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#562 – Electroboom!

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The tiny batteries model, or: "You don't know the half of it"

"You keep using that word.
I don't think it means what you think it means."
 -- Inigo Montoya
Here is something that KVLers will find... unconceivable. (I will come back to this post for formatting and for adding the pictures in a couple of days)

Let's start from Faraday's law, in its modern integral form

    circulation of E = - d/dt flux of B

We already established that there is no particular place on the path where we can localize the inductive EMF represented by the surface integral on the right. Even if we split the circulation of E in the path integrals along several segments we can partition the path into, none of the segment can account for the inductive EMF on the right. If we bring the whole surface integral on the left hand side of the equation we get

    circulation of E + d/dt flux of B = 0

But this won't make E conservative.
There is, though, some mathematical trick we can pull to transform the surface integral of B into a line integral of something related to B and then incorporate this something into the integrand of the original path integral of E.

What we will find is the circulation of something that is not E, but something else that has zero circulation and as such admits a scalar potential (which I will call phi to avoid any confusion with voltage).

Spoiler alert part I: it turns out that 'that something else' is the conservative part of the electric field E, a quantity that I will denote with Ecoul.

Spoiler alert part II: the electric field E can be seen as the composition of its conservative (irrotational) part Ecoul with its non-conservative (solenoidal) part Eind. This is the Helmoltz decomposition of a generic vector field and it holds under very general assumption (basically always):

    E = Ecoul + Eind

Moreover, to avoid confusion, I will also use the symbol Etot, instead of just E, to the denote the electric field.    

    Etot = Ecoul + Eind

But it has to be clear that Etot(x,y,z,t) (that is E(x,y,z,t) ) is the one and only electric field an electron, or any test charge, will experience at the point (x,y,z) at time t. Electrons do not have an accountant to tell them how much of the electric field they experience is due to the changing flux and how much to the displaced charge. The just react to the whole shebang.

We can start to massage our relation starting from the the vector potential A. Since div B = 0 we can express the magnetic field B as the curl of another vector field A:

    B = curl A

Our Faraday equation will become

    circulation of Etot + d/dt flux of curl A = 0

We can now use Stokes' theorem to turn the surface integral of the curl of A into the path integral of A along the boundary of the surface

    circulation of Etot + d/dt circulation of A = 0

If the ring is stationary we can bring the time derivative inside the integral

    circulation of Etot + circulation of dA/dt = 0

Now we can incorporate the second circulation integral into the first and we obtain the circulation of a field that is conservative

    circulation of (Etot + dA/dt) = 0

But notice what the integrand is: it is Ecoul, the conservartive PART of the total electric field

    Ecoul = Etot - Eind = Etot - (-dA/dt) = Etot + dA/dt

Ecoul has zero circulation and as such admits a potential function. This potential function is the scalar electric potential phi (some call it V, generating confusion) that obeys what we could call KsPDL (Kirchhoff's scalar Potential Difference Law).
It represents a partial description of the system because phi completely describes Ecoul, but only PARTIALLY describes Etot. In order to know Etot (the actual electric field felt by the charges) we need to know BOTH potentials: the electric scalar potential phi AND the magnetic vector potential A.

    Etot = - grad phi - dA/dt

Where does the tiny batteries model come from?
The tiny batteries model is not a model of the complete physical system "ring with resistors" described by Etot, but only a model of the effects of the partial, conservative part Ecoul alone. As a matter of fact, the tiny batteries represent the term associated with the negative of the induced field Eind = -dA/dt that we need to strip from Etot to get the conservative field Ecoul

    Ecoul = Etot - Eind = Etot - (-dA/dt)

This figure show the fields inside the conductor and the resistors of Lewin's ring for the case of zero-resistance wires.

