Hi. All right, I'll do a video on it. So many people have sent me this asking: can I comment on this Veritasium video? The big misconception about electricity. So definitely watch it first.

Don't watch my video. Stop this now. Go watch it if you haven't seen it linked up and down below. So let's go through it.

I'll go. I won't go through the whole video, but I'll go through, uh, various points in the video and add some commentary. and then we'll discuss how he actually gets the answer that he does and the implications of it. Imagine you have a giant circuit consisting of a battery, a switch, a light bulb, and two wires which are each 300 000 kilometers long.

That is the distance light travels in one second, So they would reach out halfway to the moon and then come back to be connected to the light bulb, which is one meter away. Now, the question is, after I close this switch, how long would it take for the bulb to light up? Is it half a second? One second, Two seconds, One over C seconds, Or none of the above Spoiler alert the answer is D One over C seconds. But technically this is actually a bit misleading because I don't know whether deliberately or mistakenly, he's left out the units on the one. It's not just one on C, it's one meter on C.

So to get your dimensional units correct, it should be one meter on C seconds. And this makes a huge difference to the answer that we're going to look at. Because if you don't include the one meter if those wires aren't one meter apart as you see here, then you actually don't get this answer which is actually one meter on C squared. And of course, if you put one meter on C seconds in there you would, then you might go.

It has to do with the distance between the wires and it does. As we'll see now, you have to make some simplifying assumptions about this circuit. like the wires have to have no resistance otherwise this wouldn't work and the light bulb has to turn on immediately when current passes through it. That's fine, but I want you.

This question actually relates to how electrical energy gets from a power plant to your home. You know, unlike a battery, the electricity in the grid comes in the form of alternating current or Ac, Which means electrons in the power lines are just wiggling back and forth. That is correct. Even if you had a completely Dc power system from source to your house, or in the case of your product, from your battery into your product, you would get the electrons only slowly drift very slow.

Like this, slowly drift from the battery to your source. So he's right. They never actually go anywhere just to teach this subject. I would say that power lines are like this flexible plastic tubing and the electrons inside are like this chain.

So what a power station does is it pushes and pulls the electrons back and forth 60 times a second. Now at your house, you can plug in a device like a toaster, which essentially means allowing the electrons to run through it. So when the power station pushes and pulls the electrons well, they encounter resistance in the toaster element and they dissipate their energy as heat. and so you can toast your bread.

Now this is a great story. I think it's easy to visualize and I think my students understood it. The only problem is it's wrong. Yes and no.

from a physics point of view. Yes, it's wrong. From a field theory. Uh, point of view.

Yes, it like electromagnetic field theory Point of view. It's wrong. But there's actually nothing wrong with using this kind of example. But in terms of actual practical engineering or Engineers have developed, uh, lots of tools, methods and laws like Ohm's law, Kirchhoff's laws, power maximum power transfer theories, Transmission line theory, signal theory, all sorts of theorems we've developed to give a more practical insight rather than what's actually happening at the physics level.

Who is taught this? Engineers are actually taught all of the stuff he's talking about in this video. In fact, it's fundamental to electrical engineering. Every electrical engineer knows about electron drift velocity and how slow it is. They know about electromagnetic fields and how the energy spoiler alert is carried in the electromagnetic field and that a current is actually uh, movement of charges in the wire like moon charges.

Electric field? uh, in the wire. So it's like we're taught this stuff. So he's I. He's really this.

He's not talking two engineers. This video is definitely not aimed at engineers because there's absolutely nothing new in this video for anyone who's trained in engineering. Guns themselves have potential energy that they are pushed or pulled through a continuous conducting loop and that they dissipate their energy in the device. My claim in this video is that all of that is false.

He is actually correct. Actually, everything he says in this video is actually correct. The energy. The power is transported in the electromagnetic field.

So how does it actually work? In the 1860s and 70s, there was a huge breakthrough in our understanding of the universe when Scottish physicist James Clerk Maxwell realized that light is made up of oscillating electric and magnetic fields. The fields are oscillating perpendicular to each other and they are in phase. Meaning, when one is at its maximum, so is the other wave. Now, he works out the equations that govern the behavior of electric and magnetic fields, and hence these waves.

