(2) What *is* electricity? I should know, maybe I once did, but I strongly suspect it all came about from being told stuff, and believing it with varying levels of reluctance. The balls in a pipe analogy is nice, but it swims amongst charges, fields, fanciful claims (like 1), and div and curl operators which leave you wondering about your misspent education, and its effect on your future (fortunately, none, I'm pretty sure it's never come up since - until now).
Digressing from answering your question for a bit, to ponder this subject in greater detail:
It's a good analogy for DC, and still kind of works for AC, but the boundary conditions are very different. Also, it's very rare that acoustic power is transmitted over any kind of distance, it's mostly a nuisance (water hammer etc.), so we have essentially no need to understand its wave nature anyway. Warning signs?
To be precise, the water (or chain of balls, or whatever general fluidic medium) pushes on itself, building pressure, which causes velocity, and so on alternately, thus we have waves. The pressure is confined by the pipe, which itself is not incompressible either -- for waves to exist at all, it's necessary that the media have finite nonzero stiffness, as well as density; together, these determine the speed of sound and mechanical impedance. Just as Zo = sqrt(mu_0 / e_0) and c_0 = 1 / sqrt(mu_0 e_0) for E&M. So, we have a system where the pipe acts to confine pressure waves within it, and which has total internal reflection (except for a small amount that leaks out, due to its expansion (stress in response to internal pressure), which is very small as the metal's stiffness is a great many times that of air). It's an acoustic waveguide. At least, to longitudinal waves; transverse waves, or longitudinal going around a bend, of course transfer momentum to the pipe, hence the system shakes and emits audible sound in those cases. (Or at ends, which arguably are some combination of a bend or restriction, so the impedance mismatch causes reflected waves; in either case, momentum is transmitted to the discontinuity.)
The big break, then, between water waves and E&M waves -- if we had the intuition about water waves to begin with -- is that they are confined (almost entirely) within pipes, whereas E&M fields are largely in the space between wires. We can have an electromagnetic waveguide, but because there is no longitudinal mode, they cannot transmit at DC, but have some lower cutoff, where transmission is a decaying exponential with distance (tunneling, as we would call it in QM). A central conductor is needed to take over at DC, so that we have a coax (TEM00) line, rather than a waveguide.
And this is not a terribly intuitive difference, it's a rather fundamental aspect of the medium -- E&M has transverse waves, liquids have longitudinal as well, and solids have shear as well -- three whole unique, interacting modes! The curse, to be a mechanical engineer, can you imagine?
Which leaves the last hope for intuition, as understanding that a wave medium has some combination of characteristics, which give rise to what modes they handle; which is a pretty big leap as far as processing all that, so I would guess not a lot of people intuit waves this generally, if they intuit any kind of waves* at all?
*To a useful level I mean, like, predictively, if not quantitatively as well. So, something more than seeing ripples on water and saying, "ooh shiny".
Anyway, digression made...
Pretty sure I never knew that a magnetic field was an electric field in the charge carrier's perspective, nor that it had "simple relativity" at its core. Why did no one say? Perhaps my educators either didn't really understand it themselves, or were too academic to see beyond established models (and therefore didn't really understand it themselves). Or I was absent that day. Or it just doesn't matter.
Yeah, this is, I guess embarrassing to say, pretty fundamental to E&M and Relativity -- but it might still be no accident that you missed this particular fact -- whether through absence, or not having made the inference. And, insights like these being what they are, it's no shame to miss such a thing -- we honor the names of those few who discover them, after all!
So:
Special Relativity follows almost directly from E&M relativity, which is where the Lorentz transformation was derived: E and M fields are aspects of the more general unified EM field, plus relative motion, motion being governed by that transformation.
It wasn't much of a stretch to take that finding, and the fact that c remains constant for any inertial observer, tack on a few more assumptions for good measure (conservation of momentum, etc.), and now you have Relativity.
