I find these guides a bit disappointing in that they always give the example of a wire loop generating an EM field, which one could sort of imagine given day to day experience with direct current and conductors. However this all breaks down when looking at regular monopole antennas - how can the conductor conduct when one of the ends is just hanging in the air? AC magic I suppose.

Similarly they are very short on details on what exactly is going on when the EM field is generated. I guess it consists of photons, but where exactly do they come from and how are they generated using (in some cases) only milliwatts of power?

Its abit outdated. But it think you may enjoy reading through Oliver Lodge's book, "Signalling Through Space Without Wires"

[0] https://catalog.hathitrust.org/Record/001617948

Photons are created when an electron drops to a lower energy level. Like your voicebox and the sound you make when you speak, it doesnt come from somewhere but is created right then

No, the "photons" here are not created by that phenomenon but rather by accelerating electrons. https://en.wikipedia.org/wiki/Larmor_formula

Cool, thanks for letting me know.

It doesn't really "generate" a field. The EM field is always there, permeating the universe. An acceleting electron will _disturb_ the EM field (depositing some energy and momentum into it), and this disturbance will propagate through the field at the speed of light (naturally, since at the right energy level such a disturbance is what we call light). At high energies the disturbance will be finely localized in space and behave like a particle, which we call a photon. It's fine to refer to it as such also at lower energies, but slightly misleading because at the very low energies that we talk about here ("radio") it is very spread out in space and behaves more like a wave (with a wavelength of ~meters). In the case of AC, electrons are moving "back and forth" over a short distance (somewhat simplified but useful picture) with the same effect. Think about moving your hand up and down through water - you will create a wave.

>The EM field is always there

Did you mean to say "the E field is always there"?

Loved this explanation otherwise.

It's one field, which can be split into E and B components if you like.

The B field is just the E field's relativistic effects to an observer not in the same motion frame.

https://wikipedia.org/wiki/Classical_electromagnetism_and_sp...

Both are always there if the circuit is running.

Also, both E and M fields are required to transport any power using electricity. This is also true for DC current. See https://en.wikipedia.org/wiki/Poynting_vector - the formula multiplies E by B, therefore if any of the two is zero no power (or information) transmission can occur. This is true over the air, as well as over a wire.

>The EM field is always there

Hmm sounds dangerously close to aether theory. I thought we had moved past this … that EM waves exist in their own right without need for a medium. Unlike sound say.

Aether refers to some historical ideas (which evolved over time), and though the word isn’t in use anymore the current model of fields has similarities (ofc in many ways very different). Have just been reading some of the history of this (Einstein plays a big role), it’s very interesting, thank you! :) You might be interested in this discussion https://news.ycombinator.com/item?id=27942970

Way over my head unfortunately

Wilczek points out that field theories are aether theories — as is relativity.

“Aether just means this one particular historical model!” is branding more than reality; and hides the fact that modern theories also describe an everywhere substrate of which particles are localized excitations and gravity is localized warping.

Air is aether.

Air is not required for an E field to exist or propagate.

EM fields propagate just fine through vacuum, they are mediated by photons.

>AC magic I suppose.

Yep. Think of a long pipe open on one end and capped on the other. If you seal the end with your mouth and blow, it will quickly pressurize. But if you seal a loudspeaker to it and sweep through the frequencies you will find that the loudness of the speaker varies proportionally to how close the tone is to a resonant frequency of the tube.

The elections in a monopole antenna have a sort of elastic relationship to one another where the influence propagates at the speed of light rather than the speed of sound. They are also able to move quite freely within the conductor like gas molecules in the tube. So if you have an antenna that’s two meters long and play a ‘tone’ with the equivalent of the loudspeaker at 150 million hz, the tube of electrons resonates.

Just like the atmosphere can couple resonant cavities of the same frequency, antennas are coupled by the electromagnetic field to resonate at the same frequency. This provides a certain ‘gain’ of the energy at the end of the ‘tube’ relative to other frequencies that aren’t resonant, which is what feeds our ears or amplifiers with something differentiable from the rest of the noise.

Circuit theory breaks down when it comes to antennas.

Circuit theory breaks down at high frequencies and the appropriate generalisation of Kirchoffs is embodied in Maxwell’s equations.

Indeed, it's a bit like Newton vs Einstein.

The one is a special case of the other, it doesn't make the former wrong but the latter gives better answers in situations where the special case constraints aren't satisfied.

Circuit theory is demonstrably wrong. The energy doesn't flow inside of a wire, it flows around the wire.

https://en.wikipedia.org/wiki/Poynting_vector

https://www.youtube.com/watch?v=bHIhgxav9LY

It is a very useful tool in practica.

