenge the Faraday's law.

I still have my setup, but I am not very interested to come to debate of the meaning of the term. Seem like it really boil down to whether all my experiment is consider path independent. I think that is the bottom line. I stand by my result( I am talking about the observation of the experiment, not the interpretation of path independent), I think at this point, I need someone that has the deep knowledge to come into determine whather it is consider under "path independent". I don't have the theorectical background to say that. too bad towards the end, it was just you and me. People seems to disappeared!

I am since hot on the trod studying electrodynamics!

 

[Antiphon]

KVL always works in circuit analysis. The professor's lecture is a deliberate paradox as follows; a circuit has zero area and cannot enclose any magnetic flux. The instant he replaced the battery by a magnetic field, he left the realm of circuit analysis and entered the realm of microwave circuit analysis. This field of study is DEFINED as the study of circuits which are not infinitesimal in size. For such circuits, you have a mix of conservative and non-conservative fields and KVL most certainly will not work any longer.

I do hope this is clear and puts the matter to bed.

 

[scoutfai]

Who is the final judge? In a forum we have no judges. The OP disappeared before all arguments and evidence were presented. It would have been interesting to know his final opinion, but it's clear that a student at his level is not qualified to judge objectively.

Yungman is still off thinking about how to circumvent Faraday's Law, and never conceded.

What is your opinion based on the evidence presented on both sides? Who is right? Is it the well known Professor with a lifetime of experience, or an anonymous student who raises the question and then leaves?

Hopefully my position is clear, and I do believe that I provided convincing evidence to support Prof. Lewin's position.

I am not a pure physics and EE engineering undergraduate so I definitely not understand the electromagnetism as well as most of you who participated in the discussion. I just tell what I feel.

I think the established scientific knowledge of mankind on electromagnetism is that everything in this field governs by Maxwell's equations (all 4 of them). Any other laws or rules (Ohm Law, Kirchoff's Voltage Law, Lenz Law, etc) can be derived from Maxwell's equations. As such, I think it is correct to say Faraday's Law always work. I think it is widely accepted that Kirchoff's Voltage Law is derivable from Faraday's Law, hence it will not be surprise in certain circumstances KVL violated by nature, but Faraday's Law followed by nature.

Thus I am in agreement to Prof. Lewin claims, at least up to now until a convincing contradiction presented to me.

 

[scoutfai]

There is another forum which had discussed about the exact same topic, but the OP make use of SPICE to simulate and asserts Prof. Lewin wrong. Basically he treats the wire connecting the resistors to act like a tiny inductor, and hence claims that what Prof. Lewin measuring is the voltage drop across the "inductor-resistor-inductor" in series, thus the difference in reading. I think it is worth reading and I share it here to all of you.

http://www.overunityresearch.com/index.php?topic=739.0"

I can see that some of you who participated in the discussion, claims that the wires of the oscilloscope forms another loop, and thus contributing an EMF.
Isn't it will be easy to verify this by shielding the magnetic field produced by the solenoid from reaching the oscilloscope's wire? If this wire causes an effect, after the shielding there should be a difference in reading. Please don't ask me how to shield it, I have no idea, I am not in this field at all. But I believe it can be done. After all, satellite has all its on board circuit shielded.

 

[Antiphon]

Let me try again in practical terms.

KVL doesn't work in the lab because circuits are not infinitesimal in size. Only a circuit with zero area in every loop is immune to the EMF of a changing magnetic field. No such physical circuits exist therefore KVL is never correct.

In the academic discipline of circuit analysis, simplifying assumptions are made, the key one being that the entire circuit is of zero physical extent. Under these and only these simplifying assumptions there is no induction, no EMF and KVL holds.

The professor violated the fundamental tenet of circuit analysis when he allowed the loop to have a non-zero area.

This is not debatable. The topic is fully and completely resolved.

 

[yungman]

There is another forum which had discussed about the exact same topic, but the OP make use of SPICE to simulate and asserts Prof. Lewin wrong. Basically he treats the wire connecting the resistors to act like a tiny inductor, and hence claims that what Prof. Lewin measuring is the voltage drop across the "inductor-resistor-inductor" in series, thus the difference in reading. I think it is worth reading and I share it here to all of you.

http://www.overunityresearch.com/index.php?topic=739.0"

I can see that some of you who participated in the discussion, claims that the wires of the oscilloscope forms another loop, and thus contributing an EMF.
Isn't it will be easy to verify this by shielding the magnetic field produced by the solenoid from reaching the oscilloscope's wire? If this wire causes an effect, after the shielding there should be a difference in reading. Please don't ask me how to shield it, I have no idea, I am not in this field at all. But I believe it can be done. After all, satellite has all its on board circuit shielded.