Those are now called Maxwell's Equations. But in 1883, one of Maxwell's former students, John Henry Pointing, is thinking about conservation of energy. If energy is conserved locally in every tiny bit of space, well, then you should be able to trace the path that energy flows from one place to another. Now, Pointing works out an equation to describe energy flux.

That is how much electromagnetic energy is passing through an area per second. This is known as the pointing vector and it's given the symbol S and the formula is really pretty simple. It's just a constant one over Mu Naught, which is the permeability of free space times. E cross B.

Now, E cross B is the cross product of the electric and magnetic fields. You put your fingers in the direction of the first vector, which in this case is the electric field and curl them in the direction of the second vector, the magnetic field. Then your thumb points in the direction of the resulting vector energy flux. But the kicker is this: pointing's equation doesn't just work for light.

it works any time. There are electric and magnetic fields coinciding. Any time you have electric and magnetic fields together, there is a flow of energy and you can calculate it using Pointing's vector. Correct! To illustrate this, let's consider a simple circuit with a battery and a light bulb.

The battery by itself has an electric field, but since no charges are moving, there is no magnetic field, so the battery doesn't lose energy. When the battery is connected into the circuit, its electric field extends through the circuit. at the speed of light. Correct At the speed of light.

That's important. This electric field pushes electrons around, so they accumulate on some of the surfaces of the conductors, making them negatively charged and are depleted elsewhere, leaving their surfaces positively charged. These surface charges create a small electric field inside the wires, causing electrons to drift preferentially in one direction. Note that this drift velocity is extremely slow, around a tenth of a millimeter per second, but this is current.

Well, conventional current is defined to flow opposite the motion of electrons, but this is what's making it happen. This is absolutely correct. and every engineer is taught this. There's nothing new here at all.

We're taught electron drift Velocity. We're talking. We're taught that current is actually, uh, the movement of electric charges um, in the wire. And the we're taught the pointing vectors and we're taught the whole shebang.

We taught the Maxwell's equations, the whole kit, and caboodle. So there's nothing new here at all for engineers. The charge on the surfaces of the conductors also creates an electric field outside the wires, and the current inside the wires creates a magnetic field outside the wires. Correct.

So now there is a combination of electric and magnetic fields in the space around this circuit. So according to pointing's theory, energy should be flowing and we can work out the direction of this energy flow using the right hand rule around the battery. For example, the electric field is down and the magnetic field is into the screen, so you find the energy flux is to the right away from the battery. In fact, now, the problem here is that this is something he doesn't address in the video.

He's talking about the pointing vector going out from the wire. Now, this is the case. When you have uh, Ac, you are this is a electromagnetic radiation, right? This is what happens. This is a big part of practical Electrical engineering is designing products so that we can contain the electromagnetic energy in the field surrounding the wire.

This is why we have transmission lines coaxial cables. This is why we have a transmission line theory on Pcbs for example. But at Dc and Dc steady state, which we're going to take a look at, the pointing vector is actually back into the wire. It's not going out.

There's no electromagnetic radiation at Dc that only happens at Ac, anything above Dc basically. and the higher frequency you go anyway. That's all theory we won't get into. but at Dc, it's actually pointing in.

It's not pointing out. So I'm not going to say that's a mistake because I know what he's trying to get at in this video. All around the battery, you'll find the energy is radially outwards. Energy is going out through the sides of the battery into the fields along the wires.

Again, you can use the right hand rule to find the energy is flowing to the right. This is true for the fields along the top wire and the bottom wire, but at the filament, the pointing vector is directed in toward the light bulb. So the light bulb is getting energy from the field. If you do the cross product, you find the energy is coming in from all around the bulb.

Now, this is correct because the light bulb is a resistor. It's just a wire that's a resistor. and this will happen on the wires as well. which he neglects here.

And of course, in his example, he assumes that there's no resistance in the wires as well because if you've got resistance in the wires, it means that there's a pointing vector going back in and there's going to be I squared r energy loss in the resistance in the wire and that's what's happening in the light bulb. It's actually, um, there's a lot of pointing vector going in because it's a high resistance thing, is dissipating the power in there, whereas the Y is going to it. hopefully low enough resistance. They're not dissipating much.

most of the energy is being transferred into the bulb. And of course, if you use superconductors for the wires, then all of the energy there's going to be no loss in the wires and all the energy is going to be displayed in the light bulb. And if you're powering the light bulb with Dc, all of the pointing vector is pointing back into the bulb. But actually, if you power your bulb using Ac, some of it is also going out as well being lost as electromagnetic radiation.

