Which is another thing I think I understood now: charge particles that are inert referenced to the magnetic flux are not interacting with the magnetic field, even if it's changing.
Which is another thing I think I understood now: charge particles that are inert referenced to the magnetic flux are not interacting with the magnetic field, even if it's changing.
Whoa! My spider senses are tingling all over.
Care to rethink this?
But you said that you are measuring the voltage across both the wire and the resistor with that configuration. Or did get it wrong?
By irreconcilable I mean that they aren't going to be the same number in a non-conservative field.
You say "be it conservative or non-conservative", but I think perhaps the Magneto-Quasi-Static idea has fooled you into thinking that the concepts from conservative fields can be applied to non-conservative fields as long as they hold steady for some period of time. I'm pretty sure that is untrue, but I'm struggling to demonstrate that.
I believe what many of us participating in the discussion initially didn't understand, me explicitly included, is that Dr. Lewins experiment must be seen as a whole, including his choice of probing the voltages. The whole idea about formulating a "law" in science is to be able to explain and predict the outcome of an experiment, and as I already said but probably nobody really took notice, the test instrument setup including geometrical arrangement of probe wires is inevitably part of the experiment. Dr. Lewin proposed a circuit and the challenge was to explain the measurements, and quite honestly, you cannot do that with Kirchhoff. It doesn't work.
The general definition of voltage depicts reality. YOUR definition of voltage depicts the struggle to understand it.
But you said that you are measuring the voltage across both the wire and the resistor with that configuration. Or did I get it wrong?
I'm measuring from one point to another. In this case, it a happens to be both across the resistor and across the partial turn, outside of any non-conservative field.
Which is another thing I think I understood now: charge particles that are inert referenced to the magnetic flux are not interacting with the magnetic field, even if it's changing.
Whoa! My spider senses are tingling all over.
Care to rethink this?Yes, of course, but I'm pretty sure about that. It explains, IMHO, that Lorentz' force and the electromagnetic force are two independent effects and not just two sides of the same coin.
"A toroidal vacuum chamber encircles the core of a large magnet. The magnetic field is produced by pulsed coils; the magnetic flux inside the radius of the vacuum chamber changes with time. Increasing flux generates an azimuthal electric field which accelerates electrons in the chamber.
In the absence of an air gap, there is little magnetic flux outside the core."
It's not my definition of voltage, it is a definition that was taught earlier in Lewin's course, among a zillion other places that it pops up.
You are just measuring a voltage due to a conservative field that is present in the resistor and between the terminals of the wire. Assuming the wire has no resistance, you can slide the meter all the way down to the left, just before you cross the lines of the mag field. You're measuring nothing else. You're not measuring the voltage due to the field in the wire. For that you need to place your meter anywhwere three-dimensionally speaking to the left of the field.
Care to provide a reference to it in Lewin's course, please?
I'll tell you what my crystal ball forecasts: that your method to measure voltage across the rod will force you to move the sensing instrument on a path that, together with the rod, will form a closed path around the variable magnetic region.
No, your insistence on a closed path is your downfall. You only insist on it because it makes your math work.
The insistence in the closed path is because we are talking about circuits, which by definition are closed paths.
How do you define the term 'equipotential'?
Let's assume I'm measuring between any two points with an analog voltmeter, just to make things a bit clearer. This would be a galvanometer in series with a resistor. So if I connect such a voltmeter to two points, current will not flow if they are equipotential, but will if there is a potential there. You can hide the entire apparatus from me, but as long as my meter and test leads are free from any external fields, B or E, I will get a certain result that will indicate whether those two points are equipotential or not. Free of external fields, there is no dispute over what voltage is. I don't need to have any knowledge of the source or cause of the voltage, or lack thereof. Or do you disagree with that as well?
Care to provide a reference to it in Lewin's course, please?
Maybe I can look a bit later, but which part do you doubt? C = 4 * pi * E0 * r or Q = CV?
It should measure zero, simply because it needs to.
Yes, of course, but I'm pretty sure about that. It explains, IMHO, that Lorentz' force and the electromagnetic force are two independent effects and not just two sides of the same coin. It would also serve as an explanation for why, as @bsfeechannel said, a wire in time varying magnetic flux doesn't have an "inner electric field" while when it is moving in a (constant) magnetic flux, there is an "inner electric field". In the case of the time varying magnetic flux the charge particles interact not with the magnetic field but with the electric field that results from the magnetic flux change. That's how I understood the Maxwell-Faraday equation: change in magnetic flux causes a rotational electric field.
First off, your machine requires two spheres, so you will have to account for the field lines going from one sphere to the other. Then you have the object you want to measure the charge of that will interact with those field lines, and the source of the field, and the whole planet beneath your feet.
And that thing about the field lines being perpendicular to the path of the spheres? Wishful thinking at its best. The moment the field induces charges on your rod, they will distort the field - not only inside the body to create the zero field, but also outside. And the distortion will be significant because the field lines needs to be perpendicular to the surface of the conductor.
And then your spheres will have induced charge themselves, that will disturb the field even more and change the charge distribution of the rod as you move near and away from it.
And why should the charge displaced on the rod jump on the spheres (which will have their own induced charge already?)
