#562 – Electroboom!

[jesuscf]

Reading books is what you should do, instead..
Start from Hayt, chapter 9 and try to understand why the author's differentiate between potential difference and voltage.

The books in your picture look alarmingly unread.

Do you expect them to read books and on top of that understand what they read? You're asking too much. KVLism is based on ignorance. The more you're ignorant, the better. Because then they can claim with even more propriety that they have "debunked" some reputable scientist, engineer or scholar.

When they resort to books, it is only to select the passages that, out of context, appear to support their false claims, and rig their experiments until they get the results they think will prove them "right".

The books they show are only to impress the casual reader of the thread, or to serve as an amulet to ward off the evil people that show their favorite ignorant blogger is fundamentally wrong.

Have you learn how to apply mesh analysis yet?  Do you want any book recommendations?

[Sredni]

Reading books is what you should do, instead..
Start from Hayt, chapter 9 and try to understand why the author's differentiate between potential difference and voltage.

Got it:  Magnetic potential difference units are amperes.  Electric potential difference units are volts.

Non sequitur and mutatio controversiae in a single sentence. Not bad.
But try again.

Magnetic potential difference has nothing to do with the separation of the concepts of
    - electric potential difference
    - electric voltage

Maxwell's book is new.  As for Hayt's book:

They still look alarming unread.
You have four different editions of Hayt and you did not find any reference on a certain closed path integral being zero in one case, and being nonzero in the other?

Did you have to buy four edition because your books consistently miss pages?

[bsfeechannel]

Did you have to buy four edition because your books consistently miss pages?

You're being too polite. What they miss is parts of their brains.

[bsfeechannel]

I see you don't know how mesh analysis work either.  Lewin has a video on that, well, actually more like 5 videos on that.  So go watch them then come back to what you said above and see if you can find where you are wrong.

Well, I learned mesh analysis in the 1970's when I had my first formal training in electronics. All my teachers were engineers. In the last 50 years or so things may have changed. I don't know, they may have changed the definition of voltage, Kirchhoff's laws, Faraday's law, who knows?

I'll check Lewin's lectures about that to see if I'm still up to date, thank you.

While I do that, let's talk about your circuit, which by the way is not Lewin's circuit. I took the liberty to edit one of your pictures so that we can understand what is going on with it.



In the picture you see four stickmen seen from above (they have ears) extending their arms along the various paths of your circuit. The red dotted line shows what is hidden by the toroid. The yellow guys are the ones that, when stretching their arms, end up "embracing" the area where the varying magnetic field B is. The guys in blue don't.

Let's take the voltages along the paths of the yellow guys first. According to your measurements, V_R1= 6.44 mV, and V_R2=61.15 mV. These resistors form a complete circuit and their voltages add up to 6.44 mV + 61.15 mV = 67.59 mV. You haven't measured the voltages across the two 10k resistors of the inner ring, but we can presume that the voltage on each of them will be 33.8 mV, because it'll be the EMF (67.6 mV) divided by two. Their voltages will obviously add up to 67.6 mV.

Now the blue guys. According to the other picture the voltage that you insist on calling V_AD, which is not of course, because you are measuring the voltage between two points of two different rings, is 27.16 mV. If we add up the voltages around their arms, we get, for the left guy 6.44 mV + 27.16 mV - 33.8 mV = -200 µV. It's not zero, either because I'm using a presumed voltage for the 10k resistor (because you didn't provide it), or because of multimeter imprecision. Whatever the case, we can see that it is two orders of magnitude less than the other voltages.  For the blue guy on the right we have, likewise, 61.15 mV - 33.8 mV - 27.16 mV = 190 µV, which is not surprising, since we have -200µV for the other blue guy. This imbalance is within 5% tolerance for the resistors you used.

Anyway, you can clearly see that the voltages along the arms of the yellow guys tend to accumulate, while the voltages for the blue guys they tend to cancel each other out.

What is the difference between them? As I said, the yellow guys are encircling a varying magnetic field with their arms, while the blue guys are not.

