Kirchhoff’s Voltage Law versus Faraday’s Law: the Conclusion
Why Physics Stack Exchange recommends it
Physics Stack Exchange users link it when questions turn on how voltage is defined when the electric field is non-conservative, as with inductors and changing magnetic fields.
Recommended by 1 people across 1 different months, 2022 to 2025.
What it is
ElectroBOOM's Mehdi Sadaghdar presents his follow-up to the online debate with MIT's Walter Lewin over whether Kirchhoff's Voltage Law holds in circuits with changing magnetic flux. He walks through Belcher's notes, Romer's paper and the Feynman Lectures to argue how voltage should be defined in that case.
What people said
Recommends Jagerber48 · 2022-07 · Physics Stack Exchange · on “Is voltage the integral of electric field or energy per unit charge?”
See this video [this video] on the debate about the definition of Kirchoff's voltage law. See around 8:15. The difference in views seems to hinge on the definition of voltage. In one case voltage is defined as $$ V^1_{ab} = \int_{\Gamma_{ab}} \boldsymbol{E}\cdot d\boldsymbol{l} $$ This definition is only independent of that path $\Gamma_{ab}$ if $\boldsymbol{E}$ is conservative implying $d\boldsymbol{B}/dt=0$ everywhere. If $\boldsymbol{E}$ is not conservative then it is generally said that voltage $V^1$ is undefined. In another case voltages is defined as $$ V^2_{ab} = \frac{1}{q}\int_{\Gamma_{ab}} \boldsymbol{F}\cdot d\boldsymbol{l} $$ In this case the force $\boldsymbol{F}$ may be supplied by
Cites Andrew · 2024-12 · Physics Stack Exchange · on “Is "voltage across an inductor" actually real, or a convenient engineer trick?”
There's a whole internet controversy about this :-) [this video] My takeaway is that, basically, you are right, this is a "trick" to simplify analysis of circuits, but incredibly useful. See also the Feynman lectures Vol 2 chapter 22.
Cites Julian Newman · 2025-04 · Physics Stack Exchange · on “Do circuits in a changing magnetic field have a well-defined "internal electrical" potential?”
I am a pure mathematician and not a physicist, and so a couple of disclaimers/apologies may be in order: Firstly, the question that I want to ask is of a sufficiently subtle nature that I need to try to be very precise about it, and the only way I can think to do that is to formulate it in a way that makes reference to advanced pure mathematics concepts. I hope this will not make the question too difficult to easily follow, and I apologise if it does. Secondly - because of my lack of knowledge of the relevant physics - it is very possible that my question will turn out to not make physical sense (i.e. it may be based on incorrect presuppositions); if so, I apologise for that, and would be gr