It takes many paths from the battery to the bulb. But in all cases, the energy is transmitted by the electric and magnetic fields. This is correct. Uh, the fundamental part about this video is that energy slash power because energy is just power over time.

So we'll call it power. Power is not transmitted in the wires technically at the physics level. Yes, according to our pointing theorem is that the energy is actually transported outside of the wire in the electromagnetic field. That's actually correct.

People seem to think that you're pumping electrons and that you're like buying electrons or something. Which is just no one thinks that. Who thinks that? For most people and I think to this day it's quite counter-intuitive to think it is flowing through the space around the conductor. But the the energy is which is traveling through the field.

Yeah, is going uh, quite fast. So there are a few things to notice here. Even though the electrons go two ways away from the battery and towards it, by using the pointing vector, you find that the energy flux only goes one way from the battery to the bulb. This also shows it's the fields and not the electrons that carry the energy.

I mean, how far do the electrons go in this little thing you're talking about? They barely move. They probably don't move at all. Now, what happens if in place of a battery we use an alternating current source? Well, then the direction of current reverses every half cycle. But this means that both the electric and magnetic fields flip at the same time, So at any instant, the pointing vector still points in the same direction from the source to the bulb.

Correct. So, the exact same analysis we used for Dc still works for Ac, and this explains how energy is able to flow from power plants to homes in power lines. As I said, the only issue I had with this is that he didn't really adequately explain Dc because Dc is actually kind of fun as we'll get into it's it's not fundamentally different, but engineers think about Dc steady state in a different way than we think about Ac. They are actually quite different things and the tools that engineers have developed and the way we use them in practical design.

It makes a difference whether you're talking about Ac or Dc, but as at a physics level, yes, it's all about the pointing fields inside the wires. Electrons just oscillate back and forth. Their motion is greatly exaggerated here, but they do not carry the energy outside the wires. Oscillating electric and magnetic fields travel from the power station to your home.

You can use the pointing vector to check that the energy flux is going in one direction. You might think this is just an academic discussion that you could see the energy as transmitted either by fields or by the current in the wire. But that is not the case. Actually, it is the case because as a huge part of practical engineering is ignoring Maxwell's equations and pointing vectors, and like actually just thinking that the current flows in within the wire instead of the electromagnetic field around it, it's only when you get to talking about, uh, you know, higher frequency cases and stuff like that, then you have to start taking that into into account and it becomes absolutely critical.

Um, in a lot of cases, most cases, actually. And yeah, but that's not entirely true. Yes, physicists may not think that, but practical design engineers on an everyday basis. Our tools and techniques.

Um, there's nothing wrong at all with thinking about current flowing within the wire itself. And people learned this the hard way when they started laying undersea telegraph cables. the first Transatlantic cable was laid. Now, I won't go through this whole uh, Transatlantic cable thing.

But basically what they're talking about here is transmission lines. And this: this is not talking about transmitting power like 50 60 Hertz power over the ocean. This is talking about sending signals over a transmission line. So this was actually the early attempt of engineers and physicists trying to figure out exactly what was going on here and then develop, uh, transmission lot what we now know as transmission line theory.

It's yes, it has to do with the pointing vectors and everything else, but really, we're talking about transmission lines here. We're not talking about like 50 Hertz power. And that's the one term you won't hear Derrick use in this video. and I think it's probably deliberate.

He didn't use the word transmission line and this, as we'll see, this is fundamentally a transmission line problem. The question he's proposed is fundamentally a transmission line problem. So yeah, the fact that he left that out. I it just.

this is what Erx engineers. They're all kinds of distortions when they try to send enormous amounts of signal worship. So what is the answer to our giant circuit light bulb question? Well, after I close the switch, the light bulb will turn on almost instantaneously in roughly one over C seconds. So the correct answer is d I think a lot of people imagine that the electric field needs to travel from the battery all the way down the wire, which is a light second long, so it should take a second for the bulb to light up.

