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I have recently watched two YouTube videos on this subject, that you can see here (first by "Science Asylum" and the other by "Veritasium").

So, both videos ask the viewer to imagine a simple circuit, a battery connected to a resistor (such as a light bulb). As the battery is connected in the circuit, it will cause the electrons in the wire to drift away from the negative terminal of the battery, dissipate energy in the light bulb and then be attracted into the positive terminal.

Veritasium video shows though that one shouldn't really think of this as some kind of "domino" effect for electrons, but rather as an EM wave propagating directly from the battery to the light bulb, as computing the Poynting vector reveals that the flow of energy is directed away from the battery and into the load (as shown in this screenshot taken from the video)red= electric field, blue= magnetic field, yellow=Poynting vector

This is used in the video to show that even if the wire segments are, say, one light year long, if the battery is 1m away from the light bulb it will take only 1/c seconds for the light bulb to turn on (watch the video if this sounds confusing, he does a great job explaining this).

However, in the video by Science Asylum there seems to be another perspective on the subject that I don't see exactly how it is equivalent to Veritasium's. Science Asylum shows that the electric field on the wire is not radial to the wire (as it seems is the case in Veritasium video, which I don't fully understand), but rather parallel to the wire (which kind of makes sense, as Ohm's law says that J=\sigma*E where \sigma is the electric conductivity, which means that the current density is in the same direction as the electric field...). But this means that when one computes the Poynting vector (as Science Asylum does in his video), it points AWAY from the wire and into the "field" around it. He then basically says (from my understanding) that the energy flows from the battery into the field around it and is then picked up by the light bulb and the wires directly from the field (doesn't say much about how "fast" is this process as in Veritasium video...).

In any case, what is the correct picture? I don't understand how both can be correct, given that they show electric fields pointing in different directions in the two videos... Is there something I'm missing here?

Thank you!

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The Veratasium video concentrates on the battery and bulb. Those are the only two objects that exchange energy. It assumes there is no loss in the wires. The Science Asylum video assumes the wires have resistance and there are losses in them.

Science Asylum shows that the electric field on the wire is not radial to the wire (as it seems is the case in Veritasium video, which I don't fully understand), but rather parallel to the wire...

This is correct... in certain cases:

  • While current is changing (because the electric field needs to accelerate or decelerate the current)
  • While constant current is moving through a resistor (because the field needs to make up for the resistance losses.

In the first case, the accelerating charges need energy, so the energy has to be supplied by the battery (via the field). But if if this is a true A/C circuit, the charges are later decelerated. The field direction reverses and the energy is returned. The net energy flow over a cycle is zero.

In the second case, the resistance in the wires means that at a steady current, a field must exist inside the wire. The stronger the resistance, the stronger the losses and the stronger the axial field inside the conductor. Since there are losses, the energy must be replaced. This appears to be the contribution that the Science Asylum video is concentrating on. It treats both the wires and the bulb as energy consumers and the battery as an energy producer.

For many power delivery circuits the power loss in the wire is a small fraction of the power loss at the load (the bulb in both cases). It can be a reasonable assumption to ignore the loss in the wires. The Veritasium video, the Science Asylum video does not.

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    $\begingroup$ I understand the importance of Poynting vector in the problem , but how does the light glow, in 1/c seconds, when the electric field from battery still haven't reached the bulb filament in 1/c seconds $\endgroup$
    – User
    Commented Nov 21, 2021 at 9:34
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You can only neglect resistance of conductors for good conductors with short distances. Power source itself has resistance too and it is not that small depending on source. It is all very very complex. Electrons are particles, electromagnetic waves are waves, however at higher frequency electrons will behave more like a wave and less like particles. Resistance of conductors at such distances would be enormous and they would work like antennas and radiate and pick up electromagnetic energy. There are also other serious limitations like nothing can't travel faster then speed of light. Scale makes difference. Electromagnetic fields also have their limits related to distance.

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