#562 – Electroboom!

[HuronKing]

But at this point in time they can base their view of classical electrodynamics on about 150 years of careful refinement by some of the most brilliant minds of the whole planet. So, I'll take that above what Maxwell (which was an absolute genius, but was also pioneering a new field) had to say in 1865. The ether is one glaring example.
A more refined view of classical electrodynamics in a less glaring one, and in fact...

Even in the context of Maxwell's work, there were things corrected in the decades following his treatise by Oliver Heaviside,

In his Treatise, Maxwell had built his theory around the vector and scalar potentials A and Ψ. They did not locate the energy correctly, however, and Heaviside regarded them as quite distant from the real workings of the field. He proceeded to work back from his energy-flow formula to find a new set of basic equations, equivalent to those in Maxwell’s Treatise but based directly on E and H and so better suited to treating energy flow. By combining two of Maxwell’s expressions relating the vector potential A to the fields E and H, Heaviside derived what he called the “second circuital law,” which related the curl of E directly to the rate of change of H—a fitting partner, he said, for Maxwell’s “first circuital law” relating the curl of H to E and its rate of change (see the box on page 53). By combining them with Maxwell’s expressions for the divergence of the electric displacement D and the magnetic induction B, Heaviside arrived at the compact set of four vector relations we now know as Maxwell’s equations.

https://physicstoday.scitation.org/doi/10.1063/PT.3.1788

But even the great Oliver Heaviside who gave us the modern formulation of Maxwell's Equations then went on to pretty famously dispute special relativity when he learned about it.

In the context of this discussion it's remarkable how much the KVL-Always-Holder depends on the appeal to authority and the quote-mining. It reminds me of anti-evolution proponents I've come across who run around quoting Darwin as if The Origin of Species is still, somehow, the state of the art understanding of the Theory of Evolution. And as I discovered many pages ago - vector calculus and non-conservative fields are utterly mysterious to the KVL-Always-Holder.

[Sredni]

The pretty much cancel each other in the conductor leaving an almost zero net electric field inside.

Right there is where you are wrong!  In Lewin's ring the the induced emf is evenly distributed in the conductors and resistors.  He failed to include that emf in the equivalent circuit, that is why he incorrectly concluded that KVL doesn't work.

So... is Belcher wrong?


Source: Belcher's note available on Electroboom's channel

Because he too gets (basically) zero net field in the copper wires.

[jesuscf]

Wanna see another professor doing the same as Belcher, and Lewin? Micheal Melloch of Purdue University - the same Micheal Melloch whose videos Jesse Gordon has linked in the comments of his videos on Lewin's ring. Too bad he is doing what Lewin (and Belcher!) is doing:

Faraday's Law Example 4 (Electromagnetic Induction) 

This is the fourth of four examples of the application of Faraday's Law. A current is ramped in a solenoid to produce circles of electric field intensity around the solenoid. The solenoid is surrounded by a conducting ring where the left half of the ring has a higher conductivity than the right half of the ring. What is observed is charge buildup at the boundaries between the two materials.

 

The charge buildup at the boundaries between the materials is what you KVLers are unable to see.
It's like glass for birds, or storks.

Excellent, I was waiting for something like this.  Now, here is a question for you:  what would happen if you replace the resistors with capacitors.  Say, instead of the 100 ohm resistor place  a 100nF capacitor, and instead of the 900 ohm resistor place a 10nF capacitor.  What would be the voltage between nodes A and D, V_AD at steady state?   Spoiler alert: I did that experiment a few weeks ago and it looks very, very bad for team Lewin!

This is another common trait of believers: once they are cornered that change the topics to something new, so that the debunking has to start from scratch and they can bask in the illusion that this time they could be right.

First is the ring with two resistors joined by conductors. Then the ring with two resistors and a battery. Then the ring with two resistors without conductors in between. Then the uniform resistive ring. Then the perfectly conducting ring. I have seen in the other thread the ring with a transitor in the loop. Now it's the two capacitors in a loop. What is next? A Josephson junction?

Two capacitors in a loop can lead to some nasty paradoxes. Will this invalidate the easily explained ring of just two resistors? Logic dictates that no, it won't. But believers are renowned for not being very good in applying logic.

