#562 – Electroboom!

[bsfeechannel]

I had already envisioned a more apt analogy, a circular canal with a circulating stream of water.

Glad that you have already understood it intuitively.

The main questions seem to be where and how those forces are applied and then how and why the system would react to changes in the path, such as taking the test leads out of the plane.

Well, if you really want to go down the rabbit hole, there's no shortcut. You'll have to resort to vector calculus. This is where the intuitive approach starts to fail, I'm afraid.

[jesuscf]

Really, almost nothing?  The attached image is from 'fromjess' experiment which shows a significant voltage drop between two points in the ring.  Hard to see, but in the attached image I think it is 184mV.  You can clearly see from the video that you can measure a sizeable voltage between any two arbitrary points around the copper ring.  As he says it in the video "so we can measure positive and negative voltages all around this dial".  How do explain that now?

What is funny is that for some magic reason the copper rings generate voltages, while the resistors drop them. As if the copper rings were not resistors themselves.

I wonder what would happen if if the resistors took up all the circumference of the rings, leaving no space for the probes to move.

So much for he Lewin clock. Entertaining. But hardly scientific.

Any arbitrary section of the copper ring under the influence of the external varying magnetic field behaves as non-ideal voltage source.

EDIT: both the copper rings and the resistors behave as non-ideal voltage sources.  The resistors equivalent circuit will be a very small voltage source with a large resistance in series. The copper (or arbitrary segment of copper) equivalent circuit will be a large voltage source in series with a small series resistance.

[bdunham7]

To go back to the inductance of a partial turn, in order to talk about the flux linked you need to define a surface. So, what is the surface enclosed by a partial turn? It's a very delicate concept and it is better to leave it alone or we would need a new thread only for that.

OK, so then lets not talk about flux and surface.  Consider a straight conductor going through a toroid core, as you would see in a current transformer.  An increasing current in the coil of the current transformer should result in voltage at the ends of the rods, no?

[rfeecs]

What is funny is that for some magic reason the copper rings generate voltages, while the resistors drop them. As if the copper rings were not resistors themselves.

I wonder what would happen if if the resistors took up all the circumference of the rings, leaving no space for the probes to move.

That is explained here:

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

[bsfeechannel]

I was being sarcastic. Anyway, thanks.

[Sredni]

To go back to the inductance of a partial turn, in order to talk about the flux linked you need to define a surface. So, what is the surface enclosed by a partial turn? It's a very delicate concept and it is better to leave it alone or we would need a new thread only for that.

OK, so then lets not talk about flux and surface.  Consider a straight conductor going through a toroid core, as you would see in a current transformer.  An increasing current in the coil of the current transformer should result in voltage at the ends of the rods, no?

Straight conductors always pose problems when inductance (external, either self- or mutual) is involved.
Make a diagram with relative dimensions specified. Off the top of my head, if I understood what you mean (this is a current transformer in reverse, where a current goes through the detecting coil and you expect a charge displacement in the rod along the axis), the changing flux will produce a changing induced electric field Eind along the axis of the torus. And this will displace the charges in the metallic conductor the rod is made of, causing accumulation of positive charges on one extreme and negative on the other. At a given instant in time, the electric field of the displaced charge will be equal and opposite to the Eind field in the rod.
Total electric field in the rod is zero, and you will observe a voltage, but to measure it correctly - apart from an insanely high impedance voltmeter - you have to place the voltmeter in the 'hole' of the torus, so as not to link any of the flux in the core.

But, please, produce a drawing.

(Why this 'degenerate' example? Have you already solved all doubts about the circular ring?)
Edit: this is a bit stranger than I first thought - I am not sure there could be a voltage across the straight wire in that position. Can we bend it a little?
Edit 2: relative dimensions of the torus and the wire, which wire has current impressed.
There is no picture attached in your post below.

[jesuscf]

I was being sarcastic. Anyway, thanks.

Sorry, I thought you were asking sincerely.  A resistor under the influence of the external varying magnetic field also behaves as non-ideal voltage source.

[bdunham7]

Total electric field in the rod is zero, and you will observe a voltage, but to measure it correctly - apart from an insanely high impedance voltmeter - you have to place the voltmeter in the 'hole' of the torus, so as not to link any of the flux in the core.

But, please, produce a drawing.

(Why this 'degenerate' example? Have you already solved all doubts about the circular ring?)

Why does the voltmeter impedance matter?  If it does, just consider the ideal voltmeter with infinite impedance, since this is theoretical and we have ideal components elsewhere.  If that is problematic, then voltmeters can be provided with some pretty high input impedances, certainly high enough to not matter much in this case.