Since KVL ONLY HOLDS where the voltages cancel each other out, we can conclude that KVL holds for the blue guys, but not for the yellow guys. Connecting the dots, KVL ONLY HOLDS for voltages that are NOT circling around a varying magnetic field, and fails when they are.

You see, all of that we concluded by simple observation. Now, we can try to predict an outcome with what we learned. If you repeat the same experiment and now place a voltmeter like the picture below (in red), we can expect pretty much that the voltage we will measure will either be zero or much lower than the voltages we previously measured. Why? Because we will have a blue guy there, who will not be able to embrace a varying magnetic field.

[jesuscf]

You see, all of that we concluded by simple observation. Now, we can try to predict an outcome with what we learned. If you repeat the same experiment and now place a voltmeter like the picture below (in red), we can expect pretty much that the voltage we will measure will either be zero or much lower that the voltages we previously measured. Why? Because we will have a blue guy there, who will not be able to embrace a varying magnetic field.

If you place the multimeter as you show in the image, what you get is the voltage drop in the resistance of the wire which is very small.  The induced EMF in the ring wire is cancelled by the induced EMF in the voltmeter probes.  Please watch Trevor Kearney's video until you understand what is going.  He explains it very nicely, starting at around minute 12:00 and then explains what to do around minute 13:00 in order to measure the induced EMF in that portion of the wire.  Here is the link:

https://youtu.be/FR8k12j7_Eo

Alternatively whatch Jesse's "Lewin's clock", where he takes the precautions pointed out by Trevor Kearney in order to measure the induced EMF in the wires.  This the link:

https://youtu.be/nAsZFP8Cfxk

Finally, you should seriously review your understanding of mesh analysis.
 

[thinkfat]

Engineer: "That model does not look right"
Scientist: "Eureka!"

When engineer say "you have to place wire here to get voltage X but have to place wire there to get voltage Y"- he gets fired.
When scientist say exactly same words - he gets worshipped.
Go figure.

Oh, but that's exactly what jesuscf says: "You have to place the wires _there_ to get voltage \$V_{AD}\$. Everything else is incorrect!"
And then he goes on to prove that KVL works because KVL works!

[bsfeechannel]

If you place the multimeter as you show in the image, what you get is the voltage drop in the resistance of the wire which is very small.

That's right. That's what we are going to measure. We are after voltages here, because we need to ascertain if Kirchhoff's VOLTAGE law holds for Lewin's circuit.

The induced EMF in the ring wire is cancelled by the induced EMF in the voltmeter probes.

OK. Let's suppose for a moment that the only thing going on in the wires (and probes, which are also wires) is the induced EMF. If instead of the meter, I hook up an arbitrary resistive load, for instance an LED, we won't have anything done there, because all the voltage that would be supposedly available by the EMF in the wire, will be cancelled by the leads of the LED, which will take the place of the probes. So for all intents and purposes, the voltage across the wire will be ideally zero, or, in practice, just the resistive voltage drop.

No wonder no one connects a load across a wire on a transformer. EDIT: the way the meter is connected in my previous message, of course.

Since the EMF is cancelled, as you say, for things connected in parallel with wires, let's see how it behaves for the resistors in series with them.

When we have a battery connected to a load, the voltages, and their respective electric fields, across the battery and the resistors are in opposite directions around the circuit. So, when we add them up, they will cancel each other out as dictated by Kirchhoff's VOLTAGE law. Or, in Kirchhoff's own words, the EMF (the voltage across the battery) will have to be equal to the current through the resistor times its resistance.



However, when we replace the battery with a wire and subject the entire circuit to a varying magnetic field, the electric field inside the resistor and inside the wire, and their associated EMFs, will be in the same direction around the circuit. So they do not cancel each other out in the equations. Quite the opposite, they'll accumulate. If I suppose that the induced EMF will have to be equal to the current through the resistor times its resistance, when I go around the loop I will be effectively counting them twice, because they have the same direction.