That is where you are massively wrong.  If your theory is correct it must predict what happens when you change something in the experiment, and that prediction must perfectly match experimental results.  That is what KVL does every single time!!!  So go ahead, make your prediction!

By the way, if these small changes to the circuit upset you, I have another circuit that will completely  freak you out!  (And KVL still works!!!).

[jesuscf]

The pretty much cancel each other in the conductor leaving an almost zero net electric field inside.

Right there is where you are wrong!  In Lewin's ring the the induced emf is evenly distributed in the conductors and resistors.  He failed to include that emf in the equivalent circuit, that is why he incorrectly concluded that KVL doesn't work.

So... is Belcher wrong?


Source: Belcher's note available on Electroboom's channel

Because he too gets (basically) zero net field in the copper wires.

You are confusing electric field with voltage.

[jesuscf]

But at this point in time they can base their view of classical electrodynamics on about 150 years of careful refinement by some of the most brilliant minds of the whole planet. So, I'll take that above what Maxwell (which was an absolute genius, but was also pioneering a new field) had to say in 1865. The ether is one glaring example.
A more refined view of classical electrodynamics in a less glaring one, and in fact...

Even in the context of Maxwell's work, there were things corrected in the decades following his treatise by Oliver Heaviside,

 I am pretty sure Heaviside says exactly the same as Maxwell about EMFs and Faraday's law.

[bsfeechannel]

Maybe for you.  Hence the importance of a formal education,

Which you don't have.

where with the proper guidance not only the correct knowledge is acquired in a timely manner,

Yeah. Become an electronics engineer in just six months. Apply here!

but the BS that characterizes team Lewin is weeded out.

If you really had a formal education in electronics engineering...

Very well genius: explain what is it a non-conservative field, in the context of Lewin's ring!

...you wouldn't be asking me to explain to you what a non-conservative field is.

[HuronKing]

Very well genius: explain what is it a non-conservative field, in the context of Lewin's ring!

...you wouldn't be asking me to explain to you what a non-conservative field is.

Robert Romer's paper explains exactly what is non-conservative about the Lewin ring. I suggest jesuscf rereads it. I had to take a semester long course in vector calculus to understand this. Kudos to anyone who can truly understand the mathematics (and all the prerequisites) required for this in a couple of weeks! Even more so if they retain this knowledge. Some of the EE students I teach have already forgotten a lot of the vector calculus by the time they get to my lab courses on power machinery.
http://www.fisica.uns.edu.ar/albert/archivos/15/119/420063006_tp_y_guias.pdf

[thinkfat]

That is where you are massively wrong.  If your theory is correct it must predict what happens when you change something in the experiment, and that prediction must perfectly match experimental results.  That is what KVL does every single time!!!  So go ahead, make your prediction!

On that thought, why don't you retry your experiment with the resistor ring with a slight change, so that the magnetic flux geometry isn't in complete symmetry with your ring, but slightly off-center? Trevor Kearney suggested this as a challenge to those who support the idea of the scalar PD between two points being the "unique" voltage in the "Lewin Ring".

You will find that the "tiny voltage sources" in your circuit suddenly have a different value in every little piece of the wire and that for anything but the most trivial geometries you will need a numeric EM field solver and a model perfectly matching you circuit, to calculate that voltage. That in itself is not problematic, what is the much bigger problem is that you will not be able to quantify the uncertainty in your calculation, because you cannot know how close your numeric model is to reality.

The next problem will be to actually measure the "unique voltage" as a proof for your models accuracy, because now your measurement setup will have to use real-world wires and all the electric fields you measure will of course depend on the path of those wires relative to the magnetic flux. So what do you do now? You already don't know to what degree you can trust your calculation (or simulation) and then you don't know if any discrepancy between the voltage you measure and your calculation is due to "bad probing" or "bad modeling". For an engineer, that's not a good point to be.

And it doesn't end there. The next problem will be repeatability, as any small change in geometry will throw off your calculation and measurements again.

The beauty of the Maxwell-Faraday equation is that is requires no knowledge about the magnetic flux or path geometry. It just requires that the path be closed (that's what the "circle" in the Integral sign means) and then gives a perfect relation between the "voltage" you measure and the time-varying magnetic flux in the area enclosed by said path and the only uncertainty is how precisely you can measure the voltage. The only snail to swallow is accepting that voltages can be non-unique and will depend on the path you measure them on.

