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May 10

Trench warfare

In sandy soil (such as in desert sand), how long does it take to dig a 2-person foxhole? How does that compare with the time it takes to build a 2-person sangar on rocky soil (provided that rocks of a suitable size are readily available?) 2601:646:8A81:6070:DD66:FADA:7337:C84 (talk) 03:10, 10 May 2022 (UTC)

Miniature foxhole in sandy soil

Fixed your link. --184.144.97.125 (talk) 05:14, 10 May 2022 (UTC)

The particles making up desert sand such as those forming the sand dunes in the Sahara are very rounded and smooth, like miniature marbles. So the angle of repose is very low; anything one might think of as a foxhole will not be stable. Even for jagged but dry sand this angle is not very high, generally below 35°.^[1] A pit that is 2 m deep will have an outer perimeter of about 18 m or more; its construction requires removing about 17 m³ of sand. That is an awful lot. One might construct a retaining wall, but then it becomes almost a civil engineering project, not a matter of simply digging a hole.  --Lambiam 22:36, 10 May 2022 (UTC)

So a shell scrape is the best that can be done? 2601:646:8A81:6070:E4C1:B321:D6C1:FE54 (talk) 09:01, 11 May 2022 (UTC)

In the Western Desert Campaign, trenches and weapons pits were revetted with sandbags, ammunition boxes or fuel cans filled with sand. An account of the work involved is here. I suspect that a couple of experienced soldiers could make a reasonable one in a few hours, given the right equipment. A spade (carried on vehicles) was preferable to the entrenching tools carried on the men's webbing equipment. Alansplodge (talk) 18:47, 13 May 2022 (UTC)

Right, sandbags -- there's your retaining wall (which, moreover, you can build as you go, simply by filling them with the very sand you dig up)! 2601:646:8A81:6070:F4FB:51FE:8474:7D14 (talk) 02:36, 14 May 2022 (UTC)

I think you have to dig the hole first, unless you can devise a way of inserting new sanbags under the ones that you have already laid. Alansplodge (talk) 11:01, 16 May 2022 (UTC)

Electric current drift speed and electromagnetic wave

In chapter “drift speed” of “electric current” articleElectric_current#Drift_speed, there are expressions about “electromagnetic wave”, “electromagnetic energie”. But nothing on the frequency or wavelength of these signals. Why ? Malypaet (talk) 21:51, 10 May 2022 (UTC)

Because typically the speed of the signal is only weakly dependent on the frequency (and the wavelength is just the speed divided by the frequency). The dependence of speed on frequency that there is, is called dispersion (because the signal spreads out as the faster frequencies run ahead of the slower ones). catslash (talk) 22:40, 10 May 2022 (UTC)

(ec) The frequency of an electromagnetic wave generated by alternating current is the same as the frequency of the current, usually 50 or 60 Hz. Let $\lambda$ denote the wavelength and $f$ the frequency. Then, in vacuum – and for all practical purposes in air – the following relation holds: $\lambda =cf^{{-}1},$ in which $c$ denotes the speed of light. In the general case the wave has no definite frequency, just like hitting a wall with a hammer generates sound waves that have an indefinite pitch.  --Lambiam 22:55, 10 May 2022 (UTC)

Mains electricity usually has a frequency of 50 or 60 Hz. The waves I work with usually have a frequency of a few GHz. Also the conductors are typically supported by an insulator which may reduce the phase velocity to c/2 or less. A short pulse such as that from a hammer blow is generally regarded as composed of a broad spectrum of frequencies, giving rise to a spectrum of acoustic waves which will be subject to dispersion (albeit not much). catslash (talk) 23:57, 10 May 2022 (UTC)

An important and very simple concept is often lost in the details: when alternating-current electricity flows in a wire, the energy is conveyed by a combination of different things:

• Movement of charge-carriers (electrons) in the form of electric current
• Alternating variation of the electric field (taking the form of a propagating electromagnetic wave)
• Alternating variation of the magnetic field (taking the form of the other portion of the same propagating electromagnetic wave)

All of these things convey the energy. The moving electrons interact with the changing fields; the changing fields interact with the electrons. Think of it in the same way that the molecules of water move when an ocean wave happens. It's not quite right to say that the water-wave "pushes" the molecules (after all, the ocean water is made of molecules); it's not quite right to say that the molecules "push" the wave (...what's making the molecules move, if they're the ones doing the pushing?) Really, it's probably "better physics" if we simply say "a wave is happening," and as part of that, the whole system undergoes changes at microscopic and macroscopic levels. Microscopic parts are moving coherently; we can model their ensemble movements using a wave equation.

