However, there are no such inductors or capacitors. If we consider their existence, they must be infinitesimal. There are infinite infinitely tiny inductors and capacitors, and for Kirchhoff to hold you will have to apply it to infinite meshes.
This is just a simple example, but we can see that Kirchhoff is not adequate to model situations like that.
For a finite number of lumped components where space and time can be disconsidered, Kirchhoff is fine.
But add space and time and you'd be better off with a theory that takes that into consideration, and that is Faraday-Maxwell.
However, there are no such inductors or capacitors. If we consider their existence, they must be infinitesimal. There are infinite infinitely tiny inductors and capacitors, and for Kirchhoff to hold you will have to apply it to infinite meshes.
This is just a simple example, but we can see that Kirchhoff is not adequate to model situations like that.
For a finite number of lumped components where space and time can be disconsidered, Kirchhoff is fine.
But add space and time and you'd be better off with a theory that takes that into consideration, and that is Faraday-Maxwell.
Say the EMF induced in the loop is 1V. Say the total resistance is 1 ohm, so you have 1 amp flowing around the loop. Take any point in the loop and go around the loop adding up the IR drop. Go all the way around the loop. You always end up with 1V, not zero.
So how are you going to model this to make Kirchoff's law work? An infinite number of resistors dR and an infinite number of voltage sources dV? (I don't think so.)
Say the EMF induced in the loop is 1V. Say the total resistance is 1 ohm, so you have 1 amp flowing around the loop. Take any point in the loop and go around the loop adding up the IR drop. Go all the way around the loop. You always end up with 1V, not zero.
So how are you going to model this to make Kirchoff's law work? An infinite number of resistors dR and an infinite number of voltage sources dV? (I don't think so.)No in this case you will end up with 0v if you measure it.
You're misinterpreting Faraday-Maxwell.
I am fairly sure Maxwell-Faraday describes a case where the loop is magnetically closed but electrically open circuit.
But maybe I wasn't clear. Say you have the resistive loop. If you could measure say a section 1/10th of the way around. (I admit it is not easy to accurately measure in the presence of the magnetic field.) So that section has resistance 1/10th of an ohm and has current 1A flowing. You should measure 0.1V. So there are 10 pieces, and if you add them up, you get 1V, not 0V. You could divide it up in other numbers of sections with the same result.
OK, well take the original demo, but instead of two resistors, make the whole loop one big resistor. That is, a loop made out of resistive material:
Say the EMF induced in the loop is 1V. Say the total resistance is 1 ohm, so you have 1 amp flowing around the loop. Take any point in the loop and go around the loop adding up the IR drop. Go all the way around the loop. You always end up with 1V, not zero.
So how are you going to model this to make Kirchoff's law work? An infinite number of resistors dR and an infinite number of voltage sources dV? (I don't think so.)
OK, well take the original demo, but instead of two resistors, make the whole loop one big resistor. That is, a loop made out of resistive material:
Say the EMF induced in the loop is 1V. Say the total resistance is 1 ohm, so you have 1 amp flowing around the loop. Take any point in the loop and go around the loop adding up the IR drop. Go all the way around the loop. You always end up with 1V, not zero.
So how are you going to model this to make Kirchoff's law work? An infinite number of resistors dR and an infinite number of voltage sources dV? (I don't think so.)
Interestingly yes you would get zero volts in this case!
It turns out you can poke any two points in this circle and have the points sit at 0V...
1) Voltage1 = Potential in point A - Potential in point B
2) Voltage2 = The energy required to move a unit of charge between A and B
It turns out you can poke any two points in this circle and have the points sit at 0V...
That is wrong. Your model is wrong. It led you to the wrong conclusion.
Do you find following model as matching your "whole loop one big 1 Ohm resistor" ?
But what happens if we instead remove the restive ring but leave the probe wires connecting to the same two points in space connected to nothing? Do we measure nothing?
No, that still would have each voltage source + resistor pair cancelling out to 0V.
I'm not sure how to make a model with lumped components that violates KVL.
QuoteI'm not sure how to make a model with lumped components that violates KVL.
LOL. You basically said: "you are wrong, but I cannot prove it"
Using Faraday's law on the resistive loop, integrating E dot dl around the loop doesn't equal zero.
KVL holds for lumped circuits. This isn't a lumped circuit.
So to dispprove KVL within Time varying magnetic fields I suggest you need to prove it in the lab.
IMO I don't think Dr Lewin did this.
We've discussed this many times in previous threads. Dr. Lewin gave his world famous SUPER DEMO as he refers to it in 2002, I guess. But he didn't invent it. It is an exact recreation of the experiment in this 1982 paper:
http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf
In the paper, everything is explained very simply without drama. It's no mystery. The meter wires are part of the circuit and the orientation of the wires determines the results.