[ogden]

So, according to your logic in Lewin's ring, the wire on the top has half the induced EMF and the wire at the bottom has half the induced EMF.  So, can you now can compute the voltage V_AD?

There is the EMF contribution of Eind, but there is also the scalar potential contribution of Ecoul. And guess what? The pretty much cancel each other in the conductor leaving an almost zero net electric field inside. Perfectly compliant with Ohm's law. The same superposition leaves a perfectly Ohm compliant resultant E field in both resistors. But being the resistance different, the field inside will be different as well.

Now, let's do 2+2: on branch 1 we have 0 field in the upper arc of conductor, strong E1 field inside the R1 resistor, and 0 field in the lower arc of conductor. The voltage is the same as that along the resistor alone: Vad1 = E1*deltaL, where deltaL is the length of the resistor.
In branch 2, for the same reasons we have Vad2 = E2*deltaL. Since the net electric field is different in the two resistors, we get Vad1 != Vad2

Hopefully you do agree that battery is EMF source, right? If solenoid does not influence voltmeter leads in Romer's/Lewin's circuit then it does not matter what kind of EMF source we are using, right? So, I take 1.5V button-cell battery with internal 100 Ohm resistance and bigger 1.5V battery with 10 Ohms internal resistance, connect them "in series" (yes, small battery is reversed). You say that somehow we can measure different voltages between two points where batteries are connected together - we place voltmeter next to button cell battery, it shows one voltage then we move voltmeter to other side next to bigger battery and we have different reading? Wow Yes, this is what Romer and Lewin are trying to prove, just with other kind of EMF source rather than batteries.

[Sredni]

Hopefully you do agree that battery is EMF source, right?

A localized EMF source, to be precise.

If solenoid does not influence voltmeter leads in Romer's/Lewin's circuit then it does not matter what kind of EMF source we are using, right?

It matters quite a lot if the difference in between localized and distributed sources.

So, I take 1.5V button-cell battery with internal 100 Ohm resistance and bigger 1.5V battery with 10 Ohms internal resistance, connect them "in series" (yes, small battery is reversed). You say that somehow we can measure different voltages between two points where batteries are connected together - we place voltmeter next to button cell battery, it shows one voltage then we move voltmeter to other side next to bigger battery and we have different reading? Wow Yes, this is what Romer and Lewin are trying to prove, just with other kind of EMF source rather than batteries.

You can redo your experiment for localized EMF sources using two localized inductive EMF sources. One lumped secondary on the left, one lulmped secondary on the right and you will see that voltage won't be path dependent.

[Sredni]

If your theory is correct it must predict what happens when you change something in the experiment, and that prediction must perfectly match experimental results.

Again: this is not my theory.
I wish it was. But not even in a thousand years I would be able to come up with such elegant, coherent and comprehensive theory. I can barely see beyond the shoulders of those giants who crafted it.

Yes, I can find what happens when you put two capacitors in a loop around a magnetic core. But the idealization of perfect conductors in between them could lead to problems. I suppose I can add a small finite resistance in the wires, and I will have a look a this problem because I find it interesting.
I cannot but notice that you did not specify the sort of excitation: is it a pulse (I guess it will lead to a short-lived oscillation), or a sinusoidal signal (we will end up with a capacitive divider, if there are no surprises), or worse a linearly changing magnetic flux that would try to force a constant current in the capacitors (this I have to think about)?
My take is that you did the experiments with a sinusoidal excitation. Is that correct?

But why is it that it's always "team Lewin" that has to solve your problems, while you guys never answer questions?

[ogden]

Hopefully you do agree that battery is EMF source, right?

A localized EMF source, to be precise.

There is no problem to make two "distributed' batteries that resembles physical layout of Dr.Levin's test circuit. So what?

You can redo your experiment for localized EMF sources using two localized inductive EMF sources. One lumped secondary on the left, one lulmped secondary on the right and you will see that voltage won't be path dependent.

How about more than half-turn of Lewin's transformer? Let's say, one full turn for each "resistor"? According to your logic it automagically becomes localized EMF source and voltages are not path-dependent anymore?

[Sredni]

There is no problem to make two "distributed' batteries that resembles physical layout of Dr.Levin's test circuit. So what?

