Kirchhoff’ Voltage Law versus Faraday’s Law: the Conclusion

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Stuff like this that expand my knowledge of electricity are why I'm a patron. That and the fact that you give scopes and other test kit away to schools. In an era where my country is actively hostile to education, anyone who supports education gets my money. Keep being awesome, Mr Sadaghdar!

Check out the X-factor on Mr Sadaghdar.. This is fun!

Wow, what a detailed video. I only have a bachelor's in Biology but took physics for "fun". I understand the concept better now. When watching the first video I was thinking that if a magnetic field passes thru the loop it has to create some inductive energy. Looks like the supporting information from the other professors covers this. I really can't follow the mathematical end of this as that was my Achilles Heel for getting my original goal of a chemistry degree. Seems my brain works up to trig but not beyond. Have to say both were great videos and with some researching what you said in the second video the calculations make sense (somewhat). Thanks again for the truth, the whole truth, and nothing but the truth. And hey, never ever let the wackos on the internet bother you.

The links in the video description are all there for me, checked Chrome and Opera, not sure about your comment though.

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I can't see the links below the video, and I also can't see the comment I made earlier. Tried two different browsers. Any idea what's up with that?

Each and every thing in this video brought back memories of physics from high school.

Dibya Jyoti Roy

This is what I can call good approach to solve science problem! Perfect investigation and explanation!

Brilliant explanation in the video.

Q.E.D translates to S.M.D (Scientific Mic Drop) right? :P

Marco Vujevic

Good luck with your studies. You sound like a good student. I could never think clearly about these stuff back in my days at school! From your name, you might be in Harvard or something! Have fun.

ElectroBOOM [Mehdi Sadaghdar]

Thanks! I'm only an EE uni student. Don't fret about it. It's just because all this maths and physics is fresh in my head. I'm sure you beat me any day when it comes to building circuits! I'm enjoyed this discussion a lot. If you want to talk more, just continue this thread or email me at hddharvey@gmail.com. Otherwise, good luck!

Have fun having dinner!

ElectroBOOM [Mehdi Sadaghdar]

You sound young! My brain doesn't work as fast as you

ElectroBOOM [Mehdi Sadaghdar]

:)

:D I need to draw it on a paper! I think we are saying the same thing in different ways.

ElectroBOOM [Mehdi Sadaghdar]

If you also accounted for both the energy done by the field AND you, then the work is always zero. That's not a useful definition for potential energy (that's how voltage is defined). If you defined GPE like that, then lifting a ball up wouldn't change it's energy.

Yes but that's not how voltage is defined. When we talk of potential energy and everything, we don't consider the energy that the field takes out, because then the work is always zero, even if it's not a closed loop! (That's not very useful). Regarding voltage, you either only consider the energy that YOU have to supply to resist the field, or the work done BY the field (assuming no acceleration) to move the charge. These two understandings only differ by sign.

But even in that case, the energy put in by a rising field is taken out by me manually forcing the charge through. considering all input and output paths, KVL holds!

ElectroBOOM [Mehdi Sadaghdar]

I'm not sure what you're saying there. But the very least if you moved a charge around the loop from the experiment, do you agree the work supplied to that charge must be non-zero?

Agree with work not being zero? No that sounds logical, if energy is put into the loop from multiple sources, then everything is messed up. It is like a circuit with multiple loops having common nodes. You have to take all of them into account to make it work.

ElectroBOOM [Mehdi Sadaghdar]

Well it's getting late in Australian time (UTC+10). I have to go to a dinner. If you want to discuss this more, I'd love to. Hopefully science wins in the end!

In batteries one guy wants to pull charge from another guy, that''s all!

ElectroBOOM [Mehdi Sadaghdar]

Yay! I might not have explained very well. You could try running over this with Belcher. I'm sure he would confirm it (his area is electrodynamics and such right?). I don't want to disagree with a professor! All my knowledge comes from one of the books he cited though, so he should agree.

One thing that confused me though was this: how are batteries any different? I think the reason is that in a battery, the charge doesn't move the whole way around (well it may, but I think that's an unimportant detail). Batteries are different I think because they're just like an advanced version of a capacitor. All the electric fields are created by charges and there's no funky stuff going on.

But I can see what you are saying. Maybe I should have been more clear. Too much detail!

ElectroBOOM [Mehdi Sadaghdar]

Well yeah, the field should die out (and then reverse direction if you turn of the supplying magnet). If the field is uniform throughout all of space then the work should be zero yeah. But in this case, the electric field points around in a circle.

