5 ms·

> But for bulk energy transfer at very low frequencies it definitely isn't the skin that carries the energy, if it were you could replace all of your copper wit

> But for bulk energy transfer at very low frequencies it definitely isn't the skin that carries the energy, if it were you could replace all of your copper with foil and call it a day. As I stated above, the copper emphatically does not carry energy. It can not, because the electric field in it is zero. What you are saying is true of electrons, it is true of current, but it is not true of energy. The energy is not contained "within" the electrons or is otherwise somehow tied to or carried by them. The energy flows through the EM field as indicated by the Poynting vector which is only nonzero outside of copper. (Outside, as in -- through the void between power sources and sinks. Not the skin.) This field is induced by the flow of electrons. Think of it this way: if energy were carried "in" the wires -- in this experiment, from the negative terminal of a battery to the light bulb (coinciding with the flow of electrons) -- what then is occurring within the wire connecting the light bulb to the positive terminal? Is energy flowing from the light bulb to the battery? If not, what makes this wire quantitatively different from the other such that energy isn't returning to the battery along this path? It's the same current after all (KCL), pointing back at the battery now. It's not a matter of "circuit theory vs. Maxwell's equations" (and I don't know why @H8crilA is framing the argument like that). Circuit theory simply doesn't say anything about the flow of energy. It deals with current flow and voltage potentials, but not energy flow (except in the cases of transmission lines and transformers). It's not "wrong" or an "approximation" in this sense -- but there's nowhere in a circuit diagram you can point to and say "this is the path the energy is following". (Unless you start decorating the diagram with arrows between power sources and sinks, which then starts to look a heck of a lot like the Poynting vector.) But if you say instead, "the energy flows through this wire" (which again, circuit theory does not claim), this is mathematically inconsistent in even the simplest circuit, since, after all -- energy does not flow in circles! I suppose one could augment circuit theory with a notion of "energy flow through a wire" by equating that to product of the current through the wire and the potential between that wire and some fixed reference (e.g. ground). This would be mathematically consistent but not give meaningful physical results -- the battery-light bulb circuit above, if tied to an arbitrary potential high above the reference, would indicate a proportionally arbitrary massive amount of power flowing "out" of the battery, and slightly less than that amount flowing back "in" to the battery. Maybe some EEs conceptualize circuits this way (maybe even I do unconsciously?) but I'm not aware of this being standard pedagogy.

jacquesm 3y ago
You have cause and effect switched. The field is the result of the flow of electrons, not the other way around. That makes for a nice shortcut ('it's all fields') but without that flow of electrons through a conductor carrying current there is no field. Fields are a direct result of moving charge and electrons carry charge. This is symmetrical, fields in turn have the potential to move charge. The fact that some fraction of those fields extends outside of the conductors (they have to, they are at right angles to flow of the electrons in the conductor) is not a very good reason to suddenly leap to the conclusion that all 'energy is transferred outside of the copper' until you actually use that component: such as in a transformer, or to model parasitic inductances between conductors. And then you'll find that for most wire thicknesses and most frequencies (except for special HF 'litze' wire) the bulk of the energy is still transferred within the circumference of the wire. That's because the EM field of a single electron is tiny and extends in theory out into infinity but in practice and at normal currents and frequencies is actually very limited. The reason why people under normal circumstances would not decorate the diagram with arrows between power sources and sinks is simple: it would be redundant. Just like we don't draw capacitors, coils and resistors over every wire. We all know they are there but for most practical work you can ignore them, in fact you do your level best to ensure that those parasitic components are as small as you can make them to ensure your circuit works as intended. But once they become more dominant (which already happens at very low frequencies above DC) you have to start taking them into account, but for most regular applications you will still find that the larger part of the field is constrained within the wire and only a tiny amount extends outside of it. So, in an extremely pedantic sense you are right: for an infinitely thin wire the EM field will lie completely outside of the wire. But for real world wires the bulk of the field is constrained within the wire.
- H8crilA 3y ago
  > You have cause and effect switched. The field is the result of the flow of electrons. Actually it's the electric field that causes the flow of electrons. The flow of electrons does not create the electric field. It can't be the other way around, as the movement of electrons does not create an electric field, only a magnetic field (which is then crossed with the electric field outside of the conductor to create a flow of energy). Electrons do not carry energy in a circuit. They use up some of the energy from around the conductor when they bump into atoms of the conductor, we call this process resistance. In particular they can be used purposefully to convert EM energy into heat, like in a light bulb. PS. I keep bringing the circuit theory in because it is the reason why people can't believe how electricity actually works. But you can forget about this if it doesn't help, it's not that important.

jacquesm 3y ago

You have cause and effect switched. The field is the result of the flow of electrons, not the other way around. That makes for a nice shortcut ('it's all fields') but without that flow of electrons through a conductor carrying current there is no field. Fields are a direct result of moving charge and electrons carry charge. This is symmetrical, fields in turn have the potential to move charge. The fact that some fraction of those fields extends outside of the conductors (they have to, they are at right angles to flow of the electrons in the conductor) is not a very good reason to suddenly leap to the conclusion that all 'energy is transferred outside of the copper' until you actually use that component: such as in a transformer, or to model parasitic inductances between conductors. And then you'll find that for most wire thicknesses and most frequencies (except for special HF 'litze' wire) the bulk of the energy is still transferred within the circumference of the wire. That's because the EM field of a single electron is tiny and extends in theory out into infinity but in practice and at normal currents and frequencies is actually very limited. The reason why people under normal circumstances would not decorate the diagram with arrows between power sources and sinks is simple: it would be redundant. Just like we don't draw capacitors, coils and resistors over every wire. We all know they are there but for most practical work you can ignore them, in fact you do your level best to ensure that those parasitic components are as small as you can make them to ensure your circuit works as intended. But once they become more dominant (which already happens at very low frequencies above DC) you have to start taking them into account, but for most regular applications you will still find that the larger part of the field is constrained within the wire and only a tiny amount extends outside of it. So, in an extremely pedantic sense you are right: for an infinitely thin wire the EM field will lie completely outside of the wire. But for real world wires the bulk of the field is constrained within the wire.

H8crilA 3y ago
> You have cause and effect switched. The field is the result of the flow of electrons. Actually it's the electric field that causes the flow of electrons. The flow of electrons does not create the electric field. It can't be the other way around, as the movement of electrons does not create an electric field, only a magnetic field (which is then crossed with the electric field outside of the conductor to create a flow of energy). Electrons do not carry energy in a circuit. They use up some of the energy from around the conductor when they bump into atoms of the conductor, we call this process resistance. In particular they can be used purposefully to convert EM energy into heat, like in a light bulb. PS. I keep bringing the circuit theory in because it is the reason why people can't believe how electricity actually works. But you can forget about this if it doesn't help, it's not that important.