Kirchhoff Voltage Law KVL exception.

[@copernicofelinis]

I would add that the voltage *across* the various arcs of wire is also the voltage *along* the portion of wire between each pair of multimeter probes. Why? Because, since there is no variable magnetic field enclosed by the loop formed by voltmeter + probes + short arc of conductor, KVL holds in every such loop. The same goes for the voltmeter across the gap: it is measuring the voltage across the space between the ring terminals (since there is no changing magnetic field in the loop formed by that voltmeter, its probes, and the imaginary path along the gap, KVL works for that measuring loop as well.) But KVL ceases to hold in the loop formed by that voltmeter, its probes, and the entire conductor. Therefore, the voltmeter across the gap is correctly measuring the voltage ACROSS the coil's terminals but NOT the voltage ALONG the coil's conductor. KVL dies in the closed loop formed by joining the path along the conductor with the jump across the terminals.

[@SiliconSoup]

Thank you for the reinforcement. I hope every viewer can read your comment and learn more about KVL.

[@copernicofelinis]

@@SiliconSoup my pleasure. The sooner this wave of ignorance is stopped, the better. It is just a matter of time before the highschool mentality of "KVL always hold" will propagate at the University level. Leonardo da Vinci once wrote " Chi non combatte il mal comanda che si facci", "those who do not fight evil, ask for evil to be done" ( I think it was him 🤔).

[@woodcoast5026]

As the video says the voltage around the loop does not sum to zero, but there is an electric field that lies along the length of the wire of the loop. It is an induced electric field E(ind). The voltmeters read zero because the coulomb charge electric field across the voltmeter in the gap opposes the induced electric field along the other voltmeter wires. The charge accumulates there because of brown the wire arc .

[@SiliconSoup]

Yes, there is an induced e-field and an equal and opposite Coulomb e-field along the wire. Across the gap, the induced e-field and the Coulomb e-field are in the same direction. They destroy KVL.

[@trevorkearney3088]

Some time back we discussed the field distribution along a path which includes the core window. This paper is an excellent source. N. J. Carron; On the fields of a torus and the role of the vector potential. Am. J. Phys. 1 August 1995; 63 (8): 717-729. It can be viewed on a couple of websites if you search for the title.

[@MattKucia]

KVL can only be applied to an open circuit if we do a "hack" and assume infinite resistance in place of a gap. That reduces the problem to the closed circuit where KVL can be applied. The infinite resistance is much higher than wire resistance so the voltage drop can only be observed there. In the end, KVL is just a tool that has limitations in the way how it is used. It seems to me like a "shadow being faster than light" type of problem.

[@SiliconSoup]

Thanks for watching and noticing that KVL didn't work. It is true that the infinite resistance much higher than the wire resistance causes the voltage to appear at the open ends, but this does mean that the KVL violation is not intriguing. If KVL holds most of the time, why does it not hold this time?

[@trevorkearney3088]

From about 19 to 26 seconds we see a model of the charge distribution along the wire due to the induced electric field. The model assumes a uniform induced electric field exists along the circular open loop path. This is a reasonable assumption where the circular open loop path is concentrically aligned with a confined uniform time-varying magnetic field, such as would arise in a long, tightly pitched cylindrical solenoid winding energised with a time-varying current. This model cannot directly apply to your experimental demonstration with the open loop wire passing through the primary energised toroidal core window. There cannot be a uniform induced electric field encountered in a traversal of the open loop path in that case, given the substantial asymmetry of the arrangement. The surface charge density distribution would be far more complex.

[@SiliconSoup]

That's true. Now I am thinking how to numerically calculate E_induced on the open wire-loop produced by the toroidal changing magnetic flux. I am thinking whether there is shortcut to use just the two circular cross-sectional flux on the horizontal plane (one inside the loop, one outside the loop), or every cross-sectional area in the 3D space along the toroid. Thinking...

[@trevorkearney3088]

@@SiliconSoup In the case of the electric field associated with the time-varying toroidal magnetic field, perhaps there is a 'dual' example in the case of a magnetic field associated with a circular current loop. The off-axis magnetic field due to a circular loop of current would suggest a pathway to evaluating the off-axis magnetic vector potential for the toroidal magnetic field. The on-axis magnetic field for a current loop is relatively easy to determine but the off-axis is more complex, since it involves elliptical integrals.

[@trevorkearney3088]

@@SiliconSoup A further line of reasoning might support the notion that one deals with the problem as the net effect of two coplanar circular surfaces. As you may know this is the approach I took in my analysis of the Lewin experiment with a toroidal magnetic field. Following Stokes' theorem, the integral form of Maxwell's equation for Faraday's Law is typically stated in terms of a surface integral on the right hand side and a line integral on the left hand side. We can define that surface however we wish for a specific path around or enclosing the time-varying magnetic field. I imagine a 'surface' confined within the toroid space which is an inflated balloon which can be stretched as far as I wish away from a fixed line integral path somewhere on the toroid. The mouth of the balloon is 'attached' to the line integral path. The balloon could be inflated to the extent that its surface returns to the fixed integral path. The result for the induced EMF would be the same irrespective of the outer limit or extent of the balloon surface. That part of the balloon surface in contact with the toroidal interior surface would play no part in the evaluation of the RHS imagined surface integral in Faraday's Law. Can we not therefore simply regard the toroidal magnetic field in the same manner as that produced in an infinitely long solenoid winding folded back on itself.