Drawing attached.  I don't know that I have any doubts about the original circular ring, I think the issues lie elsewhere.  But please, tell me if the drawing matches what you were thinking and responding to.

Edit:  I'm sorry, I didn't specify actual numerical dimensions because I didn't have any specific ones in mind.  Which dimensions are necessary?

[Sredni]

There is no drawing attached that I can see.
You probably did not see the edits I made in my previous message.

Anyway, the more I think about it, the more I hate partial coils, especially straight wires. We need to go around the core to see a voltage that we can measure in the gap. When there are only partial turns, we usually complete the link with the probes, so we cannot measure the voltage of a partial turn (the multitap transformer discussed in another page). We can compute the contribution of partial inductance as path integrals of the vector potential. I am not sure it's possible to measure partial contributions.

[bdunham7]

Sorry, here's the drawing.  I'd like the rod to stay straight for now just so I can see where this goes. 

Dimension, lets have the rod be 1cm diameter x 100cm long, the torus can be 10cm OD, 8cm ID and 1cm height.  There can be 10 windings and the current can be increasing at 1000A/s.  Or any other numbers that are convenient.  The rod can be copper or iron.

We can compute the contribution of partial inductance as path integrals of the vector potential. I am not sure it's possible to measure partial contributions.

How you define and measure voltage is certainly germane.  But saying you can't measure the voltage of part of a turn, presumably because your test leads are subject to a field that exactly counteracts the partial contribution is different than saying that the voltage isn't there.  That's a definitional issue.  I have a couple of ideas, but I'd like your take on this first.

[Sredni]

there are too many degeneration to give a quick answer. Partial turn, straight wire, in the middle of the torus... I need to work out the actual induced field of a toroidal core.

Partial turn is a problem because it does not link any flux per se.
Straight wire is a problem because it does not have external inductance.
Middle of the torus is a problem because if we consider a filamentary current, the field is curl free... and this is related to the fact that there is no area associated to a segment. And if I go to infinity, we have all planes to choose.

Interesting problem, but unnecessary to understand the Faraday-Kirchhoff dispute.

I need to think about it. For the moment I tell you this about the inability to measure.
You can have a voltage across a straight piece of wire in a nonconservative field due to the displaced charge, but you might not be able to measure it because you always complete a loop when you place the instrument across it. So you end up either linking the whole emf or none of it. This is why I hate partial turns. But when you complete the loop with your probes and the internal resistance of the voltmeter, you remove the charge from the extremes of your piece of wire and place them at the interfaces with the internal resistance of the voltmeter. So, there no longer is a voltage once you close the circuit, and even with an infinite resistance voltmeter, you still have to complete the circuit with the probes so you won't be able to read for example 1/10th of the emf. You will read the whole emf.

And this is what happens with the voltmeters at the exterior of Lewin's ring as well. When you consider the loop formed by the farthest resistor, you complete the half ring with your probe and read the whole EMF: and in fact the voltage of the far resistor is altered by one emf; we say we use Faraday. When you consider the loop formed by the nearest resistor, you complete the other half-ring with your probes but this time you do not link the emf (or, if you will, you link 0 times the EMF), and we can be sure that the voltmeter reads the voltage across that branch; we say we use KVL on this loop.

Would it be the same to consider a straight rod near an infinite solenoid? For that I have the analytical expressions of the fields, it's a tad less degenerate case.
I'll have some sleep first.

[bsfeechannel]

A resistor under the influence of the external varying magnetic field also behaves as non-ideal voltage source.

But, but, but, but fromjesse said that the copper rings generate voltages, while the resistors drop it! How can I properly learn Ohms law, KVL, good probing and oscilloscope operation if you guys keep contradicting each other? Aw, unbelievable!

[bsfeechannel]

Interesting problem, but unnecessary to understand the Faraday-Kirchhoff dispute.

I guess this is an important issue since KVLers out there are claiming that the wires in the loop are standalone inductors that generate voltage to the circuit. This may come from the fact that you can actually calculate the inductance of a straight stretch of wire. You can but there's an implicit assumption that they do not consider. Since the the magnetic field intensity generated by the current in the wire is inversely proportional to the distance from the wire, just consider a rectangle whose one of the sides is the wire, and whose width is a distance for which the magnetic field intensity is negligible. That's the area you will consider for the calculation of the induced voltages around this rectangle. So you are assuming that this piece of wire will be somehow part of a circuit whose return path will be sufficiently away from it.