Not to diminish Einstein's work of course -- it was no small feat bringing together these perhaps dubious assumptions, making a rigorous mathematical description, and then a bit later, formulating the full 4-D spacetime equations (General Relativity). More to say that he was building on things that were already well known at the time, but no one had yet made the insight to say spacetime itself behaves that way.
So, the student is most likely to learn this, kind of incidental rather than explicitly, through the Lorentz force for example, and the usual induction topics. (But yeah, just go infer all of physics from a handful of equations, what's so hard about that, right?
) So, PHYS 102 or something like that, or the early EE fields courses, but again maybe not stated so explicitly. Otherwise, the introduction to Modern Physics (SR and QM) should make it clear.
Engineering curricula being what they are (hastily jam-packed with tools, thin on theorems and proofs), Modern might not be seen at all, or skimmed over -- I forget. (I have the fortune to have a physics degree as well, so I appreciate this may be a LOT less obvious to those without!)
I'm not actually sure if I remember hearing about this exact statement (E and M being relative), or if I read it much more recently, honestly. It's been a long time since I had Modern...
On the upside, I'm not sure that it makes all that much of a difference -- it's a rather rare occasion indeed that we need to deal with electric or magnetic induction at relativistic velocities,
and other than that, the usual (static) induction relations are sufficient.
Or, for another thought experiment -- consider spinning a magnet fast enough that it emits significant electromagnetic radiation -- i.e. by itself, without surrounding antenna structures. It simply has to spin so many orders of magnitude faster than any material can bear. (To be a properly resonant dipole, it needs a tangential velocity very near c, after all.)
So, to be sure, don't beat yourself up about it.
So is this quasi-classical description fairly right?: Electrons (and protons) have charge (excepting exotic matter), and are responsible for (all?) electric fields. Solid matter has electrons and protons, generally held together by electric fields at an atomic scale (not a nuclear scale). Some electrons are mobile in a metal, but otherwise follow the same rules which pack them in at a nominal spacing, so they are a barely compressible fluid (effectively in fixed sized piping). It takes mechanical force (for example an acoustic wave) to squeeze or stretch such materials, whether that be the bound nuclei or free electrons. The former does not alter the bulk charge, but does alter the size. The latter is the reverse. This force is the level of compression of the material, better described as its pressure.
Yes, that's more or less correct -- electrons are bound to nuclei by the Coulomb force and organized as quantum wave functions, because of course this is all very small stuff, and electrons are relatively large and poofy in comparison. So instead of classical orbits we get probability clouds, and instead of orbital periods we get photons corresponding to transitions between energy levels. We can ignore that quantum stuff, to the extent that we allow that matter simply clicks together however it does, and gives us these bulk properties that we can work with -- such as conductivity, rigidity, etc.
For example, mechanical rigidity is given by interatomic attraction on one hand -- mediated by ionic charge when applicable, polarization (var der Waals forces, etc.), atomic orbitals (molecular bonding), etc., and repulsion on the other -- mediated by the Pauli exclusion principle of what would otherwise be overlapping atomic orbitals.
Noteworthy I guess, that there are some neutral sources of EM waves -- for example the \$\pi^0\$ meson decays into a pair of gamma rays, despite having no (overall) electric charge; or the neutron into a proton and positron. Both are composite particles under current understanding (QCD, with the quarks and all that), there's internal structure there -- so it's kind of cheating to assert this. The only neutral, truly elementary (apparently structureless) particles are neutrinos and some bosons, and we might exclude the bosons as force carriers, leaving neutrinos as actual matter... if you can call them that. Absolutely, for sure, 100.00..% of familiar fields are driven by the displacement of electrons (and occasionally of free protons or other nuclei).
Note that the electron gas in a solid, doesn't have much for wave properties, in terms of what we'd think about with ordinary neutral gasses. The mass is so minuscule compared to the charge, inertial effects are almost imperceptible and EM waves dominate. Even at atomic scales where you might hardly think of magnetic fields, they're relevant. So, your usual bulk effects dominate -- any electron wave is just EM waves, maybe dragged down a bit, so, having some dielectric constant and loss tangent.