The problem is that if you replace the battery with say 100 tiny batteries, you are still using lumped localized batteries. You will no longer have simple conducting wires connecting the resistors.

How about more than half-turn of Lewin's transformer? Let's say, one full turn for each "resistor"? According to your logic it automagically becomes localized EMF source and voltages are not path-dependent anymore?

You need to see where the variable magnetic region is, with respect to the circuit path.
Inside.
Outside.
They are different concepts.

[jesuscf]

Maybe for you.  Hence the importance of a formal education,

Which you don't have.

where with the proper guidance not only the correct knowledge is acquired in a timely manner,

Yeah. Become an electronics engineer in just six months. Apply here!

but the BS that characterizes team Lewin is weeded out.

If you really had a formal education in electronics engineering...

Very well genius: explain what is it a non-conservative field, in the context of Lewin's ring!

...you wouldn't be asking me to explain to you what a non-conservative field is.

I know what a non-conservative field is.  Now, you tell me, let see if we are talking about the same thing.

[jesuscf]

Very well genius: explain what is it a non-conservative field, in the context of Lewin's ring!

...you wouldn't be asking me to explain to you what a non-conservative field is.

Robert Romer's paper explains exactly what is non-conservative about the Lewin ring. I suggest jesuscf rereads it. I had to take a semester long course in vector calculus to understand this. Kudos to anyone who can truly understand the mathematics (and all the prerequisites) required for this in a couple of weeks! Even more so if they retain this knowledge. Some of the EE students I teach have already forgotten a lot of the vector calculus by the time they get to my lab courses on power machinery.
http://www.fisica.uns.edu.ar/albert/archivos/15/119/420063006_tp_y_guias.pdf

Ok, then in three small sentences or less explain where the non-conservative field is in Lewin's ring.

[jesuscf]

That is where you are massively wrong.  If your theory is correct it must predict what happens when you change something in the experiment, and that prediction must perfectly match experimental results.  That is what KVL does every single time!!!  So go ahead, make your prediction!

On that thought, why don't you retry your experiment with the resistor ring with a slight change, so that the magnetic flux geometry isn't in complete symmetry with your ring, but slightly off-center? Trevor Kearney suggested this as a challenge to those who support the idea of the scalar PD between two points being the "unique" voltage in the "Lewin Ring".

You will find that the "tiny voltage sources" in your circuit suddenly have a different value in every little piece of the wire and that for anything but the most trivial geometries you will need a numeric EM field solver and a model perfectly matching you circuit, to calculate that voltage. That in itself is not problematic, what is the much bigger problem is that you will not be able to quantify the uncertainty in your calculation, because you cannot know how close your numeric model is to reality.

The next problem will be to actually measure the "unique voltage" as a proof for your models accuracy, because now your measurement setup will have to use real-world wires and all the electric fields you measure will of course depend on the path of those wires relative to the magnetic flux. So what do you do now? You already don't know to what degree you can trust your calculation (or simulation) and then you don't know if any discrepancy between the voltage you measure and your calculation is due to "bad probing" or "bad modeling". For an engineer, that's not a good point to be.

And it doesn't end there. The next problem will be repeatability, as any small change in geometry will throw off your calculation and measurements again.

The beauty of the Maxwell-Faraday equation is that is requires no knowledge about the magnetic flux or path geometry. It just requires that the path be closed (that's what the "circle" in the Integral sign means) and then gives a perfect relation between the "voltage" you measure and the time-varying magnetic flux in the area enclosed by said path and the only uncertainty is how precisely you can measure the voltage. The only snail to swallow is accepting that voltages can be non-unique and will depend on the path you measure them on.

But will KVL hold after everything you listed above?  Of course yes!  Furthermore, the voltage potential difference between two arbitrary nodes will be a unique scalar at any fixed time t.   Do you understand the difference of the voltage between two nodes and the voltage you measure between those two nodes?  As soon as you measure the voltage in any circuit, the instrument is modifying the circuit, and if you don't account for that, the results you get may be so baffling as to make you proclaim that "KVL is for the birds".

[thinkfat]

Ok, then in three small sentences or less explain where the non-conservative field is in Lewin's ring.