That makes sense, because in such case we are dealing with a constantly rising field. Although theoretically it makes sense, that's not a real worlds scenario and the field should oscillate back. SO I wasn't really paying attention to this. In my mind both my electric and magnetic fields were fixed values we moved our charge through. And that's why I also assumed a fix field uniform in space.

ElectroBOOM [Mehdi Sadaghdar]

The energy supplied to the charge isn't coming from nowhere of course. It's coming from the magnetic field or from you as you drag the charge around the loop. So it doesn't violate conservation of energy so long as you consider all forms of energy.

(That energy that you provide is dissipated as heat of course.) The point is the work around the loop from the experiment is not zero. You can consider the work done by the fields, or against the fields. It results in the same conclusion.

For example, consider the case of the loop from the experiment. As I explained, the electromagnetic force is parallel to the wire the whole way round. If you get a charge and try to move it around against the current, you'll have to supply energy the whole way round.

If you think that the work done by or against the electric and magnetic fields around a loop is always zero, then we do disagree. Are you disputing this, or something else?

Ok. Well in that case, the work you do on the charge if you move it around a closed loop need not be zero. Consider a magnetic field moving out of the page. If a charge is moved across the page, the magnetic field will try to 'curl' the charge around in a loop. If you instead try to move the charge around in the opposite loop, you will have to supply force the whole way - the work around the loop still may not be zero.

Maybe we are not! This always happens

ElectroBOOM [Mehdi Sadaghdar]

I don't see where Feynman defines voltage that way. Feynman just uses the line integral based on what I saw in the chapter. I guess in a way, both are the same: if you define voltage as line integral around outside of the component, that value is equal to -Ldi/dt. These two views are not conflicting views. I'm not sure where we're disagreeing.

It was simple, I just said if we through a charge into fields, meaning we are providing speed and direction and then we move it in a loop. You could assume we have a charged metal ball and we move it around in electric and magnetic fields.

ElectroBOOM [Mehdi Sadaghdar]

But that's not a redefinition, what I said is what Feynman said in his book. He specifically says the voltage across the inductor is NOT integral of E.dl through the inductor, and is -Ldi/t. Yes the voltage is dependent on integral E.dl through external components, but with the same analogy we can say the voltage across external components is dependent on -Ldi/dt of an inductor. so -Ldi/dt is the real voltage! But the fact is that, there are two voltages that are equal in value because components are put in parallel, because KVL holds!

ElectroBOOM [Mehdi Sadaghdar]

Oh sorry, could you maybe summarize your scenario for me. I may have misunderstood.

That way, you can still use the E.dl definition. It also makes sense since only considering E.dl paths around the outside is literally what you do when probing it: you don't wrap your probe around the inductor!

You are changing my analogy! I just said we take a charge and move it inside fields.

ElectroBOOM [Mehdi Sadaghdar]

Well that's one way to interpret it, definitely. Redefining voltage does work to resolve the issue. I prefer what Feynman did though: just consider voltage around the outside of the component instead (only consider E.dl paths around the outside).

Ah I see now! You can't define voltage as integral of E.dl only, especially across an inductor. The voltage across the inductor (even with contained fields) is not integral of E.dl across the inductor. That's the whole point. The voltage across the inductor is -dPHI/dt = -Ldi/t

ElectroBOOM [Mehdi Sadaghdar]

The energy is dissipated in the resistors. There is a constant work that needs to be done to move the charges around through the resistors. At no point in this cycle does energy go the other way. The energy that the charges dissipate is received from the magnetic field. (One thing that used to confuse me is that this would seem to provide free energy, since you could just leave loads in the magnetic field and let them absorb energy. If you account for the countering magnetic field though, generated by the loop, it makes sense. If the loop draw a huge amount of power, it would create a massive countering field, so that you're not getting free energy).

The reason is, if you define voltage as integral E.dl (I don't believe you need to alter this definition to make KVL work), then measuring E.dl inside the component may produce results that violate KVL. However, as Feynman showed, if you measure outside the component, KVL won't be violated (assuming no leaky fields). So 'from the outside' the component still looks like a normal component with a normal, measureable voltage across it.

I'm a bit confused here. How is the work around the loop is not zero, it means we will end up with excess or lack of energy. Excess is not acceptable, because it means free energy, but also lack means we are losing energy to something. But in my model of moving a charge in a loop we don't really have a way to lose energy.

ElectroBOOM [Mehdi Sadaghdar]

Yes. If everything is contained, you can use KVL pretty nicely despite the fact that the work around a loop may not be zero - as Feynman showed.

