> isn't it the electromagnetic field then (that consists of photons) that moves the energy from source to sink because photons are capable of moving energy rather than the electric field between the wires?

Yes, that's my understanding also; I focused on the electric field in my last post because that's what differs inside and outside a conductor; the magnetic field exists and has the same orientation both in and outside a conductor carrying current. But it's the product of the two which defines the Poynting vector, which indicates the flow of energy in the EM field.

What I've calculated so far (for the case of two infinite parallel wires) does indicate that the Poynting vector is concentrated around the wires -- it drops off approximately with the 4th power of the distance from either wire (though there's a decent saddle between them). I plan still to calculate some integrals around the wires because I'm curious actual numbers. For reference the expression I've derived is:

|S| = Pr² / (ln(2r/a) × ((y² - z² - r²)² + 4y²z²))

where:

S = Poynting vector

P = power delivered

2r = distance between wires

a = diameter of wire (this only creeps in when relating voltage between the wires to charge on the wires)

The Poynting field points uniformly from the source to the sink, in the +x direction (same axis as the wires). The y axis points from one wire to the other.

Ah that makes a big difference. Note how all of this started:

> The energy doesn't flow inside of a wire, it flows around the wire.

As though all of the energy flows outside of a wire, which doesn't make any sense at all (and still doesn't!), if it did then the wire itself would never heat up, which given the fact that there is a voltage across the wire (low, but still, it is there) and current flowing through it does not make any sense at all.

And the 'B' component of the fields created by a current carrying wire is in fact the magnetic field (and a magnetic field as I'm sure you are aware doesn't need a 'return wire' as such, as any magnet demonstrates, and there too the field is much stronger at the poles of the magnet), these fieldlines would be best visualized as concentric circles around the wire ( https://www.researchgate.net/figure/The-magnetic-field-lines... ) with the spacing dropping off as you get further away from the wire ( http://physics.bu.edu/~duffy/semester2/c15_inside.html ), and it definitely would be present inside the (single!) wire.

The electrical field by itself doesn't do any work, but has the potential to do so and this potential diminishes the further along the path from 'source' to 'sink' and on the return leg through the wire. The magnetic of the free electrons in a conductor also doesn't do any work. But when you start moving those electrons their magnetic field is doing work. The electrons themselves only move a fraction while they move the magnetic field lines 'along' with them in the direction of their travel and the strength of the electrical field between the two conductors is a measure of the potential energy available to do work. In a pure DC setup this shows up as the voltage across the wires relative to a reference ground (say, a sense wire on the - pole of the battery in the simplest possible circuit, a power source coupled to a single loop of wire without any visible load, the wire is the load). As you move around the circuit you'll see a nice and predictable drop in voltage as the potential of the fields to do work diminishes until it reaches zero at the point of reference. You'd see the same drop in voltage if you picked the + as the reference, only the magnitude would be reversed, but the product of voltage and current across any given section of wire of a particular length would be constant.

In an AC setup some of the radiated energy would 'escape' from the wire and if you engineer your AC setup carefully to maximize such loss you have an antenna. Conversely, that antenna would be able to capture an external magnetic field and turn it into electrical energy again (technically: potential energy, the circuit would have to be closed somehow for current to actually flow). If you carefully engineer this to transfer energy between two points you end up with a closely coupled set of two loops of wire aka a transformer.

I think what is happening here is that OP mistook the Poynting vector (a mathematical construct derived from the cross product of electrical and magnetic fields) for 'reality' in the same way that the map is not the territory, it is a very useful tool to show the flow of energy in a system, essentially it allows you to decompose the 'A' and 'B' fields of a system of wires, for instance a current carrying loop and a load.

But it's wrong to say that the Poynting vector moves the energy outside (or even mostly outside) of the wire, even a single one because you are now talking about the whole system rather than just a single wire and in that system the plane described by the loop of wire is still 'inside' the wire. All the Poynting vector does is to show how strong the cross product of electrical and magnetic fields are at any given point and what the magnitude (power delivered) and direction (where the source is and where the sink is). But that's a simplified view that does not take into account the interior resistance of the source and the interior resistance of the wire and if you don't take into account you end up with a system that is not realistic and which leaves a lot of real world phenomenon unexplained (conductor losses, source losses).

So by switching from one wire to two wires and a load the picture became needlessly complicated, you don't actually need a separate load to demonstrate all of this (the resistance of the wire is a load!). And then all of the rest of the bits fall into place much easier, after all the work done by the magnetic field doesn't care in which direction the current flows and doesn't even care about the direction of the field, it will simply excite the atoms of the material that the carrier is made out of and it will do so proportionally to the resistance of the carrier resulting in heating the material up (which in turn shows up as new photons, IR ones...). This is is self evident: if it didn't you would violate the conservation of energy rules, you can't excite the atoms in the material without energy transfer of some sort, and in this case the energy transfer at the quantum level is mediated by the EM fields of the free electrons interacting ('bumping into', if you want to use a simplified view) with the EM fields of the electrons in the material itself. The more such free electrons (the larger the current) the more such interactions and the higher the voltage the taller the stack of such interactions, hence P = I * V (momentary) and over time that translates into energy delivered.

Too late to edit 'A' should of course have been 'E'. (E -> electrical field, B -> magnetic field).