\${\nabla \times E = -\frac{\partial B}{\partial t}}\$
Hint: left side of the equation.

[jesuscf]

If your theory is correct it must predict what happens when you change something in the experiment, and that prediction must perfectly match experimental results.

Again: this is not my theory.
I wish it was. But not even in a thousand years I would be able to come up with such elegant, coherent and comprehensive theory. I can barely see beyond the shoulders of those giants who crafted it.

Yes, I can find what happens when you put two capacitors in a loop around a magnetic core. But the idealization of perfect conductors in between them could lead to problems. I suppose I can add a small finite resistance in the wires, and I will have a look a this problem because I find it interesting.
I cannot but notice that you did not specify the sort of excitation: is it a pulse (I guess it will lead to a short-lived oscillation), or a sinusoidal signal (we will end up with a capacitive divider, if there are no surprises), or worse a linearly changing magnetic flux that would try to force a constant current in the capacitors (this I have to think about)?
My take is that you did the experiments with a sinusoidal excitation. Is that correct?

Yes, please make the excitation sinusoidal.  It is easier to calculate (actually trivial), test, and measure.  Assume the amplitude of the induced emf is again 1V.

But why is it that it's always "team Lewin" that has to solve your problems, while you guys never answer questions?

Because team Lewin doesn't make experiments or perform measurements.

[ogden]

There is no problem to make two "distributed' batteries that resembles physical layout of Dr.Levin's test circuit. So what?

The problem is that if you replace the battery with say 100 tiny batteries, you are still using lumped localized batteries. You will no longer have simple conducting wires connecting the resistors.

No. I suggested to make long, two curved batteries that resemble experiment configuration. Anyway result of curl integral does not change - you have long battery, tiny battery with long terminals or 100 tiny batteries in series. I do not see where you are going-to with your argument anyway.

How about more than half-turn of Lewin's transformer? Let's say, one full turn for each "resistor"? According to your logic it automagically becomes localized EMF source and voltages are not path-dependent anymore?

You need to see where the variable magnetic region is, with respect to the circuit path.
Inside.
Outside.
They are different concepts.

Not wat I did mean. Think transformer where you connect (short) one to another two secondary windings, one made out of 10 Ohms wire single turn, another out of 100 Ohms wire turn. Connections are made at one side of transformer. Question: voltages in those two windings are path-dependent or not?

[jesuscf]

Ok, then in three small sentences or less explain where the non-conservative field is in Lewin's ring.

\${\nabla \times E = -\frac{\partial B}{\partial t}}\$
Hint: left side of the equation.

Yes, but the right part of the equation makes it conservative again!  The only way it will be non-conservative is if you do this:

\${\nabla \times E = 0}\$

Which is what Lewin define as KVL for any circuit (but only works with DC).  But Maxwell says that for KVL you need to include all EMFs, including induced EMFs!

[thinkfat]

That is where you are massively wrong.  If your theory is correct it must predict what happens when you change something in the experiment, and that prediction must perfectly match experimental results.  That is what KVL does every single time!!!  So go ahead, make your prediction!

On that thought, why don't you retry your experiment with the resistor ring with a slight change, so that the magnetic flux geometry isn't in complete symmetry with your ring, but slightly off-center? Trevor Kearney suggested this as a challenge to those who support the idea of the scalar PD between two points being the "unique" voltage in the "Lewin Ring".

You will find that the "tiny voltage sources" in your circuit suddenly have a different value in every little piece of the wire and that for anything but the most trivial geometries you will need a numeric EM field solver and a model perfectly matching you circuit, to calculate that voltage. That in itself is not problematic, what is the much bigger problem is that you will not be able to quantify the uncertainty in your calculation, because you cannot know how close your numeric model is to reality.

The next problem will be to actually measure the "unique voltage" as a proof for your models accuracy, because now your measurement setup will have to use real-world wires and all the electric fields you measure will of course depend on the path of those wires relative to the magnetic flux. So what do you do now? You already don't know to what degree you can trust your calculation (or simulation) and then you don't know if any discrepancy between the voltage you measure and your calculation is due to "bad probing" or "bad modeling". For an engineer, that's not a good point to be.

And it doesn't end there. The next problem will be repeatability, as any small change in geometry will throw off your calculation and measurements again.