Energy does flow 'inside' a wire at low frequencies. The skin effect gets higher and higher as the frequency goes up until you reach a point where it is all skin effect. But even that 'skin' isn't idealized it definitely has a thickness, about 30 u at 5 MHz and 6.5 at 100 Mhz.

There is a neat little calculator here:

https://www.omnicalculator.com/physics/skin-depth

No. DC energy also flows around the wire. In particular it's not the electrons that carry the energy, though they can receive it from the fields and depose inside the conductor (like in a light bulb).

Wires, or conductors in general, are so useful because they allow us to manipulate the EM fields and channel the energy very efficiently.

It's an very common misconception coming from circuit models.

The easiest way to see that is to notice that the electric field must be zero inside a conductor that conducts a constant amount of current, because if it wasn't then the electrons would have moved. No electric field = zero transferred power, via the Poynting vector.

Complete nonsense, the current carrying capacity of a wire is directly proportional to the surface area of the cross section of the wire. If it were the skin it would be proportional to the circumference and it clearly is not. I have no idea where you came into this idea but it is just completely wrong. You can test it for yourself with $50 worth of gear.

You two are talking past each other. @H8crilA is talking about energy, you are talking about current. Energy flow is the product of the electric and magnetic fields [1]; electric field within a conductor is zero, therefore energy flow within a conductor is zero.

[1] https://en.wikipedia.org/wiki/Poynting_vector

Yeah exactly. In particular a flow of current (movement of electrons or other charged particles, measured in Amperes) is not required for energy transfer, though it is a part of the efficient way of energy transfer via conductors/wires. Including in PCBs and even inside of integrated circuits.

> In particular a flow of current (movement of electrons or other charged particles, measured in Amperes) is not required for energy transfer

No, it isn't as any transformer or transmitter would show you. But that's not what this is about. It's about as useful as telling architects to use quantum mechanics because that's the fundamentals of what they are doing or having every electronics design model each and every conductor as a transmission line. That's what Spice is for, to ensure that from an EM point of view the design is valid (and to ensure that you're not radiating EM).

But it's in the end a discussion about fundamentals and as you pointed out circuit theory is so damn useful that it gets you 'close enough for government work'. That there is a whole pile of field theory that you could use to model the same is true but it isn't so damn useful and in practice would just complicate matters considerably requiring every electronics engineer to engage is high level math. Just like we're not going to ask carpenters and bricklayers (and architects) to take into account the fact that Newton 'got it wrong' and we should all be using Einstein's equations instead.

Engineering uses the tools appropriate for the task. If that tool is Maxwell's equations because we're dealing with stuff that should be modeled as a transmission line and the field component is the dominant one then so be it. But for most practical electronics circuitry you can use V/A/R just fine. When modeling capacitors and coils Maxwell's equations are applicable but you can likely still get away with approximations as long as you realize that that is what you are doing. When modeling a complex high frequency circuit things change rapidly and modeling your interconnects as transmission lines makes good sense because that is ultimately what they are and ignoring that aspect will make it much harder to design something that actually works.

So the statement that 'energy does not flow through a wire' makes sense in an EM theory view of electricity, which is fine for pedantry but won't get you places if you are moving bulk charge from point 'A' to point 'B' to get some useful work done. Just like EM theory in turn isn't correct either, the quantum physicist would tell you that your theory is 'just an approximation' and that you are 'doing it wrong'.

For the subject matter, antenna design the field is obviously the important part otherwise you're not getting anywhere at all. For DC to low KHz circuits that do not contain large inductors you will be able to keep things fairly simple. As soon as you start working with inductors you will have to 'level up' in your view of how the circuit works and if you don't you'll probably end up with something that is either sub-optimal or that subtly differs in its actual operation from what you think you've designed.

If you want to build GHz circuitry there is no way that you're going to avoid getting to know mr. Maxwell better.

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.

> 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. 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.

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.

> 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.

I really hate to start quoting basic wikipedia articles but I have some other stuff to do and I don't want to leave this dangling, from:

https://en.wikipedia.org/wiki/Electric_field

This is the second sentence in that article:

"Electric fields originate from electric charges and time-varying electric currents."

> I keep bringing the circuit theory in because it is the reason why people can't believe how electricity actually works.

Circuit theory is simply a very useful approximation and how 'electricity actually works' is highly counter intuitive because for starters we got the flow of electrons wrong (they flow from - to + and not the other way around). Still, conceptually, everybody that does electronics for a living will model the flow from + to - because of convenience. But strictly speaking that's not how it 'really works'. But nobody cares they just have a job to do and the tools that suffice for that are the tools that will be used.

Finally: the QM reconciliation of EM and Gravity is for now an unsolved problem so there is a fair chance that in the long run you'll be able to make the argument that 'EM is not really how it works'. But for now it's good enough.

> You have cause and effect switched. The field is the result of the flow of electrons, not the other way around.