The same is true of the electricity in a wire: the whole system undergoes changes: electrons drift back and forth, subject to the changing fields. The fields change, and as electrons move, those electrons change the net field. How much is the field "caused by" the electron motion? How much is the field "causing" the electron motion? Well, the answer comes from the complete solution to the wave equation, which involves "lots of difficult math." How much complexity do you want? A simple form that works is "Ohm's law", while there are plenty of more complicated treatments for different applications. The most common model that works without loss of generality is the set of equations we call Maxwell's equations (specifically, the form that includes a non-zero and corrected term for J in the fourth equation).

There can exist solutions where the electrons and the electromagnetic field terms have different behaviors. How complicated do you want things to be? Professional physicists can spend years studying complex variations of these equations in special cases, and also in the quest for better generalizations that work universally.

One specific application where we actually care about the wavelength of the moving charge-carriers (as opposed to the wavelength of the electromagnetic wave) would be in the microanalysis of the physics inside a semiconductor. We have an article-section about one formulation of this kind of model; and if you're really dialed in to your mathematical physics, you can immediately see a sort of a wave equation popping out of that diffusion term, especially if you make it nonhomogeneous ("apply an external time-varying field" and see what happens!) Hey, that is exactly the wave that makes real-world radio amplifiers different from (and worse than) textbook radio amplifiers!

Nimur (talk) 18:02, 11 May 2022 (UTC)

Per Nimur, electromagnetism is really complicated, which is why we have heuristic solutions that allow us to skip over all of the messy stuff like "how does energy get from the battery to the lightbulb in an electric circuit" and "what are the electrons actually doing when we say electricity is flowing" and stuff like that. Besides the simplified math of Ohm's law and Maxwell's equations (and yes, Maxwell's equations are not a complete mechanistic picture, just a better heuristic than Ohm's Law) there are things like the sea of electrons model for conductors and the Hydraulic analogy for electric circuits. Even things like drift velocity can distract from the actual physics behind how electric circuits may power a device. This video by Science Asylum is the one of first in a BIG series of videos from numerous YouTube explainer channels which try to explain the matter. It's actually something of a controversy in the YouTube Science Communication space, largely because This video from Veritasium contained a somewhat confusing thought experiment that was imprecisely explained, generating like a million response videos from other science YouTubers, and This more recent clarification video from Veritasium on the same subject. I would watch those videos to start to understand at least the complexity of understanding what is really happening with electrons and energy in electrical systems, and remembering that it's not what your intuition says it is. --Jayron32 18:19, 11 May 2022 (UTC)

Those were entertaining videos. I am astonished by the reluctance of people to accept the idea that the energy can "leap", so to speak, across a gap... I wonder if this denialism could have been avoided if the very simple explanatory power of this statement: "it is possible to transmit power wirelessly" - most people already know this! - so even when there is a wire, some of the power is not flowing through the wire!

I think the problematic bit comes around when the stronger statement is made... (in some of the videos, I heard some explanations that could be interpreted as "none" of the power flows in the wire; or "none" of the power is in the electrons). That's a can of worms - because that depends on the set-up. It is possible to construct either scenario.

Anyway, this whole situation is essentially the "transmission line problem," which is covered in about nine thousand variations of increasing complexity in this entire textbook, and if you want more, there's this entire textbook that takes it to a whole additional level, and just as I opened with, you can spend years studying the nuances and subtleties - but at a certain point, even the most dedicated student sort of loses interest and moves on to more interesting and productive applications of electromagnetics,...

Nimur (talk) 02:32, 12 May 2022 (UTC)

Now don't overcomplicate things. Classical electrodynamics is doable once you develop some intuition for it. Don't use modern physics when classical physics suffices. As long as you're not building radios or electronics, you rarely need more than Ohm's law (maybe with complex numbers instead of real numbers when dealing with AC, but only on very long lines or when using big coils). I wish people wouldn't mention modern concepts like molecules, electrons and photons when talking about stuff that can be handled with classical physics. PiusImpavidus (talk) 09:29, 12 May 2022 (UTC)

Yes indeed, everything PiusImpavidus says. catslash (talk) 10:11, 12 May 2022 (UTC)

Obviously. It depends on what the purpose is; if you're just building a circuit most of the time you just do "Ohm's law" and "Kirchhoff's circuit laws for the ideal case and budget for "losses", and call it a day. If you want to get in to the "why is this happening at all? How does electricity work?" question, at a fundamental physics level, it gets much more complicated, and non-intuitive. --Jayron32 11:48, 12 May 2022 (UTC)