So it is pretty obvious that something else is going on. We need to have in the wire an electric field that has the opposite direction of the electric field in the resistor along the circuit. Just like we had, when there was only a battery. And we do. It is the electrostatic, or coulombic electric field that is generated by the displacement of charges produced by the induced electric field in the wire.

So now the puzzle is solved. What the wire is doing there is to produce the necessary coulombic field, which is conservative, by the way, to cancel the field in the resistor along the circuit in the equations, and as an aside, provide a return path for the current.

However we have a caveat. Since the coulombic field has the same magnitude as the induced field in the wire, and they are in opposite directions, they will cancel each other out, and the field inside the wire will be zero, rendering part of the induced EMF there as effectively zero. The "rest" of the EMF plus the coulombic field will be in the same direction inside the resistor and they will add up to be equal to the total induced EMF. That's a pretty cool mechanism that  works very conveniently.



So yeah, the meter is telling the truth. The total EMF in the wire is just the residual voltage necessary to satisfy Ohm's law. KVL unfortunately for this case (or for this path, if you prefer) kills itself so as to make sense from the point of view of the fields. It survives, however, outside the magnetic field. But inside, for-fluxing-get it. The energy is obviously coming from whatever is generating the varying magnetic field, just like in a transformer or loop antenna, or any arbitrary loop (conductive or not) subjected to an "interference" ( which etymologically means bringing [something] into ).

EDIT: last image replaced, grammar and typos corrected.

[Sredni]

Also, do you remember that time you asked me if I had a toroid?  Well, I have one now!

The induced field generated by a toroidal core is not circularly symmetric around the section of the core. It's more like the magnetic field generated by a single loop of current:



The induced field is stronger inside, being maximum on the axis of the toroid, where all 'cross sections' of the core contribute constructively and decreases faster than 1/r at the exterior. Therefore, your circular ring - even if it is perfectly circular and perfectly concentring to a perfectly circular cross-section core - will not experience the same Eind field in all points of its circumference.
The infinite long solenoid, with its perfectly circular Eind field lines, on the other hand, allows you to pull the trick of considering the contribute on arcs of equal length to be the same. But a toroidal core? No.
Therefore your answer about having

V_{A_to_R1}=16.9mV
V_{R1_to_D}=16.9mV
V_{D_to_R2}=16.9mV
V_{R2_to_A}=16.9mV

in the approximately circular ring around your square section core is... you guessed from the preview... WRONG.

And this is where I wanted to take you - and Jesse - some ten-fifteen pages ago when I asked you to specifiy your 'McDonald voltages' for all parts of that 'killer question' circuit that Jesse kept reposting. But you guys ran away like politicians from a truth serum.
Like you seemingly did when I asked you to explain why Hayt - which defines voltage as the path integral of the electric field - makes a difference between potential difference (to be used in the static case) and voltage/emf (to be used in the dynamic case).

[emece67]

.

[jesuscf]

Also, do you remember that time you asked me if I had a toroid?  Well, I have one now!

The induced field generated by a toroidal core is not circularly symmetric around the section of the core. It's more like the magnetic field generated by a single loop of current:



The induced field is stronger inside, being maximum on the axis of the toroid, where all 'cross sections' of the core contribute constructively and decreases faster than 1/r at the exterior. Therefore, your circular ring - even if it is perfectly circular and perfectly concentring to a perfectly circular cross-section core - will not experience the same Eind field in all points of its circumference.
The infinite long solenoid, with its perfectly circular Eind field lines, on the other hand, allows you to pull the trick of considering the contribute on arcs of equal length to be the same. But a toroidal core? No.
Therefore your answer about having

V_{A_to_R1}=16.9mV
V_{R1_to_D}=16.9mV
V_{D_to_R2}=16.9mV
V_{R2_to_A}=16.9mV

in the approximately circular ring around your square section core is... you guessed from the preview... WRONG.

And this is where I wanted to take you - and Jesse - some ten-fifteen pages ago when I asked you to specifiy your 'McDonald voltages' for all parts of that 'killer question' circuit that Jesse kept reposting. But you guys ran away like politicians from a truth serum.
Like you seemingly did when I asked you to explain why Hayt - which defines voltage as the path integral of the electric field - makes a difference between potential difference (to be used in the static case) and voltage/emf (to be used in the dynamic case).