I literally said "this field is induced by the flow of electrons." (Specifically, the magnetic field. The electric field is due to charge difference between the wires.)

> for real world wires the bulk of the field is constrained within the wire.

No, there is none - zero - nada - electric field perpendicular to the wire within said wire. If there were, the electrons would all flow to one side of the wire -- but, as you agree, they don't for DC, they are distributed throughout the bulk.

(There is a small electric field within the wire parallel to the wire; this is associated with the resistivity and energy loss in the wire, which is not related to power transfer. Its Poynting vector points outward from the wire, not to or from the source.)

So, you are proposing the the electric field of electrons moving inside a wire somehow have their fields appear outside of the wire rather than proportional to the distance from the electron (Coloumbs inverse square law)? As though the medium in which a particular electron is suspended can create an exclusion zone for its electric field?

That's interesting but contrary to just about everything that I've ever learned about this stuff. My understanding to date is that there is an electric field in a wire because if there wouldn't be then there would be a non-uniform distribution of electrons in the wire, in other words, without an electric field in the wire there would be no current to begin with, the fact that there is a current is proof that there is an electric field in the wire. I would expect that field to be aligned with the direction of the wire and constant in magnitude relative to the flow of the current. Anything else just simply does not make any sense to me.

Consider the x component (along the wire's length) and the y and z components (along the wire's radius) separately.

There is a E field component along the x axis within the wire, correct. This provides the force which causes the electrons to accelerate. The field is slight -- remember it's just the voltage from one end of the wire to the other (millivolts) divided by its length. Notably, this component does not impart energy to the load -- it corresponds directly to energy dissipated in the wire itself (i.e. its Poynting vector points toward the center of the wire).

But along the wire's radius, within the wire, there's no net E field. Each electron (and each proton!) contributes a small field (which does extend immediately from the electron-point-source as you say), but the electrons arrange themselves within the metal such that the net field along these axes in the wire is zero. (If they were not arranged so, the nonzero field would push them toward this arrangement. Since the electrons aren't moving along these axes, the field along these axes is zero.) In the intuitive sense -- uniform static distribution of electrons begets a uniform static field among them.

Outside the wire -- assuming the wire has a net charge (positive or negative) -- we do see a radial electric field, because the electrons are not free to move to/from the wire through free space to neutralize this field. And if there are two wires of opposite charge (as in the circuit described), the fields sum constructively (as one wire's field is radially outward, the other's radially inward). This field is much larger, particularly if the wires are physically near each other, since it derives from the voltage difference between the wires, rather than across them. (And most importantly, the Poynting vector of this field points toward the load.)

You may be right that the region outside the wire where energy flows may be small and near the wire (working through some math now) but it's definitely outside the wire for the reasons given above, and flows between sources and sinks according to the Poynting field, not along any path that's visually represented in a circuit diagram.

> There is a E field component along the x axis within the wire, correct. This provides the force which causes the electrons to accelerate. The field is slight -- remember it's just the voltage from one end of the wire to the other (millivolts) divided by its length. Notably, this component does not impart energy to the load -- it corresponds directly to energy dissipated in the wire itself (i.e. its Poynting vector points toward the center of the wire).

Ok so far that is in accordance with how I understand things to work, assuming a 'good conductor' and low impedance for AC or varying current.

> But along the wire's radius, within the wire, there's no net E field.

Because there are no electrons flowing in that direction, and even if there were there would be others canceling that out (this holds on average for thermal noise as well, which would show up as minor current fluctuations), to get an E field at right angles to the wire you'd have to to see a voltage difference between the center of the wire and the outside of the wire, and barring local effects there will be no such thing. Essentially because there is a dead short between those two points (a very short piece of a section of the wire) Right?

> Each electron (and each proton!) contributes a small field (which does extend immediately from the electron-point-source as you say), but the electrons arrange themselves within the metal such that the net field along these axes in the wire is zero. (If they were not arranged so, the nonzero field would push them toward this arrangement. Since the electrons aren't moving along these axes, the field along these axes is zero.) In the intuitive sense -- uniform static distribution of electrons begets a uniform static field among them.

Except for the limit case of a single electron moving in a conductor, that presumably would result in a net (extremely small) field, but for larger numbers of electrons (any practical measurable current) that would all cancel out within the wire perimeter.

> Outside the wire -- assuming the wire has a net charge (positive or negative) -- we do see a radial electric field, because the electrons are not free to move to/from the wire through free space to neutralize this field.

Because the wire perimeter is defined as the area where the conductor ends (which makes me wonder how that transition would work in a material that consists of an outer core that gradually becomes higher impedance).

> This field is much larger,

Right, because it can't neutralize because it is in a dielectricum.