But what we've learned in this video is it's not really what's happening in the wires that matters. It's what happens around the wires. Correct, It's what happens around the wires. And this is why his answer.

d is totally dependent on this one meter gap, which is deliberately introduced into the question because if he stretched these wires out to a circle uh, you know this huge diameter circle then you wouldn't get that answer if you move it to two meters, the answer is actually uh, two meters on C. It's not Uh one on C anymore. So his answer is very deliberately tied to the distance between the wires. And this is basic transmission line theory.

And the electric and magnetic fields can propagate out through space to this light bulb, which is a whole one meter away. correct in a few nanoseconds. That's right. So he's taking like he is correct.

He's telling you the information, but then he's sneakily leaving out the information the the meters in the equation. Um, in the actual answer, like should be one meter on C. So he's deliberately leaving him that out Because then if you if that one meter on C was in the answer, it would twig in your head that aha, it has to do with the distance between the cable and so that is the limiting factor for the light bulb turning on. Now the bulb won't receive the entire voltage of the battery immediately.

It'll be some fraction which depends on the impedance of these lines and the impedance of the bulb. And here's where he starts to imply transmission lines. When you start talking impedance, you start talking transmission lines like this. So yeah.

But he's I think very sneakily left out that deliberate word. So yeah, I think it's a bit disingenuous to leave that out, but I can understand him not going into details because this video is not aimed at an engineering audience. It's just not. There is absolutely nothing new whatsoever in this video for anyone who's learned, uh, engineering.

So yeah, it's it's aimed at the general public. So yeah, I'll give them a pass now. I asked several experts about this question and got kind of different answers, but we all agreed on these main points. so I'm going to put their analysis in the description.

I have not looked at that to learn more about the particular setup, but I believe they're going to transmission people. Don't think it's real? Yeah, we can. We can definitely invest the resources and and string up some lines and make our own power lines in the desert. You're gonna get called out on it.

I agree. I think you're gonna get called out. Yes, he's gonna get called out by engineers who think that this question is a little bit sneaky because and the things that you left out of the video are, yeah, important. But everything he fundamentally said in the video is correct.

So I've got to give him props for the video. It is good in that it helps people know about Maxwell's equations, pointing vectors, and how the energy does actually flow outside the conductor. But there's some details deliberately left out here, and it's It's kind of a little bit annoying for us engineers, and because on a daily basis we don't really have to deal with Maxwell's equations and pointing vectors, we do most of our practical engineering using the tools and techniques we've developed to make it much simpler and much more practical. We just don't need to think unless we're at high frequencies and other sort of like extremes.

We don't really need to think about energy flowing outside the wire. Having it flow inside the wire is fine. Stick around to the end of the video because I'll show you uh, what Richard Feynman says on the subject and he kind of agrees with me and other engineers that meh, you don't really like these pointy vectors. Yeah, that's how it seems to be really working at the physics level, and it's really interesting and stuff, but you don't really have to use that on a practical basis.

and it's fine if you forget that energy flows outside the wires instead of inside the wires. I think it's just kind of wild that this is one of those things that we use every day that almost nobody thinks about or knows the right answer to. These traveling electromagnetic waves around power lines are really what's delivering your power. But another problem with this video and it's one that irks engineers is that no mention was made of skin effect of cable.

Uh, for example, where the the diameter of the cable matters. He did not mention that at all and that varies with frequency. And at Dc there is no skin effect. There's no at Dc there's no electromagnetic radiation going out.

Um, but at Ac there is. And a good part of engineering is trying to design products to contain this electromagnetic energy which is outside. Uh, the cables take a piece of transmission lines or Pcb traces, which are transmission lines, for example. I've done many videos on this talking about how you know Pcb routing matters.

Let's say you have a trace which is going. You know, routing across, snaking across your Pcb like this, and you have a big ground plane under for example. Well, the higher frequency you go, the more the energy. doesn't.

the energy, uh, the power isn't actually spread across the ground plane like this, or the return current as we talk about in Pcb design. it's not just spread out across the ground plane. the energy actually follows the trace. it actually follows in the ground plane.

Even though the ground plane is one big continuous sheet of copper, it follows under the trace. Like this, the rest of the copper doesn't matter the more higher frequency you go. So he's not mentioned practical aspects like the skin effect and or mentioning at Dc that the pointing vector is going into the wire like this and the magnetic fields aren't actually pushing the electrons to the outside. If there was, then, well, at Dc, we wouldn't be able to transfer large amounts of power.