All models are wrong. A phenomenon can be most readily understood by examining the simplest model that exhibits it. Even the hydraulic analogy exhibits markedly different particle and signal velocities. It also admits the question of how or whether these depend on the driving frequency. catslash (talk) 12:31, 12 May 2022 (UTC)

Yes, but you forgot the functional part of that quote "but some are useful". Ohm's and Kirchhoff's are fantastically useful models. --Jayron32 15:15, 12 May 2022 (UTC)

I also can't concede that any reasonable taxonomies of science would place the concept of "molecules" in the arbitrary category of "modern theories" 🤣

I think if we actually delve into a bit of history, we find that wave equations were formulated for rigid bodies ("molecules") long before they were formulated for electromagnetic fields! We might even say, "classical physics" is strictly the study of the various forms that the wave equation takes, and "modern" physics is about finding wave equations in new places one would not have looked prior to, say, the year 1880 - which is hardly even modern anymore!

I'm being a bit pedantic, but I think we should not conflate "complicated" and "modern." Many of the simplified models - the things like writing "V = I R" - are actually very modern inventions. Mr. Ohm did not write that kind of thing: Herr Ohm was what we might call ... a "classical physicist." He lived during an era before most scientists knew or accepted the atomic theory as we know it today; he lived long before our most famous experimental demonstrations that probed (and proved) various subatomic structures, let alone any "modern" explanatory theory for their workings... but actually, Herr Ohm wrote a wave equation to describe electricity as a transmission between as-yet-undiscovered microscopic particles. And then others linearized this wave equation: "V = I R" is a modern simplification of a classical physics treatment that largely promulgated in the 20th century. Actually, Ohm writes:

“ ...habe ich ei nen besondern Fall bis ans Ende geführt, und an ihm ersehen, dass die Formel die Art des Wogens der Kraft, wie ich es vordem beschrie ben habe recht genügend darstellt. ” — Georg Ohm, Die galvanische Kette, mathematisch bearbeitet, available online via Google Books

The point here is, Ohm's law as you know it today — "V = IR" — is "modern physics". Ohm's law as known to a classical physicist — Georg Ohm — who lived and died before any new theories by Planck and Dirac and Einstein —was written in a classical physics form — as a wave equation propagating among as-yet-undiscovered corpuscles.

$\chi \omega {\frac {du}{dx}}=\chi '\omega '{\frac {du'}{dx}}+\chi ''\omega ''{\frac {du''}{dx}}$ ... from the same book, around the section deriving the electric tension propagating amonst rigid bodies. (Page 140, in the version I linked). I think it's clear that Ohm's classical wave equation is a lot less modern than your scalar simplification, and yet, because he's German, his notation is more modern and more recognizable to us today than the writings of many of his English contemporaries! (Henry Cavendish is sometimes credited with discovering the same relationship even earlier than Ohm, but ... despite writing his works "in English," nobody today can actually read or understand Cavendish).

Whether either theory is "correct" or "useful" may be subjective, and we can debate and compromise on those points - but I think we can not really budge on the factual issue of whether Ohm's own formulation is "modern." It's more than two centuries old!

Wave mechanics is almost the defining character of classical physics! And let us avoid conflating "simple" with "old", "complicated" with "modern." These are unrelated adjectives!

Nimur (talk) 16:44, 12 May 2022 (UTC)

I was making a bit of fun (as you all noticed, I presume). But I'm serious that I want to keep the microscopic stuff out if things can be explained with macroscopic physics. Maybe it's my background in astrophysics, but I'm generally happy to deal with continuous things (matter, charge, radiation; yes, I know when you can't). PiusImpavidus (talk) 18:57, 12 May 2022 (UTC)

My points were never to be historically rigorous with describing the different approaches. It was merely that understanding what electricity is doing is only tenuously connected to understanding what electrons are doing. There exists very simple mathematical models that allow us to do basic electrical work and build and analyze circuits without any real understanding of the nature of electrons or of electric fields or of electric energy and what it is "really" doing. --Jayron32 13:38, 13 May 2022 (UTC)

Sorry if I came across as if I were making grumpy accusatory insinuations about the earlier posts - that wasn't my intent - I seem to have a tendency to sound crotchety when I write! I'm happy to see enthusiasm for science, it takes a lot of different forms! Nimur (talk) 20:26, 13 May 2022 (UTC)

We ought to have said that increasing the frequency decreases the skin depth and hence the effective cross-section of the conductor - and so increases the drift velocity for a given total current. catslash (talk) 23:54, 13 May 2022 (UTC)