I just have to ask: do you fundamentally understand the Maxwell-Faraday Equation? I have my doubts. Otherwise you would not claim that the circuit consists of only two resistors connected by wires that can be seen as "dead shorts" and will have no voltage across them.
Do you agree that the Maxwell-Faraday equation relates a time varying magnetic flux to an electric field? Do you agree that this changing flux _causes_ an electric field in the wire? Do you agree that an electric field is a difference in potential? Do you agree that a potential difference is measurable as a voltage between the wire ends?
This is very much how a transformer works.
If you agree on all this, then you should be able to see that Dr. Lewins circuit is not just two resistors. It is in fact a transformer (or maybe generator) with the single secondary winding cut open in two places to insert resistors.
And it is the voltage across those two wire that you need to take into account when you add up all the voltages in the loop.
OK. So let's suppose that the wires in Lewin's circuit have a 0.1 ohm resistance. R1=100 Ω and R2=900 Ω. So, around the loop, we will have 100 + 900 + 0.1 + 0.1 = 1000.2 ohms. Now let's suppose that the EMF generated by the varying magnetic field induces a current of, say, 1mA. Multiplying that current by the resistance of each wire (0.1 Ω) will give us 100 µV on them. The voltage on R1 will be 100 mV, while on R2 we will have 900 mV. Adding all voltages up, we will have 1.0002 V. So there you have it. The voltages around the loop will still not be adding up to zero.
I started writing a detailed response. But I think I let the posts of @bsfeechannel just stand on their own. I mean, just look at the calculations.
I conclude as follows:![]()
and will now stop
.
Have a nice day.
Yes. That's why we study vector calculus at any engineering graduation course before we study electromagnetism. Because to understand this bleep you need to think "fourth-dimentionally". I.e. you need to understand that electricity and magnetism are not phenomena confined to electronic components, and how this thing behave in space.
So, frame of references, relative positions, relative velocities, paths, rates of change. All of that counts.
The oscilloscopes "know" what branch they are measuring because they form a loop with each resistor. If you pause Lewin's presentation on Youtube ( /watch?v=nGQbA2jwkWI ) at 41:54, you'll see that the scope on the right forms a loop with R2. In that loop, there's no varying magnetic field. So, all the voltages will add up to zero according to Faraday's law and, in this case, to KVL, which is nothing more than a special case of Faraday's law when you have no varying magnetic field inside the path of the circuit. So the voltage on the right scope will have to be exactly the voltage on R2.
Voltage can be path dependent if you are dealing with a non conservative electric field (i.e. one generated by a varying magnetic field).
Since the wires have very low resistance compared to the resistors, they can be considered practically dead shorts.
Yes I did and they still do not add up to zero.
BS must be pointed out and identified every time it shows up!
Please, don't say "a current is induced". Maxwell-Faraday clearly tells us that there is an electric field resulting from the changing magnetic flux. Current is what results out of Ohms law.
That's three lines of blather that doesn't answer my question.
You're telling me that the display of my oscilloscope depends on not only how I connect it, but where I physically place it.
Although that may be true at some very minor level due to interference and other effects, it is nonsense here.
Suppose I had long cables on the two scopes and swapped their physical positions left and right, well out of reach of any magnetic field from the experiment. Now they read the other way?
How about if I take the leads out perpendicularly and use two channels of one scope?
How about if I just use one scope?
These are just simple thought experiments that seem to me to reduce the experiment as claimed to an absurdity. I know some people have looked at this experimentally and I have no comment on those arguments because I haven't looked at them closely.
OK, if you are depending on the physical layout of the test leads, rather than the ultimate location of the oscilloscope (a much less ridiculous choice) than you need to reexamine the statement that there is no flux through that outer loop.
In order for the solenoid to induce a current in the loop, there has to be a net flux change inside the loop, but those flux lines have to eventually wrap around and go back to their opposite pole. If they do that inside the loop, then they cancel out the net flux. If they do that anywhere outside the loop, then your 'no varying magnetic field in the loop' becomes very questionable and would need to be measured by making another loop as physically close as possible but with a separate resistor not connected to the inner loop.
Now if you look at how most actual voltage measuring instruments work, whether they are an analog meter or oscilloscope, they measure the difference in absolute potential across their two input terminals. They can do this either by reacting to electric fields directly or by allowing a small amount of current to flow. In other words, the ideal voltmeter, however it works, reacts just like my hypothetical electrometer pair. The voltmeter doesn't actually care about path dependence or anything else in the DUT, just about the potentials presented at its inputs. It just measures the difference between two scalar quantities.
Since this a time-variant system, the wires also have inductance. I suspect that both the inductance and resistance are low enough in this case that they don't matter, but without numbers I can't say. I think we can agree that the oscilloscopes read what they do because they are reading more or less the voltage drop across each resistor that results from the induced current. Without examining Lewin's apparatus or experimenting myself, I couldn't say exactly how that was achieved. A lot of the attempted explanations and experiments that have been shown regarding this seem as flawed as the original, but I'm pretty sure the answer is simply that there is another layer or two of complexity beyond the simple path-dependence that Lewin was demonstrating.
Wow. The argument that never dies.
There (at least) two ways of modeling this:
Maxwell's equations model the electric and magnetic vector fields at every point in space.
Circuit theory uses a lumped circuit to model the voltages and currents. KVL and KCL always hold in lumped circuit models.
Here are some great videos that explain it all:
I started writing a detailed response. But I think I let the posts of @bsfeechannel just stand on their own. I mean, just look at the calculations.
But when electroboom did the experiment he accounted for many of this things... and KVL worked as expected:
One more thing: bsfeechannel, I called you out and you didn't deliver.