And at Ac because 50 60 Hertz is almost Dc that we, it's not quite. But you know it's really low frequency stuff, so there is some skin effect there, but it's incredibly low, so none of this is covered. None of this is even hinted at uh in the video. In fact, the entire video just sort of implies that.

Well, the diameter of the cable doesn't matter because all the energy flows on the outside. If that was the case, then we'd be able to string all of our megawatts of power down the transmission lines with a, you know, a tiny little 30 gauge wire or something. And that's not the case. because once again, practical engineering and Ohm's law, Kirchoff's laws and everything else must be obeyed.

So there shouldn't be any engineers out there who are amazed at this. And yeah, and a lot of engineers will call him out because, well, we just think about things in a different way. It's the fundamental uh physics versus uh, practical engineer mindset. and this is just like when Electro Boom had the big debate with Uh.

Professor Walter, uh Lewin about uh, does Kirchoff's uh voltage law hold in electromagnetic fields Anyway, I won't go through the whole thing, but basically, it's the engineering mindset versus the physicist mindset. And the physics isn't wrong. Um, it's absolutely Derek is correct in practically every point he makes in here that the energy is actually transferred. The power is transferred in the electromagnetic field outside of the wire.

But then at Dc it's like a different question. But ultimately the physics does hold and these pointing vectors are where the magic happens with the energy transfer. At least that seems to be the case, but you know, there's a lot of debate still about this kind of stuff, but nobody has proven that pointing's theorem is wrong. So anyway, let's take a look at how we would solve this actual particular question.

Derek has, uh, proposed from an engineering point of view because it's really simple. So how do electrical engineers solve this sort of problem and show that the light bulb can turn on within a couple of nanoseconds? Well, it's really simple. It's really basic. It's practically engineering 101 really.

It's a called a lumped element model. So we're going to simulate this as a transmission line because this is fundamentally a transmission line problem. To electrical engineers and in practice as well, this would be a transmission line problem. So we can model a transmission line and in this case, show you how the light bulb is able to turn on within a couple of nanoseconds instantly.

Okay, so we've got the model up here. Okay, the wires are a meter apart like this and it's half a light second across in either direction. Now, this. Uh, if you've got wires one meter apart like this, it depends on how you calculate it.

But basically this is a transmission line of roughly 800 to 900 ohms characteristic impedance. Not that that matters. Uh, for what we're going to do here, it's just like it'll have a nominal characteristic impedance as a transmission line. Okay, so what we've got here is the voltage source.

We've got the switch. I have to have a ground symbol in here, otherwise it won't simulate. We've got our lamp, which I've just put as a 100 ohm resistor here. and then what we do is we simulate our transmission line with what's called this lumped element model and this is where we break up the transmission line into fundamental little circuit elements that we know and we can analyze.

In the case of a transmission line, you have Lcs and Rs resistance, inductance, and capacitance, and you have capacitance between the line like this I've just put in one micro farad. Doesn't matter what the values are, there's going to be some capacitance between these wires even if they're a meter apart. And actually a standard engineering trick question is to calculate the capacitance between the earth and the moon. Um, and that just comes up.

They just like to throw that in as an exam question and there's going to be capacitance there. So there's going to be capacitance between these wires one meter apart like this. And of course, wires have resistance as well. But because Veritasium has said we're ignoring, uh, the resistance of the wires, I've set the resistance of the wires to zero.

Not that it matters for this, uh, simulation. And of course, every wire. Every Pcb trace, every component, lead. everything.

Every one conductor in electronics has some form of inductance. so we're going to have an inductor. I put one micro Henry. The values don't matter.

Okay, so each unit length of the transmission line, it can be a centimeter an inch. It can be a meter. It doesn't matter what it is, right. A unit length will have capacitance and series inductance and series resistance.

which we're going to have zero. So you put that in your schematic like this, and then you just duplicate it, duplicate it, and you go out to infinity. Or not. quite infinity.

Almost infinity. A half light second worth of, uh, infinity. And you also do it in the other direction as well. And that simulates your transmission line.

But we don't have to do anything more than one element here to show what's going on. but I've just put in two because you know it looks a bit better. Now, of course, the end of this transmission line is shorted like this at each end. So once we turn that switch on and everything's settled down, all the transients have gone away.