And what do you want to do in the nonconservative case? "extend the ends out to the point where the fields are negligible"What fields? Not the B field, it was never outside the core to begin with. So it must be the electric field. It can't be Ecoul, since it is generated by the charges themselves. Must be the induced field Eind, then. And you expect to see the displaced charge where there is no Eind field? If there is no more Eind field, what keeps the charges segregated at the extremes of the rod? All that charges of the same sign crammed together at one extreme? Wouldn't you think they'd repel each other?
And then you bring the alleged charge transferred on the spheres back together in the same place where you can measure it? My crystal ball was right. You are closing the path, after all (but let's not talk about this now). Even admitting you can magically duplicate (this could actually work) or take the charge of one extreme of the rod and the charge on the other extreme and then infer the voltage between them - you would see a voltage between them even in the electrostatic case. (because you have removed the external field Eext that causes the electrostatic induction of the rod). So, should we also say that there is a voltage between two points of a conductor in an electrostatic field?
Tequila is my lady, tonight.
As for the difficulties, experimental physics isn't simple!
Difficult, but I don't think theoretically impossible.
But I couldn't see an easy way to prove that.
But IMO it doesn't matter, closing the path far away from the action has negligible effect and you shouldn't rely on technicalities, infinitesmals or magic to make a practical theory work.
So let me get this straight. You can't prove none of your claims and you want to reinvent the wheel with a "practical" theory that doesn't rely on "technicalities, infinitesimals or magic" that again you can't even demonstrate in practice because "experimental physics isn't simple".
On the other hand, Faraday's law of induction, which renders KVL useless for varying magnetic fields, is not only easily provable, but also easily demonstrated by anyone with a spool of wire, a battery and a meter. That's how Faraday himself discovered the phenomenon. You don't need a fancy physics lab.
Start with the long U-shaped conductor. Is there potential across the ends or not?
As I was responding to Sredni and thinkfat it occured to me that there's another issue with the equipotentiality argument. In the static, conservative, irrotational field, there isn't an E-field inside the conductor because the charges instantly rearrange themselves to oppose it. Thus there is no net force on any charge within the conductor. In the case of a charge moving in a magnetic field, you accept that there is an non-conservative field inside the conductor acting on the charges, right? But then we get to the MQS system, and even though there is clearly a local force acting on charges inside the conductor--which is the EMF--
and those forces continually push charges through the conductor, that the conductor is nonetheless equipotential in the same way as in the static case, and for the same reason--there's no electric field in a conductor.
I believe what many of us participating in the discussion initially didn't understand, me explicitly included, is that Dr. Lewins experiment must be seen as a whole, including his choice of probing the voltages. The whole idea about formulating a "law" in science is to be able to explain and predict the outcome of an experiment, and as I already said but probably nobody really took notice, the test instrument setup including geometrical arrangement of probe wires is inevitably part of the experiment. Dr. Lewin proposed a circuit and the challenge was to explain the measurements, and quite honestly, you cannot do that with Kirchhoff. It doesn't work.
I beg to disagree. A proper experiment would had included many measurements from different geometric probing configurations. Lewin purposefully picked a configuration that he believed would eliminate the effect of the varying magnetic field in the measurement equipment while measuring the voltage between the top and the bottom of the ring. He ended up cancelling the effect of the magnetic field both in the probes and in the ring! That is equivalent to measure the voltage across the resistors directly.
Lewin then assumes that the voltage across any two points in the ring wire is zero volts, because he applies ohms law and the wire resistance is almost zero, and he goes AHA! KVL doesn't work!!! The problem here is that Lewin forgot that a piece of wire in a circuit under the influence a varying magnetic field doesn't behave as zero ohm resistor but as non-ideal voltage source. When you account for that extra little piece of information, all of a sudden KVL works perfectly, no matter the probing geometry, if you include the probes as part of your circuit.
Quote"A toroidal vacuum chamber encircles the core of a large magnet. The magnetic field is produced by pulsed coils; the magnetic flux inside the radius of the vacuum chamber changes with time. Increasing flux generates an azimuthal electric field which accelerates electrons in the chamber.
In the absence of an air gap, there is little magnetic flux outside the core."
I suggest watching that other MIT video, https://youtu.be/u6ud7JD0fV4. The thing is, the measurement loops C1 and C2 are not influenced by any magnetic flux. The demonstration even uses a toroid core to make sure that there is no flux outside of the core. There's nothing you'd need to cancel or compensate for. And the setup is not even very peculiar, the probe wires are just laying there on the bench with no particular care taken to fixate them anywhere. They're just "flopping around in the breeze".
But anyway, would you be able to explain what the oscilloscope shows in that video with just KVL?
I actually like that setup, because the core is a solid loop, there is no point in arguing "stray magnetic fields" and no way to contort the setup to "eliminate bad probing".
Check this video from 'fromjesse' with the very same experiment where he explains much better than me what is going on. The title of the video says it all: "The Lewin loop inside an iron core - KVL still holds":
Sir, this is EEVBlog.
I can't imagine how you could possibly read a denial of Faraday's Law in anything I've written. If some of it seems too far out there, address a few simpler ideas.
Here is a non-closed path example without any as-of-yet uninvented machines, except I'm not sure they have electroscopes this good. What happens when the current is turned on?