Only the ring on the right expresses a conservative field, and as such it can be represented by tiny lumped components obeying K"V"L (it's KsPDL, actually). I am using tiny batteries because it makes easier to see at first glance the polarity.It would be more accurate to use tiny generators, since in general the EMF contribute is time-varying, but if we freeze the system at a particular instant in time, we can pretend we are dealing with tiny batteries.

fig model with tiny batteries, no resistance in wires

The model can be generalized to the case of resistive wires. In practice we break the ring in tiny segments for which we have two contributes: the tiny resistor that represents the conductivity of the material and the tiny battery that represent the 'EMF eraser' that will recover Ecoul from Etot.

fig model with tiny batteries and resistors

This being the model of a mathematical part of the system, it will break the laws of physics obeyed by the actual, complete, system. Case in point: Ohm's law. Consider any portion of copper conductor and we will see that a piece of metal with a resistance that is almost zero will appear to drop a voltage (actually it's a scalar electric potential difference) of, say, 0.25 volts when a current of just 1 mA flows through it.


Jesse Gordon:

--- Quote from: thinkfat on December 01, 2021, 08:06:59 am ---Regarding the "tiny voltage sources", the funny thing (which is a bit sad also) is that all the "experimental proof" by Jesse and e.g. Cyriel Mabilde are just cunning demonstrations of how to create paths that enclose a variable amount of magnetic flux. The sad part is that they're unable to see it and will keep claiming it is proof of "KVL holds". But in reality they're not measuring a gradual voltage build-up in the "Lewin Ring", but just the EMF induced in their measurement loop. This under the condition that there is only negligible current flowing through the ring and the measurement loop, of course.

--- End quote ---

The funny and sad thing is that you don't see that by measuring the voltage induced across a half of the dB/dt area we're actually unambiguously physically measuring the actual voltage induced in that half !

Think about it. Look at the circular area of dB/dt of my Lewin Clock. Now imagine we removed exactly half of that but maintained  D shaped aree at the other half with exactly the same dB/dt in that half as was there before. The dB/dt exactly the same.

Running the probe lead straight through the center of the circle does objectively unambiguously physically measure the voltage induced in that half of the winding.

And thus KVL holds my my Lewin Clock topology.

Jesse Gordon:

--- Quote from: bsfeechannel on December 05, 2021, 12:04:41 pm ---
--- Quote from: jesuscf on December 05, 2021, 05:40:19 am --- For this 900 ohm resistor measurement, I had to be more careful not to pick up an induced voltage in the probing wires, so I used the setup shown in one of the attached pictures.

--- End quote ---

Cool! That's what I thought. Jesse measured the wrong voltage. He let his probes pick up induced voltage.

--- End quote ---

Nonsense. I practiced safe probing, and KVL works. Welcome to the real world kiddo  :-DD :-DD :-DD.

--- Quote ---Thank you, jesuscf. We finally managed to show that Jesse's experiments are a hoax.

--- End quote ---
My experiment is not a hoax.  The reason you couldn't see my experiment in my garage is because you were in your mums basement at the time  :-DD :-DD :-DD.

--- Quote ---No wonder he left the discussion. He knew he would be caught and exposed sooner or later by your imaginative intellect.

--- End quote ---
I didn't leave the discussion, unlike you, I don't live in my mom's basement so I have to work and I have friends and family to interact with so I can't be arguing on here every day.

I told you I'd limit my posting days to 2 days a week here. Since I was too busy last week that gives me 4 days here this week if I have time LOL.

Besides, I've already determined that you don't know what you're talking about by how you absolutely refused to answer the questions I asked. Sure, you would ask your own question and answer that, but you absolutely refused to actually exactly answer my question, which I will repeat for you below in case you forgot it.

Question: In the following diagram, in a real life physical lab test performed with real (time synchronized) volt meters with a real transformer and real resistors CONNECTED AS SHOWN, will the readings of all the volt meters sum to zero, within the accuracy and resolution limitations of the volt meters? YES or NO.

(Or if you believe SOMETIMES is the answer, then answer SOMETIMES and explain one scenario for a YES condition and one scenario for a NO condition WITH THE VOLT METERS AND ALL COMPONENTS CONNECTED AS SHOWN - Running additional conductors through the transformer core is not allowed - nor is removing existing conductors from through the transformer core!)