The current will actually flow all the way through the wire, right through the end bit, and through the lamp and back for the half light second or whatever. It is okay, but when you turn on a switch like this, you are doing what's called a transient. And a transient means you've got time 0 and then you've got x time after that. So we're going to simulate this in the time domain starting from time 0 when we turn on the switch and we're going to see what happens.

But I'm actually going to leave these electrically open at the end, because at time Zero, when we turn that switch on, the signal hasn't had time to propagate the half light second all the way across right to here yet. So when you turn that switch at time zero, or time, you know, at one nanosecond or one microsecond or something, it hasn't had time to get all the way to the end yet. So it's almost so as far as the circuit is concerned. As far as the simulation is concerned, as far as the real world transmission line is concerned, this is an open circuit at either end.

So that's what I've done. I've kept them open here because we can't simulate it as short enough time to simulate the half light second and everything else, but every engineer knows this stuff, right. It's incredibly basic stuff anyway. So let's simulate this.

Let's run it and see what happens. Now, what I'm going to do is: I'm going to plot the voltage across the lamp here. so that's Vr1 minus that node, minus that mode. So the voltage across the lamp, and we're also going to get current through the lamp as well.

So we're going to get voltage and current graphs. I'm going to start at time 0. I'm going to simulate this for 100 milliseconds or 0.1 seconds and I'm going to there's my step. Time is going to be one micro second.

So let's go. We're running the simulation and we will get the results from T. Zero Bingo. Look at this at T equals zero Here, This is the volts.

Okay, so this is the voltage across the resistor. Look at this. It jumps up to one volt immediately. and then it jumps up to 10 milliamps absolutely immediately.

And if we zoom in there like this, you can see that it's there. It is. There's a transient right at time Zero. We can actually get in there finer than that, And we can see that it's like two microseconds.

Half that in one microsecond. It's ramped up right to one volt instantly. Within a microsecond, there's a volt across that resistor. Now, of course, this is because we only simulated at a one microsecond.

period. If we simulated it at one nanosecond, we'd see it ramp up in a nanosecond. So why does it do this? Well, everyone who knows basic capacitor theory knows why. It's because the cable capacitance right near as in, like, right at the switch and the Uh lamp.

Here, the capacitance between the two wires that are one meter apart. Remember, they will have a tiny miniscule amount of capacitance. Then that capacitor at time zero is a short circuit. So it's almost as if there's a short circuit in here like this.

and a short circuit at the lamp within like one meter like this. And of course, you won't get one volt across the lamp. As as Derek said in the video, you're only gonna like it'll They'll only turn on a small amount. Whatever that happens to be due to the circuit parrot characteristics, right? The capacitance across a meter and stuff like that.

It's not much, but in theory it's going to switch on instantly because it's only like a meter away. Well, as the answer to the question says, it switches on in one meter divided by c the speed of light. So it switches on like within a couple of nanoseconds. And it does that because of the capacitance of the line.

This is basic transmission line theory. There's nothing special going on here at all. This is Engineering 101. Every engineer knows this.

But of course, what happens after that? We won't go into transmission line theory. and like, no wave propagation and the whole rest of it, we just won't. Okay, the fact is, this is how you answer the question and of how the light bulb switches on almost instantly when you close the switch. Suffice it to say though, that after X amount of time, you will actually reach what's called steady state.

And that's when. Uh, the transmission line doesn't matter anymore. The capacitance doesn't matter anymore. The inductance doesn't matter anymore because the inductors and capacitors.

They only matter for uh, transient cases. Or Ac cases for Dc because we've just got a battery. Um, then you're eventually going to reach Dc What's called Dc steady state? And that's when it's those inductors are no longer there, the capacitors are no longer there, and all you've got is the line resistance. And that's it.

And then the current will actually flow. will have to flow by definition, all the way to the end to the short circuit. And like that stuff, the lamp wants to stay on for a long period of time once it reaches steady state. Then, yeah, it's got it.

The current has to flow through the entire loop. It won't flow through the capacitance anymore because nothing's changing. There's no transient circuit, there's no Ac. there's not the capacitor, it's just an open circuit.

and the inductors are just short circuits. Once again, Fundamental Dc circuit theory. Now, the voltages and currents we saw there are by no means close to representative to what you'd actually get in this physical scenario. And that's not the point.

