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Let's imagine that we have battery connected to wire and the only component in circuit is light bulb and let's say we got 5V in battery. I'm looking for the intuitive explanation and not with the formulas. It should still be possible to explain this logically with basic concepts.

The way I understand 5V is at the anode, electrons are separated from the + charges of the battery by the specific distance such as due to this distance, 1C charge of electrons have 5J potential energy and we can say if 1c charge of electrons move all the way through wire from anode to cathode, they will lose 5J of energy(even though, electron at the anode won't travel all the way to cathode as we know electron in circuit actually travels very slowly with very low speed and it's mobile electrons of the wire that each of them travel) - but I can say 5V means if we assume electron at the anode could travel all the way to cathode, it would lose 5J energy.

Now, what actually lights up a bulb is the closest electrons to the bulb as they travel into the bulb, heat it and produce light. For sure, now, these electrons of 1c charge(closest ones) won't have 5J of potential energy(much less). 5 voltage means only those at the anode have 5J energy, but at any other point of the circuit, electrons will have much less energy. Even though, electrons at the bulb, definitely have some potential energy, which will be converted to kinetic energy which in turn get converted to heat energy which produces light, but I think this explanation of converting energies doesn't hold true and they say it's Electric field and magnetic field energy that actually light up a bulb.

Question 1: Is my understanding correct that mobile electrons already present in wire won't have the same potential energy of 5J as the ones at the anode ?

Question 2: Why is potential energy => kinetic energy => heat energy incorrect and why do we bring poyinting theorem into the picture and say that it's the E and B energy that actually light up a bulb ? Note that I don't know much about poyinting and would love to look at it easily if possible.

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Question 2: Why is potential energy => kinetic energy => heat energy incorrect

Within one second of you closing the switch to light up the bulb, the steady state flow of electrons is already basically setup. Since all the electrons are already moving in the wires at the steady state behaviour, the kinetic energy is already setup and there is thus no more need to convert potential energy to kinetic energy. Mind you, the electrons moving past the light bulb, where the heat is being generated, have the same kinetic energy of motion exactly the same as before entering the light bulb, because we know that there is no bunching up of the electrons (which would have a charge accumulation and thus made a change in electric field or voltage). The rate of electrons leaving the light bulb is the same as the rate of electrons entering the light bulb. And using the same wires for the input as the output, then guarantees that the speed of electron motion is also the same. So the kinetic energy part is not going to change anywhere in the circuit. The conversion thus cannot be the kind that you are thinking of.

[W]hy do we bring [Poynting] theorem into the picture and say that it's the E and B energy that actually light up a bulb?

Because for every single physical phenomena, there should only be one theory for it. e.g. all motion should obey (classical) mechanics, until quantum mechanics takes over. All electromagnetism should obey Maxwell's equations. All thermodynamics should follow Carnot, Boltzmann and friends. You cannot hope to have a consistent understanding of our universe and have energy being brought by electrons. Poynting worked out that if we follow the consequences of Maxwell's equations (but there is some choice involved here), then the electric and magnetic fields must carry some energy and momentum, and worked out how they would bring energy into the circuit.

In particular, the electric and magnetic fields would bring energy from the space outside the wires and bulb, into the wires and bulb, precisely in the way so that the constant kinetic energy of the electrons would not be affected, whereas the energy being brought in would exactly equal that of the heat produced in the bulb.

Once Poynting's theorem is shown to work, there can then be no other acceptable explanation for how electrodynamics handles this energy transfer issue. All other explanations, tacking on energy to the electrons in other ways, will not be able to capture the true generality of how things actually work.