Jesse Gordon:

--- Quote from: Sredni on December 07, 2021, 05:20:22 pm ---Of course. The MIT is notoriously known for its scarcely prepared professors of physics and engineering.
Here is yet another professor who does not understand the basics of electromagnetism!
Shame on you, MIT!!!
Listen to the guys in a garage, instead. They have an oscilloscope, so they clearly know what they are talking about.

--- End quote ---

You know, right there is rock solid proof that you don't know what you're talking about.

Think about it. You keep going on about us "guys in their garages." That is like the purest form of argumentum ad hominem because being in a garage has absolutely nothing whatsoever to do with whether we are right or not.

The fact that you argue based on personal attacks regarding completely unrelated issues which have no bearing on whether we're right tells me that's all you got.

Since you brought up my garage, why don't you get a scope for your mom's basement and do some experiments? Your moms basement will be just as cool as my garage if you add a scope for sure.

You could even convert that 1980's CRT tv you got down there into a scope if you want..

Want digital storage? well how about analog storage? You can convert your VHS recorder to a waveform storage unit.

You already accidentally admitted to enough facts that you've really cornered yourself.

You gloriously cited this this textbook:

For ease of reading and searchability, I reproduce it here:

--- Quote from: Desoer-Kuh ---
Lumped circuits are obtained by connecting lumped elements. Typical
lumped elements are resistors, capacitors, inductors, and transformers.
We have encountered them in the laboratory, and we can see them in our
radio sets. The key property associated with lumped elements is their
small size (compared to the wavelength corresponding to their normal
frequency of operation.)  From the more general electromagnetic field point
of view, lumped elements are point singularities; that is, they have negligible
physical dimensions. In this way they are similar to a particle.
Lumped elements may have two terminals, as in a resistor, or more than
two terminals, as in a transformer or transistor. For two-terminal
lumped elements, it can be shown that the general laws governing the
electromagnetic field, together with the restriction on physical size indicated
above, imply that at all times the current entering one terminal is
equal to the current leaving the other terminal, and that the voltage difference
between the two terminals can be unambiguously defined by physical
measurements.  Thus, for two-terminal lumped elements, the current
through the element and the voltage across it are well-defined quantities. For
lumped elements with more than two terminals, the current entering any
terminal and the voltage across any pair of terminals are well defined at all times.
  For the remainder of this book, any interconnection of the lumped
elements such that the dimensions of the circuit are small compared with the
wavelength associated with the highest frequency of interest will be called
a lumped circuit.
  As long as this restriction on the size of the circuit holds, Kirchhoff's
current and voltage laws (to be discussed in Secs. 3 and 4) are valid. This
restriction is a consequence of the fact that Kirchhoff's laws are approximations
of Maxwell's celebrated equations, which are the general laws
of the electromagnetic field.  The approximation is analogous to the fact
that Newton's laws of classical mechanics are approximations to the laws
of relativistic mechanics.  Even though they are approximations, the laws
of Newton and Kirchhoff can be applied to a large number of practical

--- End quote ---

Clearly, the output voltage of my transformer secondaries in the diagram directly below are "unambiguously physically defined by physical
measurements" as described in the revered textbook cited directly above.

The fact that you won't even concede that KVL holds in this case shows you really don't know what's going on, you don't have a scope, and you've got less training on the topic than I do if that's even possible LOL.

KVL clearly holds (and should hold!) both on paper and in the garage!  :-DD :-DD :-DD

What else is there even to talk about?

Might as well pull up your crystal ball. BS has one you can borrow if you like, it kept shorting out on him so he had to get a new one. Thinkfat has one you can borrow a well, it's only been used once.


--- Quote from: Jesse Gordon on December 13, 2021, 01:32:04 am ---Nonsense. I practiced safe probing, and KVL works. Welcome to the real world kiddo  :-DD :-DD :-DD.

--- End quote ---

"Safe probing" is for the weak. Real men measure the "interference".


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