The beauty of the Maxwell-Faraday equation is that is requires no knowledge about the magnetic flux or path geometry. It just requires that the path be closed (that's what the "circle" in the Integral sign means) and then gives a perfect relation between the "voltage" you measure and the time-varying magnetic flux in the area enclosed by said path and the only uncertainty is how precisely you can measure the voltage. The only snail to swallow is accepting that voltages can be non-unique and will depend on the path you measure them on.

But will KVL hold after everything you listed above?  Of course yes!  Furthermore, the voltage potential difference between two arbitrary nodes will be a unique scalar at any fixed time t.   Do you understand the difference of the voltage between two nodes and the voltage you measure between those two nodes?  As soon as you measure the voltage in any circuit, the instrument is modifying the circuit, and if you don't account for that, the results you get may be so baffling as to make you proclaim that "KVL is for the birds".

My question would be: do you really believe that Dr. Lewin is such a massive fool that he didn't understand that the volt meters (or oscilloscopes) he used and the paths they were connected through were part of the circuit? His experiment was particularly crafted to display path dependence of voltages. Dozens of others have recreated it and came to the same observation. It isn't even new or original, I'm sure that other MIT video that has been referenced here (the one with the ring core) predates Lewins setup by 10 years or so.

With regards to whether KVL holds in that circuit or not - it doesn't, in the circuit Lewin chose for his experiment. It may very well hold in the circuit you created, but it is a different circuit, by your own words, because the electric fields are observed along different paths. It is also very, very peculiar and so full of uncertainties that it will be very hard for you to claim that the results you obtained are "exact" and "true". Your measurements were one or two percent off from your calculation as I recall, but can you say where that error came from? Probing? Calculation? Assumptions? Resistor tolerance? Volt meter error? That's why I called it a Nothing-Burger.

[jesuscf]

My question would be: do you really believe that Dr. Lewin is such a massive fool that he didn't understand that the volt meters (or oscilloscopes) he used and the paths they were connected through were part of the circuit?

Yes.

[thinkfat]

Ok, then in three small sentences or less explain where the non-conservative field is in Lewin's ring.

\${\nabla \times E = -\frac{\partial B}{\partial t}}\$
Hint: left side of the equation.

Yes, but the right part of the equation makes it conservative again!  The only way it will be non-conservative is if you do this:

\${\nabla \times E = 0}\$

Ah, no. The right part doesn't "make" the left part conservative. The right part just says "there is a time-varying magnetic flux" and the left part says "there's an electric field with a curl", and the curl is what makes the left part non-conservative. As to answer the "where", the "curled" electric field is in a plain perpendicular to the magnetic flux vector.

[jesuscf]

With regards to whether KVL holds in that circuit or not - it doesn't, in the circuit Lewin chose for his experiment. It may very well hold in the circuit you created, but it is a different circuit, by your own words, because the electric fields are observed along different paths. It is also very, very peculiar and so full of uncertainties that it will be very hard for you to claim that the results you obtained are "exact" and "true". Your measurements were one or two percent off from your calculation as I recall, but can you say where that error came from? Probing? Calculation? Assumptions? Resistor tolerance? Volt meter error? That's why I called it a Nothing-Burger.

The main source of error, I believe, is probing.  One has to be very careful for the varying magnetic field not to affect the measuring instruments.  I find it interesting that you are willing to dismiss my experiment because I got a less than 2% discrepancy with the theoretical KVL calculation, but you are willing to immediately accept Lewin's results when he doesn't even provide any actual numerical measurements from his experiment.

Also, have you done the experiment yourself?  Do you have any measurements? 

[jesuscf]

Ok, then in three small sentences or less explain where the non-conservative field is in Lewin's ring.

\${\nabla \times E = -\frac{\partial B}{\partial t}}\$
Hint: left side of the equation.

Yes, but the right part of the equation makes it conservative again!  The only way it will be non-conservative is if you do this:

\${\nabla \times E = 0}\$

Ah, no. The right part doesn't "make" the left part conservative. The right part just says "there is a time-varying magnetic flux" and the left part says "there's an electric field with a curl", and the curl is what makes the left part non-conservative. As to answer the "where", the "curled" electric field is in a plain perpendicular to the magnetic flux vector.

Yes it does!  That is why KVL do work.