A stretch of wire very close to a return ground plane for instance will have to be calculated taking into consideration this geometry and will of course have an inductance that will be very different from the same piece wire hanging out in the breeze.

In short, the wire is never consider alone. It is implicitly considered part of a complete loop.

[thinkfat]

So, what is wrong with measuring voltages correctly?  The experiment is there: the voltages add to zero.  KVL holds if you know how to measure voltages in a varying magnetic field.  Lewin didn't measure in his experiment correctly and he got the wrong conclusions from his results.  RSD Academy summarizes it nicely:

"Dr. Lewin is disagreeing with the vast majority of the scientific establishment, he's disagreeing with the vast majority of textbooks, he's  disagreeing with the vast majority of professors of both electrical engineering and physics and his postulation that Kirchhoff's voltage law doesn't hold is based on a incorrect application of ohm's law not knowing how ohm's law has to be applied to a voltage source.  Then he performs an experiment to prove his premise but he doesn't take precautions to make sure that the magnetic fields don't affect his measurements."

I don't think there's a "correct" way or a "wrong" way to measure the voltages. Every outcome of the experiments, be it from Lewin or "Electroboom" or Mabilde or "fromjesse" can be explained with Faradays law. What is also undeniable is that the measurement instruments and their arrangement are inevitably part of the experiment. There is no "magic probe" you could poke anywhere and have a result that is independent of the setup.

Fun fact: in Lewins experiment, and also in the MIT Courseware video, the probe leads _may_ be affected by the magnetic flux, but since the path they're taking is only through a "conservative" region of the electric field, the effect cancels itself out.

Anyway, this is becoming really quite academic. I understand why engineering minded people try to avoid this stuff like the plague, after all the whole electronic industry is trying hard to confine those effects within the boundaries of components and rather work with transformers described by datasheet values instead of diving into vector analysis and calculus. It is really only to keep the "magic" contained in small boxes that can be linked together in a way that lets you forget that fields exist and only need circuit theory and KVL to get by. As soon as Physics enters the stage, the hurt starts. That's why RF and "high speed design" is considered "black magic", because you cannot get by without considering Physics. I think it's good that there are Dr. Lewins out there to remind us that blind application of method will fool you.

PS: Dr. Lewin is not incorrectly applying Ohms law. He just doesn't consider any discrete part of the loop being a "voltage source", because he doesn't attempt to "lump" the circuit to apply KVL.

[thinkfat]

Humor me, guys. See the attached picture. All wires are actual wires and interact with fields, but have negligible resistance. R1 can be any value, I don't think it matters. Assume EMF=1V. Predict the voltages shown on V₁ and V₂, using KVL and Faradays Law.

[rsjsouza]

(this post is just to tag this thread to show up in my updated threads list, which I have been following with interest. Nothing new I can contribute at the time. Sorry about the noise. Carry on...)

[bdunham7]

In short, the wire is never consider alone. It is implicitly considered part of a complete loop.

That may make your theory and math work out more clearly to you, but I think it is a mistake.  It's true that, for example, a wire going straight through a current transformer is considered to be 1 turn because there is typically a return wire somewhere, but that's not why it actually works.  The interaction between a varying magnetic field and the charges in a wire is a local (microscopically so) effect and Faraday's Law is a mathematically proven observation that says that for a given area and a varying total flux through the area, the EMF around the perimeter area adds up to a number, and that number only depends on the rate of change of the total flux.  So, for example, it doesn't matter where in the toroid of the current transformer the wire is, it still reads the same because...math.  And in the Lewin device, it doesn't matter if the solenoid is off center, the total EMF on the ring adds up to the same amount.  That doesn't mean that the EMF is always evenly distributed nor that we can always consider it only as a total around the perimeter.  It so happens that for a CT and for the Lewin device with resistors, perhaps you can ignore local differentials.  Can we imagine a circuit where the local variations do matter? 

[jesuscf]

A resistor under the influence of the external varying magnetic field also behaves as non-ideal voltage source.

But, but, but, but fromjesse said that the copper rings generate voltages, while the resistors drop it! How can I properly learn Ohms law, KVL, good probing and oscilloscope operation if you guys keep contradicting each other? Aw, unbelievable!

Nice try at deflection.  There is no contradiction.  Here it is again so you can understand:

1) thick wire = large voltage; very small resistance

2) tiny resistor = very small voltage; large resistance

That is why fromjesse used SMT resistors and wide copper tape.  Did Lewin used tiny resistors and thick wire in his experiment?  I doubt it!  This should also answer your previous question about making a ring with only resistors in series.