I don't want to get bogged down in the deed in the quantitative details of what the actual answer is, because it doesn't matter. The whole point of this uh concept is to show how Derek can come to the conclusion that the answer is d one on C seconds, which is actually incorrect. uh, dimensionally unit wise, it should actually be one meter on C seconds. Now, I'm not sure if that was a slip up or whether or not that's deliberate, because if you put in one meter on C seconds, then that would, uh, imply that the answer is related to the one meter difference, uh, spacing between the conductors.

And it is. this uh answer does not hold if you actually put this thing, stretch it out into a circle. For example, because you don't have that initial capacitive coupling between here, you've got to go. Well, technically, there is, at some absolutely minute, ridiculously small half a B stick level, but you will not get the answer.

one meter on C seconds, you'll get some other answer which is faster than going all the way, like right through the whole loop. But it won't be that one meter, one on C seconds. So this is fundamentally set up as a transmission line problem and with the one meter gap between there to give that incredible answer that stunned everyone like, oh, how can that? How can that be? It's because they're one meter apart and there's capacitance between the wires. Of course, you don't have to technically model this as a transmission line.

You can just go. Okay, there's two wires and there's capacitance and you can just have the capacitors in there. But ultimately, this is a transmission line problem because it's a step response which generates multiple frequencies using fourier. Of course, because a step is made up or any uh, square wave is made up of a fundamental plus all the harmonic frequencies I won't go into uh, fourier.

but then it acts as a step response transmission line and this is exactly what it is. And this is and this answer only holds if they're a meter apart. So is it a trick Question? Is it disingenuous? Yeah, you could make the argument there, but the whole idea is to give people something that sort of like shocks them into thinking oh like wow, how can this happen But I come on, it's a transmission line. But if he said up front or if he put the one m in there the one meter and said oh, this is a transmission line um, although he did mention impedance sort of alluded to it, but if you mention that sort of thing, the game's up right to every you.

don't shock any engineer at all by this, it's just oh yeah, of course. duh. So the response of how this circuit actually works in practice over time is actually modeled and will work as a real transmission line. It's just that in in practice, yeah, I've put one micro farad in here, but in practice, the capacitance is going to be absolutely tiny, the inductance is absolutely tiny, and the amount of power you get in to the lamp over here, it's not fall, but it's there.

And that's the whole point of this to show that. Yeah, it can flow in the electric, It can flow in the fields. The energy can actually flow in the fields. But in this case, it's like all explained by Basic Engineering 101.

like cable capacitance, transmission line stuff. There's nothing special you don't have to worry about. You know, pointing vectors and then everything else. and energy flowing outside the wires.

It like that's just like hand waving stuff. Like electrical engineers. This is how they're going to look at and solve the problem. practically.

So yes, Derek is correct, and the whole video is essentially correct. That energy flows outside the wire in the pointing vector. It's and that's just like the physics of how it actually works. But here comes the interesting part.

You know how I mentioned steady state. Okay, when you analyze these sorts of things, you analyze a trend. You do transient analysis, which is what we just did. But once all the transmission line settles down, all the waves have stopped going or ringing on the transmission line.

everything's stopped and settled down. and you're 10 seconds later or whatever, right? And that light bulb's just constantly on. In Decent. That's called Dc steady state.

and this is a different analysis mode. Engineering has all these different types of analysis. There's transmission line analysis, there's transient analysis, Dc, and steady state analysis. These are like fundamentally different things taught in engineering.

And because there are these different modes, So once it's all settled down and as I said, the current, the capacitance doesn't matter anymore. The inductance doesn't matter anymore. The current is flowing all the way out right to the end. Like that, and it's flowing around the whole thing.

Everything's steady state. Nothing matters but the cable resistance anymore. Then you have to ask the question again. Is the power or slash energy focus energies just power over time is so we use the word power.

Is the power flowing in the wire itself? Or is it flowing through the Uh outside the wire in the electromagnetic field? Well, at Dc, there is no electromagnetic radiation. Okay, it's it's Dc. Nothing's changing, Nothing's switching. there is.

It's simply staying input. Now, of course, when current flows through a wire, you use the right hand rule. When current flows through a wire, you get an electric field around it. But that electric field is not moving.

