The circuit is simple enough that very little circuit analysis is actually needed on it.
We know the voltage around it is 1V, We know the total loop resistance is 1 KOhm so trough I=U/R=1V / 1KOhm = 1mA.
At this point the voltages and currents across components are known so the circuit is solved.
Since you are looking for the textbook definition the voltage between points AB is both 0V and 1V.
Well, clearly Kirchhoff doesn't hold for the most elementary of the circuits when varying magnetic fields are present.
What you might have tried to do (at least I have) was to replace the wire and the field by a battery or some other lumped generator like in the picture below.
However, when you do that, obviously you will have to account for the electric field that this component will introduce along path #2. But path#2, we've already seen, has no electric field. So this is not a circuit of exclusively lumped components and no circuit analysis from the point of view of Kirchhoff can be employed.
But all is not lost. The answer to the next question may seem kind of obvious, but I am trying to prevent any hasty conclusions. I had to spend some time meditating about it myself.
I elongated path #2 so that we have a larger area without any varying magnetic field to the right like in the picture below. My question is, please, what is the voltage between points A' and B' via path #3?
The voltage along that path is also 1V because i assume there is no wire there.
Node | Node | Path | Voltage (V) | Reason |
A' | A | #2 | 0 | Ideal wire |
A | B | #1 | 1 | EMF across resistor |
B | B' | #2 | 0 | Ideal wire |
B' | A' | #3 | -1 | EMF across the air |
A' | B' | #3 | 1 | EMF across the air |
B' | A' | #2 | 0 | Ideal wire |
Node | Node | Path | Voltage (V) | Reason |
A' | A | #2 | 0 | Ideal wire |
A | B | #1 | 1 | EMF across resistor |
B | B' | #2 | 0 | Ideal wire |
B' | A' | #3 | -1 | EMF across the air || battery |
Total | 0 | No varying magnetic field in the mesh | ||
A' | B' | #3 | 1 | EMF across the air || battery |
B' | A' | #2 | 0 | Ideal wire |
Total | 1 | Presence of varying magnetic field in the mesh |
Node | Node | Path | Voltage (V) | Reason |
A' | A | #2 | 0 | Ideal wire |
A | B | #1 | 1 | EMF across resistor |
B | B' | #2 | 0 | Ideal wire |
B' | A' | #3 | -1 | Battery |
Total | 0 | No varying magnetic field in the mesh |
Node | Node | Path | Voltage (V) | Reason |
A'' | B'' | #4 | 1 | EMF across the air |
B'' | A'' | #2 | 0 | Ideal wire |
Total | 1 | Presence of varying magnetic field in the closed path |
I am grateful to Mr. Sadaghdar for a number of discussions about Faraday’s Law and KVL, which have improved my understanding of both.
Many introductory texts on electromagnetism are not precise about what exactly they mean by the voltage drop across the inductor, and many students come to incorrect conclusions about what this actually means. The most common misconception is that the - LdI/dt voltage read by the voltmeter just above represents a −∫abE⋅dl through the inductor. But if the inductor wires are perfectly conducting, this integral is zero because there is no electric field in the wires.
Thank you for all your replies.
We can see pretty much that this is theoretically and physically impossible, because a battery and a resistor can't occupy the same space at the same time.
So, not only this circuit more than violates--it rapes--Kirchhoff big time, as we have seen, but also cannot have an equivalent version with lumped components.
Now I owe you an answer to your question, what part of Feynman's lectures, namely Chapter 22 is being misunderstood? The short answer is all of it. It is so because people are disregarding basic assumptions that Feynman adamantly stresses in his text.
An answer a little less short is given by Prof. Belcher in his "MIT-quality report" where he elegantly showed where exactly Mehdi, and for that matter all those who still believe that KVL can have the slightest chance to hold under a varying magnetic field, goofed it up. However, after the report, Mehdi continued to espouse his previous ideas, which means that he didn't in fact learn anything. Perhaps, noticing this, even before Mehdi made his second video, Prof. Belcher said in his report:QuoteI am grateful to Mr. Sadaghdar for a number of discussions about Faraday’s Law and KVL, which have improved my understanding of both.I.e., my understanding improved.
Belcher concludes:QuoteMany introductory texts on electromagnetism are not precise about what exactly they mean by the voltage drop across the inductor, and many students come to incorrect conclusions about what this actually means. The most common misconception is that the - LdI/dt voltage read by the voltmeter just above represents a −∫abE⋅dl through the inductor. But if the inductor wires are perfectly conducting, this integral is zero because there is no electric field in the wires.
So, replacing perfectly conducting wires with batteries, or generators, is a noob mistake. It's a trap for young players. This means that the circuit below is not modelling Lewin's circuit.
In fact, Lewin's circuit is not lumpable, because we do not have anywhere inside the loop where we don't have varying magnetic fields, where we could replace the EMF with a battery and get away with it. The voltages that you can measure at the terminals of the resistors of the internal loop are the result of electric fields that are being generated along the very same path where the resistors are.
The failure to understand this basic principle of electromagnetism leads to all kinds of wrong conclusions.
- All other elements are not enclosed in a magnetic field so circuit analysis methods should work on them.
Well in terms of being unlumpable i still don't see how my lumped transformer model is wrong here:
https://www.eevblog.com/forum/chat/does-kirchhoffs-law-hold-disagreeing-with-a-master/msg2138140/#msg2138140
[snip]
No need to tell me that a mesh model is not exactly the same as a real circuit. I know its not! No mesh model is, because we can't create these ideal circuit components in real life, but when modeling is done right it acts just like the real thing despite being simplified.
I said in my last post that i know its not the exact same circuit.
But where do you draw the line.
But where do you draw the line.
Your model says you will find 250mV across all wires. Theory says it is zero.
Your model says you will find 250mV across all wires. Theory says it is zero.
Which exactly theory says it is zero?
Are you saying that for EMF voltage to appear - full winding is necessary? In your understanding there is no 1/4 * EMF voltage on the 1/4 winding (tap)?
Are you saying that for EMF voltage to appear - full winding is necessary? In your understanding there is no 1/4 * EMF voltage on the 1/4 winding (tap)?
Where have you been lately? Have you followed our discussion since Jan 23rd?