adx: if you follow Poynting then copper wires are the low-frequency equivalent of light fiber, a transformer is impedance matching, and a resistor is a low-frequency black-body.
I'm reasonably happy with that occult-like thinking. Metal is a shiny reflector, transformers are used in RF for purposes other than isolation, and a microwave-powered incandescent emitter might not be such a silly thing in some piece of equipment. But there comes a point where even the silliest engineer will reject something too silly for even their silliest of comedic senses
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For acoustic waves, half the energy is in the pressure, and half in the velocity (much like in light, half is in E, half is in B).
I'm fairly sure if I learned facts such as that (for E and B) and it was presented as something understandable, then EM would have made a lot more sense to me. Instead I got invisible mathematical concepts, and things like the graph you see so often repeated (with the arrows, that I can only assume is as utterly opaque to others starting from nothing as it was to me - no one says it is a graph of field strengths along the line of propagation, leaving less mathematically inclined people to guess it is a picture of some kind of magical aether strings being poked at by sharp sticks which physically wave about).
Anyway, the acoustic wave thing might help explain (to others and myself) about Poynting and the 'difference' between DC and steady state.
A hydraulic circuit works a bit like an electric circuit (balls in a pipe), so turning on a switch (opening a valve) allows pressure to 'flow' at the speed of sound to the load, and current flows at the same time. This description (and hence model) of course has little to do with the pieces of fluid that carry the pressure and end up in the load, it's about a pressure wave causing the molecules to accelerate and flow almost instantaneously (compared to how long it would take the fluid to go around the circuit). Once this transient settles, and flow becomes steady state, nothing changes in the nature of how energy is delivered to the load - it is still described by a transverse (between pipes) pressure difference being sent back and forth, and how fast all the fluid molecules are moving around the circuit. If either end changes the pressure, the other end will see it at the speed of sound. Same if poking at something with a stick. If modelling that, a wave effect governs that transfer of pressure at only two possible velocities: + and - speed of sound (to and from load). Anything which uses that model to calculate power, can only assume it travels at that same speed and from a transverse pressure difference. If DC steady state, there are still molecules pushing on each other electrically, with mass, and a limit to how quickly that can do work at the other end.
For a hydraulic circuit at DC it is easy(er) to poo-poo the notion of a Poynting-like vector where the current is represented by some out of pipe "field", because the momentum part of the wave transfer is due to the inertial mass of the molecules (which is thought to reside in the molecules and pipe). It also doesn't change, so the energy transferred via pressure isn't mediated by the mass (so you could then turn around and say it clicks over to infinite speed at exactly 0Hz).
But for an electrical circuit, the momentum arises from electrical field effects, which can be outside the wire. Because the momentum isn't located to inside the electron, it is possible that the field changes as it passes by other parts of the circuit - with no net energy change but more possibility for action than with a particle with internal inertia.
And oops that's me again for the night.