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.