Recent content by Stefan Gustafsson

From your diagram: V1 = -emf/2, V2 = emf/2 ∫E dl = V2-V1 = emf (Walk around the circuit in the direction of the current, V2 is counted positive and V1 is counted negative because you enter from the negative side) So, summing the voltages around the loop givs the emf, just as Faraday's Law (FL)...

The voltage you are measuring in this case is just the line integral of the total E-field in a straight line from a to b. There is nothing special about this voltage - voltage in a non-conservative field is path dependent. The discussion about Kirchhoff being wrong or not is pointless. It all...

Yes, that is exactly why "potential difference" is not clearly defined in this situation.

Well the original question asked for "Find UAB, the potential difference between points A and B". It never says that they are asking about the "electrostatic potential" Since "potential difference" is not clearly defined in a non-conservative field (which you have in the original question) you...

As long as you stay in region X the voltage Vab and Vbc is path independent.

Yes, but when he is talking about region II he is talking about the full region outside the magnetic field. This region has a hole in the middle. As he says in the paper this region is not simply connected. My region X is simply connected - the total E field in region X is conservative...

I actually don't care about the electrostatic potential difference. It is purely a theoretical concept - it is not something you can measure. You have to calculate it by splitting the total electric field in Em and Es which is often very complicated.

As long as you stay in a region with a conservative total field (Like region X in my problem), there is no question: You find the voltage between two points by using the line integral of Etotal*dl between the two points. This gives exactly the same result as using a voltmeter and it is...

I am saying that there is no point in separating the E field in a Em and Es. The only thing that counts is the total field. If the total field is conservative in a region, then there is a well-defined voltage and potential. If the total field is non-conservative then the voltage and potential is...

This is just your opinion. My opinion is that voltage and potential are really undefined in a non-conservative field, but the most reasonable definition of the voltage between two points is the line integral of Etotal. I also believe that this is the definition used by for example Walter Lewin...

VM1 = -i*r VM2 = i*2r Easy application of Faraday's Law and Ohm's Law. Voltage and potential is not really defined in a non-conservative field so there is no one single correct answer to this question. But I think the most sensible answer is that the voltage is path dependent. Go back to...

I think we agree that both voltmeters will show 2V. (1A * 2 Ω) A much easier explanation for this fact is to simply use Faraday's Law. $$ \oint \vec E d \vec l = -{d \phi \over dt} $$ Note that ## \vec E ## is the TOTAL field. If we apply this for example to the loop A -> V1 -> B -> A , the...

Great! At least we agree on this. I will have more comments about this tomorrow - it is getting late here in Sweden now. But in your answer you did not mention anything about the segment B-C. Could you please tell me what voltage and voltmeter reading you expect there? Also, one additional...

Lets look at another problem for a second. Answering this should not require much effort. The black line is a wire with resistance 1 ohm/cm B is a linearly changing magnetic field that induces a current of 1A in the wire. Outside the shaded region there is no changing magnetic field L=2cm...

I am not sure exactly what circuit you are referring to here. Could you perhaps post a simple image of what you are talking about?