So as long as you include the correct components into your model, KVL will work (to the extent of the accuracy of the underlying discrete model). I think Lewin does sort of have a point though. It probably helps to be aware of the 'abstractions' that your making - KVL working doesn't change the fact that the work around a loop may not be zero. It also means you need to be careful when interpreting measurements on loop from the experiment since it would be hard to understand otherwise: I suspect the measurements with 'perfect' probing may not make sense when compared to the discrete model you showed, for example.

I see. So we are on the same page, as in uncontained fields result in huge complications.

ElectroBOOM [Mehdi Sadaghdar]

You said KVL works almost always. It means it may not work some times. I need an example!

ElectroBOOM [Mehdi Sadaghdar]

What do you mean?

OK, now that you almost always, youhave to bring an example where it doesn't work!

ElectroBOOM [Mehdi Sadaghdar]

The voltage across the mutual inductor from the experiment for example doesn't correspond to a voltage you could actually measure in the usual sense (unless you ran the probe wires around the loop). Mostly though, the 'weird fields' are contained to one element so we can just think of a voltage across it in the normal way, like Feynman et al showed.

But yeah, the work around the loop isn't zero. So in that sense KVL doesn't hold. I think this is resolved by considering KVL in two lights: a physical sense and a practical sense. The fact that the voltage around a loop may not be zero doesn't change the fact that KVL works almost always since physical voltages don't necessarily correspond to voltages in a circuit model.

Yes. I'm sure that Belcher would confirm my points. Most of my knowledge comes from "Introduction to Electrodynamics" by DJ Griffiths which I think is a book that he cites. I think the mathematical steps you made around 10:40 are slightly flawed but the overall conclusion that KVL works isn't wrong. It's just that *technically* given how voltage is defined it doesn't hold. But like Feynman said, with a few assumptions, KVL can be made useful.

that should be right, considering also the walls of the wire oppose to the charge jumping outside

ElectroBOOM [Mehdi Sadaghdar]

Ok I think that explains the confusion. In my view, you assume the charges are at rest to start with. When the magnetic field changes, an induced E field is created, which applies a force on those charges. This force ends up being (at least roughly) parallel to the loop and pushes the current around it.

Oh I see, we are talking about different things. You are talking about fields moving the charges, but I'm talking about moving the charges in any angle we like in the fields.

ElectroBOOM [Mehdi Sadaghdar]

The reason a current flows in the wire is because of the changing magnetic field which creates and electric field around the wire. The current running through the wire does create its own fields (i.e., magnetic fields), but we can neglect that here. I'm not sure what you mean by "any angle". Are you referring to the fact that the magnetic field depends on the direction of the charge?

Yes Lorentz force is the only force, I just don't understand why you say it is always parallel to the wire

ElectroBOOM [Mehdi Sadaghdar]

Because the charges are flowing along the wire, so the total force on the charges is parallel to the wire. (The Lorentz force is just the electromagnetic force. If you ignore gravity et al, the Lorentz force is the ONLY force on the charges).

I don't understand, are you talking about fields created by the current running through the wire and how they place force on the moving electrons in the wire, or fields from "external sources" to the wire, effecting the charges in the wire? Because other sources can create forces at any angle, like when you put a magnet beside the wire, the wire can move away because there is a force perpendicular to the wire.

ElectroBOOM [Mehdi Sadaghdar]

EDIT: Sorry I meant "The fact that the work around the loop is NON zero is true regardless though."

The thing with classical electrodynamics is that you have to be very careful about your frame of reference. Changing your frame of reference results in the fields to behave differently. Luckily, as Einstein showed, due to special relativity, you still get the same *results* regardless. This is what prompted the unification of the electric and magnetic fields into one electromagnetic field - special relativity helps do this. I just assumed a frame of reference where the conductor was stationary to simplify it. The fact that the work around the loop is zero is true regardless though.

No I mean the electric and magnetic forces can be placed randomly.

ElectroBOOM [Mehdi Sadaghdar]

Oh by the way, when you throw a charge into electric and magnetic fields, the electric force is always directed between the two charges, and magnetic force is always directed at vXB (force is perpendicular to v) Why do you say Lorentz force is parallel to wire?

ElectroBOOM [Mehdi Sadaghdar]

The reason I mentioned the rotary E fields is to explain the fact that accounting for the magnetic force doesn't resolve the fact that the work around the loop on a charge is zero.

You mention external forces. The Lorentz force is the ONLY force that acts on the charge (unless you want to consider gravity or the other two fundamental forces!).