You seem to agree that in my setup V_{A_to_R1}=V_{R2_to_A} and V_{R1_to_D}=V_{D_to_R2}.  Is that correct?

[jesuscf]

In case anybody is wondering about drilling ferrite cores, keep in mind that they are really hard to drill  (that's is, it took me ~1 h to drill 6.5 mm )

Also very brittle!

[Sredni]

Also, do you remember that time you asked me if I had a toroid?  Well, I have one now!

The induced field generated by a toroidal core is not circularly symmetric around the section of the core. It's more like the magnetic field generated by a single loop of current:



The induced field is stronger inside, being maximum on the axis of the toroid, where all 'cross sections' of the core contribute constructively and decreases faster than 1/r at the exterior. Therefore, your circular ring - even if it is perfectly circular and perfectly concentring to a perfectly circular cross-section core - will not experience the same Eind field in all points of its circumference.
The infinite long solenoid, with its perfectly circular Eind field lines, on the other hand, allows you to pull the trick of considering the contribute on arcs of equal length to be the same. But a toroidal core? No.
Therefore your answer about having

V_{A_to_R1}=16.9mV
V_{R1_to_D}=16.9mV
V_{D_to_R2}=16.9mV
V_{R2_to_A}=16.9mV

in the approximately circular ring around your square section core is... you guessed from the preview... WRONG.

And this is where I wanted to take you - and Jesse - some ten-fifteen pages ago when I asked you to specifiy your 'McDonald voltages' for all parts of that 'killer question' circuit that Jesse kept reposting. But you guys ran away like politicians from a truth serum.
Like you seemingly did when I asked you to explain why Hayt - which defines voltage as the path integral of the electric field - makes a difference between potential difference (to be used in the static case) and voltage/emf (to be used in the dynamic case).

You seem to agree that in my setup V_{A_to_R1}=V_{R2_to_A} and V_{R1_to_D}=V_{D_to_R2}.  Is that correct?

In my world they are all identical and zero, if we use perfect conductors. In the real world they are equal to the current flowing in the ring times the resistance of the length of the arc, whatever that maybe. I can easily calculate their value no matter how the ring is shaped and placed.

In your world, if by V you intend the scalar potential difference... Good luck! Unless you have perfectly symmetric rings perfectly centered around a perfectly symmetric core, you need to resort to numerical computation to get their values.

Moreover, when variable magnetic fields are present, the scalar potential difference does not give the full story. It is a partial result in that it describe only a part of the actual electric field in the ring.

Have you started reading Hayt, yet?

[ogden]

In my world they are all identical and zero, if we use perfect conductors. In the real world they are equal to the current flowing in the ring times the resistance of the length of the arc, whatever that maybe. I can easily calculate their value no matter how the ring is shaped and placed.

Engineer just measured 12VAC on transformer output. Wannabe scientist: as resistance of transformer secondary winding is zero, then voltage on terminals of transformer secondary is I*R meaning - zero. [edit] Those guys claim to know Faraday's law? C'mon.

[Sredni]

In my world they are all identical and zero, if we use perfect conductors. In the real world they are equal to the current flowing in the ring times the resistance of the length of the arc, whatever that maybe. I can easily calculate their value no matter how the ring is shaped and placed.

Engineer just measured 12VAC on transformer output. Wannabe scientist: as resistance of transformer secondary winding is zero, then voltage on terminals of transformer secondary is I*R meaning - zero. [edit] Those guys claim to know Faraday's law? C'mon.

We really are back to square one, aren't we?
In my world voltage is path dependent so I can have zero voltage ALONG the coil filament, and 12 V ACROSS the coil's terminal.

This is what the math says. And this is what the physics says. The amount of fuel per passenger when you go from LA to NY is different for different paths: if your path goes through Chicago it's one number; if you go through Lima, Peru, it's another.
Apparently this simple concept is inconceivable to KVLers.