(Which conversely is why MHD (magnetohydrodynamics) is such a brainf**k: the inertial, propagating mechanical-wave and EM-wave, and dissipative (resistance or turbulence) modes, are so complex and interdependent that about all we can do is simulate them numerically or experimentally. And on top of that, the ionization/recombination and other chemistry of physical plasmas. So, MHD is a very challenging subject, and a big reason why fusion has taken so long to research. Besides the very low funding level, I mean.)
Other than that, pressure is less of a real physical artefact relating to the matter, and more an external philosophical measure of the potential to do work - the so-called potential energy. Force (converted from pascals for atoms and volts for electrons) in newtons, times distance (in metres) is the actual energy (joules).
Physics tends to work more in energy, and energy seems to be more fundamental to quantum processes. For classical problems, it tends to be a shortcut -- who cares how something gets there, just figure out where the energy goes -- but we might just as well imagine we're being smart using forces and trajectories to solve a problem, when the energy truly is more fundamental, while the trajectory is irrelevant, or even a fiction.
And yes, in any case, energy is an abstract quantity; it's not easy to teach I think, and coming up with analogies and explanations, may range from the philosophical to metaphysical...
Current flowing in a DC circuit is a feature of charge, in a hydraulic circuit electrons and protons (and neutrons) flow, in an electrical circuit only the electrons move. Both happen as a result of the mechanical pressure, which supplies the potential energy, but it is the duration of this pressure which transfers real energy (power). In a lossless circuit (superconductor / superfluid) no pressure is required to keep the fluid flowing, so it takes no energy. In an open circuit pressure might be as high as you like, but nothing moves, so that takes no energy.
So back to point (1) above, it's like dragging a brick along the ground with a string (in my very TBD vlog I go off on a tangent and precisely grind a V-notch around it to stop the string getting abraded, thereby getting all sorts of street appeal for being "interesting"): Once the superfluous setup montage ends, I am pulling the string in at a constant rate, performing what some would loosely call work, while getting all sorts of strange looks (I prefer to call them views). Undoubtedly transmitting power to the brick scraping surfaces (remember there are two) - but how? There is a negative pressure in the string, it is moving. Is the energy flowing "through" it? With respect to me as a stationary observer? I think it is. But I am putting the ground in compression (I am kicking it under the brick), it is moving relative to the string. So is the energy "really" flowing through the space between string and ground, on account of it enjoying both pressure difference and relative motion? With respect to the system on the physical scale of energy transfer (the current loop)? I think so. But its exact path (see Feynman lecture 27-4, handily provided in this thread), like the "potential" energy, are philosophical constructs designed to imagine something that doesn't seem to physically exist, not in this realm anyway. So it's a pretty tough call to make a statement that one particular location is "right" and another "wrong".
Well, two things:
1. Energy is relative, just as E and M are relative to velocity -- the most immediate admonition this suggests is, we must be careful and consistent with what frame of reference we are working in.
2a. The string is a different kind of wave medium -- in this case a solid one, so you can transmit three kinds of waves (with them all depending on the string being under tension, to propagate correctly, and even then at a dependent velocity). And of those, really just the longitudinal mode (static tension) is doing anything, I mean you can shake the string and, what's going to happen, maybe the brick slides microscopically off-center when it does, sometimes; nothing on average.
2b. The tension doing work is DC, so we really don't have any insight into the wave mechanics, and where the energy is flowing (or not!).
Note that the tension (in the mental sense, hah) between "DC flows in wires" and "AC flows around wires" doesn't need to reference a different medium, to still be relevant. We can happily ignore the fields around a DC battery, or most AC mains cables, and yet still have RF energy for example, very noticeably travelling in the space between wires, even in the same sorts of cables, at the same time. I think the quibble is just that: we don't particularly care about the fields at DC, and at AC we have other phenomenon more directly relevant, like skin effect and "path of least impedance" (image currents under signal traces, etc.) which are more descriptive. I think if anything, the confusion is really just this old dichotomy between DC and AC current flow paths, with some fields thrown in for spice.
Tim
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