[Sredni]

In short, the wire is never consider alone. It is implicitly considered part of a complete loop.

That may make your theory and math work out more clearly to you, but I think it is a mistake.  It's true that, for example, a wire going straight through a current transformer is considered to be 1 turn because there is typically a return wire somewhere, but that's not why it actually works.  The interaction between a varying magnetic field and the charges in a wire is a local (microscopically so) effect

This locality thing is something I hear from time to time. Some of the people who bring it up tend to think to Maxwell's equations as vector algebraic equations. They are not. They are vector partial differential equations, and as such they need boundary conditions.
So, if your experiment with the straight wire was just to show that (dang, I was trying to get a quantitative answer...), well I'm sorry but I have to inform you that the information about a piece of wire alone is not sufficient to predict how it will behave in a complete circuit. You can treat it as it is and show that there is charge displacement - probably with a sensitive electrometer. But when you put it in a circuit it's the whole circuit that dictates how it will behave. For example, a piece of straight wire inside the variable magnetic zone can have current flowing from extreme A to extreme B if it part of a certain loop, and current flowing from B to A if it is part of another loop. In any case, the charge that was there when the rod was stand-alone, is no longer there when it's part of a circuit.

I stand by my position: you can see charge at the extremes, but if you try to measure the voltage with a voltmeter you will necessarily end up linking integer multiples of the EMF. And this applies to, say, a 3/4 loop of wire around the core. There's no need to invoke the degenerate case of straight wire. Any partial turn will do.

As I said before, the concept of partial inductance is a very delicate one and that is why I am reluctant (pun!!!) to discuss it in this context. It will confuse KVLers even more and it will lead to endless thought experiments that seem to validate the idea that the wires behaves as batteries. They do not. Look at the fields. Look at the total electric field in your circuit or even rod and compute the path integral to find the voltage. There is the answer.

[bdunham7]

but if you try to measure the voltage with a voltmeter you will necessarily end up linking integer multiples of the EMF.

OK, last question before I actually present something on the locality issue.

Do you need to use a voltmeter (with test leads) to measure voltage?

 

[Sredni]

Interesting problem, but unnecessary to understand the Faraday-Kirchhoff dispute.

I guess this is an important issue since KVLers out there are claiming that the wires in the loop are standalone inductors that generate voltage to the circuit. This may come from the fact that you can actually calculate the inductance of a straight stretch of wire.

Yes, I understand that the point he's trying to discuss is that "if it behaves as a tiny battery because it displace charges, then why can't wires be thought as batteries". But it does not matter the the piece of wire be straight and in the dead center of the torus. I was thinking how to derive the whole Eind field of a toroidal transfomer with increasing current in the whole space. At this point, if the objection he is trying to make is the one above, I can use a piece of wire in the field of an infinitely long solenoid. The answer is the same: the wire will experience the Eind rotational field, it will displace charge (with relaxation times, instant after instant) and it will make the total electric field inside it zero. Voltage computed as path integral of Etot along the rod is zero. Voltage computed as path integral of Etot in the space around the rod from the same endpoints will not be zero EDIT post-nap still be zero on paths that do not go around the core, and will be the full EMF for paths that do go around the core. See my answer post-nap on the next page.
But when the rod is part of a closed circuit there no longer is charge at its extremes, it has been 'conducted' away to eventual discontinuities in resistivity or permeability. So the tiny battery is no more. You can see the charge at the open terminals of the coil the tiny rod belongs to, or at the interfaces with the resistor that represents either the load or the internal impedance of the voltmeter. But tiny rod is no more a battery.

Regarding partial inductance, I reiterate my reluctance in discussing it in this venue. It will only be a distraction. But I do agree with you (and Bruce Archambeault) that "the concept of inductance, without defining a complete loop of current, is completely meaningless!". I could make only one exception with regard to the straight wire: it does have an internal inductance per unit length. The reason internal inductance can be defined is that you can limit the surface through which you consider the flux: it's delimited by the lateral surface of the rod itself. For a cylindrical conductor you get the well know mu/8pi henries per meter. But, before the KVLers get too excited - that is self-inductance and is usually much smaller than the external inductance which, in Lewin's experiment, has negligible effects.
And yes, I agree on the method to compute partial inductance of a segment of wire, even if I prefer converting the surface integral into the path integral of A (which ends up vanishing at infinity and give no contribution of the 'lateral' sides). But a segment in the dead center of a toroid left me a bit confused as to which direction to use to go to infinity. Never mind.
To sum up my opinion on partial inductance: to me it is just a bean-counting tool that helps identifying which parts of a loop (for which we can talk about proper inductance) contribute the most EMF. But that EMF - as we know - is no longer there once you consider the interaction with the charges that have been displaced.