[jesuscf]

In my world they are all identical and zero, if we use perfect conductors. In the real world they are equal to the current flowing in the ring times the resistance of the length of the arc, whatever that maybe. I can easily calculate their value no matter how the ring is shaped and placed.

I see.  I have nothing to discuss with you then.

[thinkfat]

In my world they are all identical and zero, if we use perfect conductors. In the real world they are equal to the current flowing in the ring times the resistance of the length of the arc, whatever that maybe. I can easily calculate their value no matter how the ring is shaped and placed.

Engineer just measured 12VAC on transformer output. Wannabe scientist: as resistance of transformer secondary winding is zero, then voltage on terminals of transformer secondary is I*R meaning - zero. [edit] Those guys claim to know Faraday's law? C'mon.

Dumb Engineer doesn't want to care about what's happening inside the transformer. He just measures across the transformer terminals and is happy. Engineer who knows Faradays Law understands why his measurements are sometimes giving unintuitive results. This is also the Engineer who's designs pass EMC testing.

[Siwastaja]

This is also the Engineer who's designs pass EMC testing.

Yeah. And EMC is still quite manageable; the mediocre engineer who only knows Kirchoff laws, will be able to try the 5-10 most commonly known "rules of thumb" of EMC design, and likely gets a pass. They don't calculate or simulate EMC; just experimental improvements, until emissions are below the threshold.

Similarly to modifying the layout and probe wiring until the results match within 2%, but with the difference that emissions do not need to match within 2%, getting under the bar is enough.

But then, try to design a modern-day radio communication device. Not a pre-certified module, the full design. Now you just can't avoid understanding the physics anymore.

And to be fair, I can't do it. But I'm grateful to those who can.

[Sredni]

In my world they are all identical and zero, if we use perfect conductors. In the real world they are equal to the current flowing in the ring times the resistance of the length of the arc, whatever that maybe. I can easily calculate their value no matter how the ring is shaped and placed.

I see.  I have nothing to discuss with you then.

This is a common trait of you KVLers: when you are faced with your self-contradictions you either censor your critics (like fromjesse, RSD Academy on their channels, where they can be censors) or all of a sudden you just find out there are other, more important thing to do and flee (like Jesse Gordon here, where he has no power to censor critics, or Mabilde on his channel, or you now). Except they always find the time to answer the easy question or starting from zero, ignoring all the inconsistencies that made em stop discussing with the other critics.

Anyway, you mentioned the magnetic potential. Hayt calls the scalar magnetic potential Vm and look what he has to say about it (this is from my fourth edition, but I am pretty sure you can find it on one of the editions you have at hand):





Oh, look: in the electrostatics case, the voltage is also scalar electric potential difference and as such is independent of path (thanks to that circulation equal to zero). In the magnetostatic case, on the other hand, the fact that the corresponding circulation is NOT zero, but I, the magnetic scalar potential ends up being a non-conservative field. The path integral becomes path-dependent and multivalued: to get the actual value YOU NEED TO SPECIFY THE PATH FROM a TO b.

And now look what happens to the electric potential in the presence of a changing magnetic flux:



Oh, look! The circulation of the electric field that in the electrostatic case was zero is now equal to -d flux/dt, and this - just like in the case of the scalar magnetic potential - makes the integral (voltage) multivalued and path dependent. YOU NEED TO SPECIFY THE PATH FROM a TO b.

This is written on the book you have what? five copies of?

[ogden]

Dumb Engineer doesn't want to care about what's happening inside the transformer. He just measures across the transformer terminals and is happy. Engineer who knows Faradays Law understands why his measurements are sometimes giving unintuitive results. This is also the Engineer who's designs pass EMC testing.

It does not matter - he is dumb engineer or dumb scientist. If he do not use proper model for analysis, he do not get proper results. Problem with all this engineers vs scientists tribe war is - both tribes do not even agree about common model which will be used for analysis. Scientist tribe say that segment of the loop can't be "lumped element" because "we say so". Engineers who say that EMF is induced in any kind of conductor, not necessarily loop - are labelled with swear words. Go figure.