You have no idea of what you are talking about. Talking to you is exactly like talking to a flat earther or an antivaxer. So I decided to go thunderf00t on you call out all your BS.
But when electroboom did the experiment he accounted for many of this things... and KVL worked as expected:
Nope. Lewin used the theory to predict that the two resistors would have different voltages. Mehdi' experiment showed that Lewin's prediction was right. Mehdi admitted that explicitly.
Then Mehdi said that although the experiment matched exactly what Lewin predicted, he, Mehdi, thought that Lewin's was wrong.
This is a case of doublethink, where someone simultaneously accepts two mutually contradictory beliefs as correct, often in contravention to one's own sense of reality.QuoteOne more thing: bsfeechannel, I called you out and you didn't deliver.
Not interested in your piss contest.QuoteYou have no idea of what you are talking about. Talking to you is exactly like talking to a flat earther or an antivaxer. So I decided to go thunderf00t on you call out all your BS.
Be my guest.
For everyone else reading, who are you going to trust? Electroboom whom uses multiple oscilloscopes in a regular basis or Lewin that had no idea on what is going on with the oscilloscope and often calls it a voltmeter?
For everyone else reading, who are you going to trust? Electroboom whom uses multiple oscilloscopes in a regular basis or Lewin that had no idea on what is going on with the oscilloscope and often calls it a voltmeter?
Maybe lighten up a bit? An oscilloscope IS a voltmeter! And 'trust' isn't the issue, I'm (maybe) interested in what is going on, not comparing the trustworthiness of two rather flamboyant showmen.
Very pertinent question. Lewin took that precaution and demonstrated both theoretically and experimentally that the magnetic field outside the solenoid, where its length is much grater than its diameter, is negligible. See his lecture about it [ https://youtu.be/MXuZ1SRjpqk ]. So, from a practical point of view, the field outside the solenoid can be considered zero.
You are assuming your meter doesn't care about path dependence, but numerous experiments show otherwise. In Lewin's experiment, R1 and R2 are subject to electric fields of different intensities (assuming the resistors have the same size). And they can even be calculated. That's why the meters are showing different voltages (assuming there's no varying magnetic field in the loop made by the meter, the probes and the DUT).
If R1 and R2 were connected in parallel and attached to a battery, the voltages would be the same no matter what, because they would be subject to electric fields of the same intensity.
Stop for a moment and think. The voltages between points A and D in Lewin's experiment cannot be the same for the two resistors, otherwise they would have different currents flowing through them, which is impossible.
NO! Charlatans like bsfeechannel must be confronted.
It seems fairly clear to me, and it seems to be fairly explicitly admitted in the second video from MIT (perhaps where Lewin got the idea) posted by rfeecs that the 'path dependence' vis a vis the voltmeters is not the path within the loop, but rather the positioning of the test leads going to the voltmeter.
As far as positioning the scope, imagine a two-channel scope positioned well above the apparatus, not to the R1 or R2 side but right between them, far enough away that any electric or magnetic field is truly negligible. Now everything is identical except the test leads going to the apparatus and their position is the only variable.
As for the rest of the issues and whether the voltages at the resistors must equal the voltage at the test points simply because wires are 'dead shorts' is something that I think involves--as I said previously--another layer of complexity.
'Voltage ambiguity' isn't really a workable concept, thus much of the consternation among the people trying (and mostly failing!) to explain this.
One thing to consider is your repeated assertion that you can't have a voltage differential in the wires because they have low resistance. So are there any conditions where that statement is not true? Are there conditions where a straight piece of wire will have a voltage differential from end-to-end?
QuoteOne thing to consider is your repeated assertion that you can't have a voltage differential in the wires because they have low resistance. So are there any conditions where that statement is not true? Are there conditions where a straight piece of wire will have a voltage differential from end-to-end?
Yes. When the wires are moving perpendicular to the magnetic field.
But in Lewin's circuit the wires are static in relation to the frame of reference. So the voltage across the wires will obey ohms law.
One misconception is that since the secondary of a transformer is just a wire, and I can measure a voltage when I attach a meter to the terminals, it is the wire that is generating the voltage.
What the wire is doing is to set a boundary condition around the loop where the rotational electric field will be forbidden to exist. This will concentrate the field between the terminals. What you are measuring is a voltage produced by an electric field that only exists between the terminals. It doesn't exist in the wire. So it cannot produce a voltage across it.
When you attach a load to the secondary and current flows, then you'll have an electric field inside the wire that will produce a voltage which will be proportional the current times the resistance of the wire. This electric field will have to be discounted from the field at the terminals, because the integral of the field around the loop is proportional to the derivative of the magnetic field ( I.e. the field in the wire plus the field in the load must add up to the induced EMF no matter what).
This is plain nonsense. It doesn't matter if the wires are moving or not. You will have a voltage whenever the magnetic flux changes. There is no term in the Maxwell-Faraday equation that has any component of spatial displacement.
But if there is no field "in the wire", how does a Variac work? Or any tapped transformer? Surely the voltage at the tap cannot be due to Ohms law if there's no current flowing? And if you connect the outer terminals of the transformer to a load, does that mean the field inside the wire collapses? Then the voltage at the tap would also collapse. But quite obviously, this isn't the case.
See above to understand why this cannot be a proper explanation.
A transformer winding is just a series of loops connected in series. The electric field resides in the space between each turn.
A transformer winding is just a series of loops connected in series. The electric field resides in the space between each turn.
WHAT! This quote needs to be preserved for posterity!
What the wire is doing is to set a boundary condition around the loop where the rotational electric field will be forbidden to exist. This will concentrate the field between the terminals. What you are measuring is a voltage produced by an electric field that only exists between the terminals. It doesn't exist in the wire. So it cannot produce a voltage across it.