It is stationary. So in Dc mode, is the power actually flowing through the wire instead of around it like it would during Ac. And you know, like transient right at higher frequencies? Well, the answer is once again, according to pointing theorem is the answer is uh, no, still does not flow through the wire because if we go to Fireman's lecture so you can see in Fireman's notes here that the pointing vector S is actually going into the Wire. this is steady state Dc.

Okay, so it's just simply a wire carrying a current. You still got the electric field which is going uh up. like going along the wire in the direction of the current flow. Then you've got the magnetic field pointing out of the wire.

but you still have the pointing vector going back in. And this is like rather academic. But technically the point in theorem maths still works out that there is still a pointing vector going in and there is argument. A lot of people don't actually believe that's uh, the case.

and at the steady state Dc it doesn't apply and stuff like that. But like I'm for argument's sake, I'm I'm not going to disagree with firemen, right? I'm I'm not a physicist, so I'm going to say yes, the pointing vector is still in there. but Fireman says it down here. You don't need to feel that you'll be in great trouble if you forget once in a while, or all the time as engineers do that, the energy in a wire is flowing into the wire from the outside rather than along the wire.

It seems to be only rarely a value when using the idea of energy conservation to notice in detail what path the energy is taking and he says it's not a vital detail. but it's clear that our intuitions are wrong, right? So I'm going to like, I'm gonna say yeah, Okay, fine. the energy slash power still flows outside the wire in the point, and it actually flows back in. But like, I can't think of a single instance in all of practical engineering where this matters, there might be some obscure thing, and in physics, research, and everything else.

And I'm and if you're doing the physics, I'm sure yet. Okay, fine. it works out. But in engineering, No.

nobody. Absolutely Nobody thinks about the power at Dc steady state. That the power is flowing outside of the wire in the pointing field, which is then going back into the wire. It's just no.

So if it's good enough for Richard Feynman to go, meh, it's good enough for me. So from my practical engineering perspective, I do know every engineer knows that energy flows outside the wire at high frequency, right? This is like a transmission line theory. This is how wave guides work. This is how a whole ton of stuff in engineering works.

and you really do have to understand that. But it's steady state Dc. There's just no, no. the power flows through the wire.

And the other thing, of course is that at Dc there is no skin effect. Okay, the point of vector goes all the way in to the middle. There is like there's no skin effect. So to say, to think that the power doesn't flow through the wire, it's just.

it's just pointless and dumb when you're talking about Dc. But once again, technically, I am going to concede that yes, the energy flow, even at Dc is in the pointing vector outside the cable. But it, that's just for academic exercises. Nobody, even firemen, just goes meh.

So there you go. Comment down below and I'm sure everyone will because this debate has been raging on since Time Immortal. And there's nothing new here. But to engineers, Derek's video was it was just like meh.

Yeah, it's a transmission line. So what? And a lot of people are going to say Yeah, it's disingenuous. But hey, if I got people interested in talking about, you know, pointing vectors and how energy flows outside the cable and stuff like that, Yeah, great. Okay, thumbs up to Derek, and I'm sure there'll also be a ton of people who will take me to task in the comments down below.

Or do I like going into the deep mass of it and and how my model here is wrong? But no, but no. sorry. This is how you get the answer here. by it being one meter apart.

When it's one meter apart like this, it's modeled as a transmission line. It's Engineering 101. if you want to argue otherwise, if once again, this is not the only way to look at it, right? A physicist will look at this, uh, question very differently to a practical engineer. but this is how a practical engineer would solve this problem right and derive and well explain how you can get that answer.

And I think it's like the easiest and simplest explanation. and it's going to be understandable by every electrical engineer out there. So thanks to Derek for putting that video up. It's fascinating.

It sparked a whole bunch of debate. Absolutely fascinating. uh, topic. And as he predicted in the video and as, uh, the professors he talked to predicted, yeah, he was taken to task over it and well, that's fine.

but nothing he said in that video is actually wrong pointing. Yeah, the energy flows outside the wire. It's the point in vectors and all that, uh, sort of stuff. It's just yeah.

especially at Dc. Um, yeah, nobody thinks that way in practical engineering. So there you go. Flame away down below.

Hope you enjoyed it. Found it interesting. Catch you next time.