[@glandeokrayo9956]

Once you realize these two things you'll find out that KVL works perfectly in this experiment without exception: 1) There is induced voltage in the voltmeter wires. If you manage to eliminate the induced voltage in the yellow and black voltmeters wires, you'll get the result you initially expected. 2) The circuit, including all the connected voltmeters, has 5 meshes.

[@SiliconSoup]

The voltmeters show there is no voltage along wires, and the is consistent with the fact that the wire is almost 0 ohms.

[@Greatbob-qu2ip]

​@@SiliconSoup kzbin.info/www/bejne/gKG5oIdnZZZ0sMk

[@razor0razor]

Just imagine there is a capacitor across the gap where you are measuring 0.121V, it is parasitic capacitance that you can not avoid. It has impedance much larger than segments of wire (close to 0 ohm) and all voltage drop is on it. KVL works just fine. It does not work if you dont include all elements into a lumped circuit model...

[@copernicofelinis]

So, you are saying that you have two elements in parallel, one with an impedance of zero ohm, the other with an impedance of infinite - or exceedingly high - value? But if KVL were to hold, these two elements should have the same voltage across them. So, is the voltage zero, or is the voltage 121 mV? I say it is both.

[@razor0razor]

@@copernicofelinis There is 0.121V over gap (capacitor, high impedance) and across part of wire goimg through "transformer" (that in lumped element model would be shown as inductor with mutual inductance to primary coil, toroidal trafo). See how he put black lead of one multimeter through transformer, so voltage cancels and multimeter shows 0V. Bad probing like Electroboom said.

[@copernicofelinis]

@@razor0razor lumped circuit modeling requires by definition that the components produce voltage and currents accessible through their infinitely close terminals, and that the circuit can be shrunk to a point. Meaning: there can not be a variable magnetic field enclosed by the circuit path joining the lumped elements and the rules of lumped circuits do not necessarily apply inside the components. In fact, KVL does not apply inside an inductor, and KCL does not apply inside a capacitor. Either you consider the coil as a lumped secondary of a transformer ( in which case you can only see the voltage ACROSS its terminal), OR you give up lumped circuit theory and apply the fundamentals laws of physics from where the simplified circuit laws are derived. If you want to look inside the inductor and understand how voltage behaves ALONG the coil you need to fold back to Maxwell's equations (and Faraday's law in particular). There is no probing error. The voltages measured by Silicon Soup are exactly those that can be computed from first principles starting from Maxwell equations. I suggest you Derive the well known expression for the voltage across an inductor: v = L di/dt. You will see that KVL needs to die to give you that result.

[@razor0razor]

@@copernicofelinis Agreed! KVL is simplified form of Faraday law that works only in lumped element model, where there is no changing magnetic fields, if there is it must be condensed into one of lumped components, inductors. If thaf is not possible then Faraday law has to be used, like when analyzing inside inductor. People are often mixing lumped components abstraction with reality bz adding extra field, then it seems KVL is wrong. KVL works as long as everything is accounted for into lumped model. Yet, why did he put multimeter wire through transformer, not around it?

[@copernicofelinis]

@@razor0razor because he would otherwise link the returning flux of the toroid. This experiment is better done with a very long solenoid - ideally infinitely long - because in that case there is perfect symmetry and there is no way to tell the inside from the outsid: every voltmeter just happen to be around the changing flux region. I have a picture that shows that but YT won't allow me to link it. Maybe next week I will add it in the description of one of my videos on Lewin's ring ( or to a new video I wanted to make, explaining the difference between across and along)

[@lalmuanpuiamizo]

I understand what makes you confused, justified so. But let me try to explain here. The multimeter that measure a voltage, it measures higher impedance point than others, so all the voltage are dropped in there, it measures that. Close the loop and test it and you will see. You dont need transformer, you will see this in DC battery source also if you measure like this. It's KVL, but to do that right we cannot ignore R and I either because they're all interrelated as we all know very well. To me this looks like confusion about internal resistance in voltage source

[@SiliconSoup]

Are you saying this measurement can be explained by Thevenin equivalent circuit, and the Thevenin equivalent circuit does not follow KVL?

[@lalmuanpuiamizo]

@@SiliconSoup Sure it can be explained by Thevenin's, and it also follows KVL. But in KVL we have to mind that, compared to other meter, the one that's reading a voltage is in open ciruit. So no matter in which point of the wire the voltage is induced, it will be shown there because there is least current (meter's burden voltage only). Great demonstration nonetheless

[@SiliconSoup]

In my understanding of KVL, the red multimeter should read a value equal to the sum of all other multimeters. Do you see that KVL fails in the demo?

[@lalmuanpuiamizo]

@@SiliconSoup The secondary loop is open, KVL applies to closed network only

[@SiliconSoup]

Really? If I have two 1.5V batteries stacked together, without any load to close the loop, then KVL is not applicable? The voltage across the two batteries (3V) can't be found by KVL?