[rfeecs]

In short, the wire is never consider alone. It is implicitly considered part of a complete loop.

That may make your theory and math work out more clearly to you, but I think it is a mistake.  It's true that, for example, a wire going straight through a current transformer is considered to be 1 turn because there is typically a return wire somewhere, but that's not why it actually works.  The interaction between a varying magnetic field and the charges in a wire is a local (microscopically so) effect and Faraday's Law is a mathematically proven observation that says that for a given area and a varying total flux through the area, the EMF around the perimeter area adds up to a number, and that number only depends on the rate of change of the total flux.

Yes, so to consider it locally you look more at the differential form of Maxell's equations instead of the integral form.

For your example with the wire segment in the middle of the toroid coil, consider the plane going through the wire.  The electric field goes in a circular direction around the magnetic cores, so two sets of ellipse shapes.  If the wire is at the center, the electric field there would be straight along the wire.

The wire is a good conductor, so it has net zero electric field inside the wire.  At the surface the tangential field must be zero.  So the charge in the wire must arrange itself to counteract the electric field.  This results in the charges moving to the ends of the wire.  One end will be positively charged, the other negative.

So now you know what the fields are and what the charge distribution is.  Problem solved.

What about voltage?  The voltage depends on path.  If you measure the voltage from one end of the wire to the other through the wire, it is zero.  If you measure by taking a path around the magnetic core, you will get the EMF.  If you measure by taking a path that does not go around a magnetic core, you get zero.

By "measure"  you could use a voltmeter, then the "path" is determined by the path of the test leads.

Another theoretical way to "measure" is to take a test charge and move it along a path and integrate the force with distance to get the potential difference.  This is E dot dl.  You don't need an actual wire to "measure" this way, and you don't need a closed loop.

Looks like Sredni posted while I was typing this so he beat me to it.

[Sredni]

but if you try to measure the voltage with a voltmeter you will necessarily end up linking integer multiples of the EMF.

OK, last question before I actually present something on the locality issue.

Do you need to use a voltmeter (with test leads) to measure voltage?

 

If you are able to measure intensity and direction of the electric field in all points of the path you want the voltage computed without disturbing the fields, no. You can create an instrument that computes the integral for you.
In circuits you usually attach a voltmeter to measure a voltage. What instrument do you use on your bench?

[bdunham7]

For your example with the wire segment in the middle of the toroid coil, consider the plane going through the wire.  The electric field goes in a circular direction around the magnetic cores, so two sets of ellipse shapes.  If the wire is at the center, the electric field there would be straight along the wire.

The wire is a good conductor, so it has net zero electric field inside the wire.  At the surface the tangential field must be zero.  So the charge in the wire must arrange itself to counteract the electric field.  This results in the charges moving to the ends of the wire.  One end will be positively charged, the other negative.

So now you know what the fields are and what the charge distribution is.  Problem solved.

What about voltage?  The voltage depends on path. 

So there's the crux of the problem.  My straight wire, or any partial loop for that matter, ends up with charged ends, which outside of the particular conditions at hand would be considered to be a voltage and could be measured with traditional test instruments.  So what is a voltage? 

[Sredni]

So, for example, it doesn't matter where in the toroid of the current transformer the wire is, it still reads the same because...math.  And in the Lewin device, it doesn't matter if the solenoid is off center, the total EMF on the ring adds up to the same amount.  That doesn't mean that the EMF is always evenly distributed nor that we can always consider it only as a total around the perimeter.

Who ever says that the EMF is evenly distributed? What is evenly distributed in the conductor is the total electric field. If the ring is off center so that Eind is not tangentially directed in the ring then you will have surface charge on the lateral surface of the conductor that will produce the correct Ecoul that will obliterate it.

We always get to the same point: the induced field is no longer there, in the conductor.
When you and bsfeechannel talked about the channel with rotating current model, you find an effective way to exemplify path dependance, but do not be fooled, that model does not exemplifies what happens in the ring. The resistors (or the gap in the naked coil) will have charge that will neutralize Eind in the conductor, and this is something that is not modeled in the rotating current model, because you would need something that neutralized the flow in the channel.
(I'm writing this in a hurry because I have things to do, but I hope it is clear that what happens in the ring, and what is sorely missed in the KVLers' view, is this compensation effect by the displaced charge. That is the constantly missing piece to correctly interpret the phenomenon.)