Sorry, I keep changing my comments because I think that they are too hard to follow. Let me phrase it like this: the Lorentz force (i.e., the total force on the charge), must be parallel to the direction of current. That means it is parallel to the the loop the whole way round and the integral of F.dl, and thus the work on the charge, cannot be zero!

If your are in the frame of reference of the stationary charges, the magnetic field does NOT act on the charges. If you are in a different frame of reference, the magnetic field DOES act on the charges. This seems inconsistent! Luckily, if you account for induced E fields also, you get the same results in both frames of reference. The fact that different phenomena seem to cause the same results in different frames of reference is what prompted Einstein to develop the theory of special relativity. It turns out that a magnetic field is just an electric field viewed from a different from of reference. I just tried to assume on frame of reference in my comments to keep it simple.

And you are right about that changing fields create rotary E fields, and that's what Dr. Belcher explains in his document. I didn't have to to explain all scenarios (video already too long) and just wanted to show that KVL and Faraday's law are pretty much the same.

ElectroBOOM [Mehdi Sadaghdar]

Oh , you added your other comments here! good. So: magnetic fields also act on stationary charges, if the field are changing. It is either fields changing or charges moving, or both!

ElectroBOOM [Mehdi Sadaghdar]

Hey you had two more long comments I was gonna read! What happened to them?! You might have confused F as E, but that F is from both E and B. And I'm talking about external sources effecting the charge. Lorentz force would be the sum of two forces at a random angle depending on how the fields are applied. And regarding taking B out of the integral, if B is perpendicular to the surface like I said, then vXB (ignoring the resulting vector) is just v.B and if B is uniform and unrelated to L, then it can come out of the integral, no? Anyway, I did tell you to take it with a grain of salt!

ElectroBOOM [Mehdi Sadaghdar]

Another note: magnetic forces only act on moving charges. Since (in your frame of reference) the charges are not moving, no current will be induced (the charges may move, but not in a way so that the magnetic force induces a current along the wire's axis). Even in a frame of reference where the conductor is moving, the magnetic force may not fully explain it. To properly model the scenario you have to realize that a changing B creates an electric field. This is what Faraday's law really says: a changing flux induces a rotational E around the loop. So it's actually the electric field and only the electric field that creates the current (in your frame of reference). This is why including the magnetic force doesn't solve the problem. The work done by the Lorentz force on a charge around the loop is still non-zero! (As I alluded to above.) Luckily, you don't need to resort to this to make KVL hold. Just do what Feynman did: assume the fields are contained in each lumped element and only draw your E.dl loops outside the elements, where KVL does hold. You don't need to 'redefine' voltage. If you do it like Feynman, you can still let V = integral E.dl AND have KVL work AND have the theoretical definition of voltage agree with what a scope would read. (If you have leaky fields, you need to model them with parasitic components obviously - or just model the whole emf around the loop with a mutual inductance like you did.)

Great video overall. I just have one issue with it. I think the reasoning at 10:48 is flawed. F.dl cannot be zero around the loop! Since the current is moving around the loop, the Lorentz force is roughly parallel to the wire the whole way round, so F.dl must sum to a non-zero quantity. (The dot isn't normal multiplication, it’s the dot product). I also disagree with your reasoning after that which leads to the correct Faraday’s law. For example, I disagree with how you took B out of the integral and discarded the cross product. The conclusion you made that Faraday = KVL by moving the term to LHS is an interesting way to think of it.

Wasn’t the point that two volt meters will have different readings? So why not simply use two oscilloscopes or two channels on one oscilloscope and show that the readings match when probed in exactly the same way?

Rav

the links should be under the main video

ElectroBOOM [Mehdi Sadaghdar]

Awesome, this points on the importance on making definitions before making statements like the one professor Lewin made, I hope he agrees with all of this, but anyways personally I learned a lot from this discussion.

Very nice -- looking forward to seeing the links on the final version to double-check

Great video, I'm glad to see that you've remained professional and respectful during this.

Wait! That's it!! It's called Grilled Cheese!! Yes, yes, that's it. So yes that's how I know that this is full of errors. I'm a Grilled Cheese expert after all, so I'm a credible source. But no, on a serious note, I feel as if he didn't give you an open minded unbiased chance, rather just dismissed your attempt to show your own findings which were contradictory to his. Just my impression on his response, which is only my opinion, which is also biased by default in defense of Medhi.

So many errors. I should know. I'm an expert on cosmetology. Err... Chemistry! No... What's it called?