How does energy conversions happen in the circuit?

Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

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.