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  • $\begingroup$ Amazing answer. Here is my though over your logic. You say kinetic energy of the electrons dont change which I dont agree with. Electrons as they move in the wire still do lots of scattering, it is just when they get slow down, electric field since it is the same everywhere, accelerates it again with the same magnitude of force so drift velocity stays constant. But electrons still lose kinetic energy but then gain again. In a bulb, the process is the same. They would lose KE and gain it again. Why do you say that KE is constant ? Average drift velocity is, but not KE $\endgroup$
    – Matt
    Jun 24 at 20:06
  • $\begingroup$ The KE is irrelevant to the energy flow. Think of a bicycle chain transferring energy from the pedals to the bicycle wheel. Yes, the chain has KE, but the KE of the chain is not relevant to the energy transfer. $\endgroup$
    – Dale
    Jun 24 at 21:53
  • $\begingroup$ Matt, the point I was making is that the flow of the electrons are fixed and time-invariant once the steady state is reached. And if you learn some quantum theory of metals, you will actually learn that electrons flowing in wires do not do scattering to the first approximation. They only scatter to impurities and phonons; these limit the increase in speed and eventually cause the system to agree with Ohm's Law. If you try to think of scattering in the classical way, you will be doomed to confusion. $\endgroup$
    – naturallyInconsistent
    Jun 25 at 4:18
  • $\begingroup$ @naturallyInconsistent i get your point, it is just potential energy must be converting to something else. as we know, electrons moving through wire lose PE. If you got 5V battery, 1c of electrons lose 5J over the whole wire - so during steady state establishment, they would not lose 5J - maybe lost 1J which was converted to KE but the remaining 4 ? I guess it gets lost to wire’s resistance and still converted to wire’s heat ?(imagine we dont have a resistor component in a wire, only battery, bulb, wire) - so we got PE=>heat conversions after steady state ? $\endgroup$
    – Matt
    Jun 25 at 6:54
  • $\begingroup$ Matt, you should have seen the NYU video that mmesser314 linked below. It covers how Poynting theorem fully covers how the whole V=IR is derived. If you think about it, the potential energy that you are talking about is also coming from electrodynamics, and so must be explained by Maxwell's. You cannot have an internally inconsistent theory. $\endgroup$
    – naturallyInconsistent
    Jun 25 at 6:58
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Your question is discussed in this confusing Veritasium video - The Big Misconception About Electricity. Be warned that some things in it are technically correct, but misleading.

The video prompted this question on StackExchange - How is the answer to this question 1/c seconds?. My take: It's confusing.

Here is a response from the NYU Quantum Technology Lab - Veritasium's Big Misconception About Electricity video and the point about Poynting. They explain some of the problems with the Veritasium video, but don't find a satisfying explanation. Their take: It's confusing.

This last video mentions that it is discussed in the Feynman Lectures. The Feynman Lectures are worth reading if you are up on your vector calculus. Feynman derives the Poynting vector along the lines of Poynting's original work. But he adds useful commentary. Even through it is counter-intuitive and not the only form the law could take, there are plausible reasons to think it is right. Feynman's take: It's crazy, but it works.

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  • $\begingroup$ Thanks. I saw both videos btw but they dont explain my question as in why is it not KE energy that gets converted to heat ? @naturallyincosistent gave good answer above where he said that KE is constant so it does not get lost but then I added my reply. you can check it out above. $\endgroup$
    – Matt
    Jun 24 at 20:08
  • $\begingroup$ Actually, Veritasium got it correct, but he was unclear in the original video. He has a follow up video that covered more details. Still, he misses the very important point that for every physical phenomena, there must be only one theory to cover it, and once Maxwell's equations give one explanation, that must be the only acceptable one. Everything else is a broken hack that only works in specific scenarios. $\endgroup$
    – naturallyInconsistent
    Jun 25 at 4:15
  • $\begingroup$ It is very sad to see that the NYU video covers correctly that Poynting looks weird to us all, but not realise that it is the only acceptable way to get the physics correct. $\endgroup$
    – naturallyInconsistent
    Jun 25 at 4:32
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Mr Poynting tells us that some form of energy travels at the outside of a conductor at the speed of light from the battery to the bulb.

When said energy arrives at the bulb, it must turn into potential energy, if it is not potential energy already, because there sure is potential energy there.

There is a bunching of charges at the ends of the resistor wire, this is the potential energy, which is constantly being used, as you described, potential energy => kinetic energy => heat energy.

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