It is not the inductance. We gone way pass that. Read the first part of this thread and you see we dismissed this long time ago. You cannot have enough inductance to do anything like this. I don't think the first wave ( me, StevenB or others that was in here) of people are interested in hashing this points anymore.

It is about induced emf in the loop. I don't think me and StevenB disagree. I have detail drawing in how to interprete the loops. please read starting at post #220, this is the point where we all tired of calling names and trash talk and really get down to let the work do the talking.

It is about whether you can measure the voltage independent to the method and how you set the probe. I proved the method and gave the reasoning on how different ways I measure the same point give different answers and there is no dispute about it. It all boil down to whether this is defined as "path dependent or not". This is quite black and white at this point.

Question is the way I measured and the way I swinged the prob ground is consider path dependent or just the magnetic field interference that cause the change in reading. So we boiled down to what is the definition of path independent.

Someone need to sort through the whole debate between me and StevenB to sort this out. Basically we both had the same observation, but he called this path dependent and I did not agree. Now someone expert in this have to come into sort this out. If what I did is consider path dependent, then there is no point in the argument, I got the definition wrong. If it is not, then I proofed my point the professor was wrong. we went way way beyone calling names, rely on reputation!

 

[yungman]

Let me try again in practical terms.

KVL doesn't work in the lab because circuits are not infinitesimal in size. Only a circuit with zero area in every loop is immune to the EMF of a changing magnetic field. No such physical circuits exist therefore KVL is never correct.

In the academic discipline of circuit analysis, simplifying assumptions are made, the key one being that the entire circuit is of zero physical extent. Under these and only these simplifying assumptions there is no induction, no EMF and KVL holds.

The professor violated the fundamental tenet of circuit analysis when he allowed the loop to have a non-zero area.

This is not debatable. The topic is fully and completely resolved.

At this point, I don't know anymore, to me, it is about the definition. If what I did is consider path dependent, he is right. If otherwise, he is wrong and my experiment proofed that.

Please start reading from post #220, that is where the meat of the experiment start when both StevenB and me get down to do the experiment and publish our result and I put in my theory of the different loops. read my attachment in #223 that explain all different observations and my theories.

 

[Studiot]

Seems to me that most minds are closed on this subject, and few are willing to accept that others may have valid points.

I find this very difficult to understand, especially when they mis-apply Kirchoff's laws.

1)
I have no trouble applying Kirchoff's laws to the Lewin experiment and have posted the solution several times. I do not need to invoke circuit theory v microwave circuit theory or other concoction, I just apply the original law, not the incorrect one so often proffered these days.

2) It is not true to say that Kirchoff's law cannot be applied to circuits of large extent - national power grid engineers do this every day for circuits of several thousand kilometer extents.

3) It is also not true to say that Kirchoff's law can be applied in every circuit. The method is not applicable to mesh analysis of non planar networks.

http://en.wikipedia.org/wiki/Network_analysis_(electrical_circuits )

 

[vanhees71]

I don't know, what you are exactly debating about. I've come into this thread just now. I've looked over this nice summary by one of you, where you describe in detail your experimental setup and the sensitivity of the measurement of the emf on the geometry of the wire loops.

To me all this looks simply like the standard Faraday law, which is one of the basic Maxwell equations of classical electromagnetism. I'm not sure what is the debate about, particularly which interpretation of the Prof. is questioned. Could you point me to the precise URL of this lecture, you mention to be online on the web?

The most general way to express Faraday's Law is the integral form

\frac{\mathrm{d}}{\mathrm{d} t} \int_{F} \mathrm{d} \vec{F} \cdot \vec{B}=-\int_{\partial F} \mathrm{d} \vec{x} \cdot \vec{E},

which is valid without approximations for all circumstances (time-varying em. fields and/or moving areas F and boundary loops \partial F.

It's only important that you take into account the complete area, enclosed by the loop with a clear definition which loop is relevant for the voltage drop measured between the two points defined by the apparatus. It's clear that a change of the shape of this "effective" loop changes the enclosed "effective area" the magnetic induction is going through defining the magnetic flux through the area (given by the area integral in the left-hand side of the above Faraday-Law Eq.).

Depending on accuracy it may be important to calculate (or measure?) the magnetic field under consideration carefully. Whether a quasistatic (stationary) approximation (strictly valid only for infinitesimally small extension of all relevant elements of the circuit) is sufficient or whether one has to take into account the full dynamical Maxwell Equations (i.e., the full wave-field solutions) is a question whether the relevant extension of the effective loops/enclosed areas are small against the wave length, i.e., c/f where f is the typical frequency of the AC run through the coil.