> particularly if the wires are physically near each other

Yes, but that's not a given and any old wire loop has its wires as far away from each other as you want them to be. Coaxial cable is the way it is to get the fields to cancel out so that the amount of spurious radiation from the cable is kept to a minimum (you can also twist the two wires around each other for some of the same effect).

> since it derives from the voltage difference between the wires, rather than across them.

You mean 'wires on both sides of the load'? Somewhere along the line we switched from discussing a single wire in isolation to two wires.

> (And most importantly, the Poynting vector of this field points toward the load.)

So we're now talking about the electrical field between the two wires on either side of the load?

> You may be right that the region outside the wire where energy flows may be small and near the wire

I don't see how it could be any other way but I'm curious as to the results of your calculations.

> but it's definitely outside the wire for the reasons given above

Ok

> and flows between sources and sinks according to the Poynting field, not along any path that's visually represented in a circuit diagram.

Ok, I think I'm finally seeing what you are getting at, you are talking about the net flow of energy from a 'source' (say a battery or a generator) to a 'load' and that energy clearly flows in one direction even if the electrons themselves make a round trip from one side of the source to the other side of the source (well, technically they don't even do that, they may well reverse direction before they get there), and that the field that carries that energy is the field at right angles to the wire rather than the field that you see across the length of the wire.

Yet another edit, much more thinking later: 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? After all you'd need something moving energy and electromagnetism can transfer energy whereas an electric field (or even a moving charge) does not? (as in: current does not equal 'work', that all depends on the associated voltage).

I think we're mostly on the same page, yes, sorry I wasn't clear, I've been talking about two wires, linking a power source with a load.

> 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.

> I think we're mostly on the same page, yes, sorry I wasn't clear, I've been talking about two wires, linking a power source with a load.

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.

> 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.

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

You can invalidate the circuit theory with, well perhaps not $50 worth of hardware, but a bit more:

https://youtu.be/oI_X2cMHNe0

I'm not sure how do you plan to invalidate Maxwell's theory, which shows that energy flows entirely outside of wires, with $50. Or any other amount of equipment. It would be very much welcome in the physics community.

This misconception is even more widespread than "planes fly because of Bernoulli" because it's so incredibly useful when designing most circuits/PCBs. Though it is, fundamentally, a lie.

PS. Circuit theory is made to match reality for the case showed in the video via the concept of a transmission line.

I'm not sure circuit theory states that energy flows within wires? Current, yes, but energy transfer is the product of current and voltage, and voltage of course exists only between wires.

Not really in the intuitive sense: https://www.youtube.com/watch?v=iph500cPK28

Someone actually went out and tested this: https://www.youtube.com/watch?v=2Vrhk5OjBP8

The electric field is very tightly constrained around the wire. The amount of energy that reaches the light through the gap is incredibly small, not nearly enough to turn on a real light bulb. The bulk of the energy does indeed have to take the path through the wire. I find that video usually leads people to an even less correct understanding than the marbles-in-a-tube analogy.

The Veritasum video can essentially be summarized, "fun fact: two parallel wires act like an antenna, and an extremely small amount of energy reaches the other end before the rest of the energy takes the long path through the wire.

The Poynting vector is the obvious choice but we cannot do the experiment to tell between the various possibilities one can get by adding more terms that obey the constraints.

It's at best a leaky abstraction but for some domains it is very useful. Antennas are 'magic' from the point of view of Ohms law and so on but once you move to the electromagnetic domain you will find equivalents for most of the elements in the original abstraction: impedance, reactance and so on.

Yep, and even common nonlinear elements like diodes and transistors are non-Ohmic.

No, they are just non-linear: as the voltage goes up the current goes up in jumps because the resistance changes in a non-linear way, but it is still resistance and you can still express the system at any point of the curve using Ohm's laws and you can still compute the power lost in any part of that system using the simplest equations.

Tricky stuff!

Yep, AC is magic.

And not just antennas.... look at computers... at 3GHz (DDR4+ ram), the wavelength is ~10cm, so looking at a single sine wave, you have 1.8volts at the cpu, zero volts 2.5cm away from the cpu, -1.8v 5cm away, zero 7.5cm, and again 1.8 volts 10cm from the cpu... now look at the distance between the cpu and ram, the other frequencies that come with the square(-ish) waves, and all the math to make a basic RAM read/write work.

Just a normal wire (or cable - the simplest component in DC electronic circuits, just a line, that does nothing) changes everything... you send a (voltage) signal in, and the current has to flow at some rate, even before the "signal" (field) reaches the other side of the cable, to "see" if the other end is "open" or soldered together or if some sort of a resistor is soldered there.

That's not how current propagates. Current propagates - broken analogy warning - in the same way that marbles would propagate through a tube. You push a marble in on one end and assuming the tube is full another marble pops out the far end. So the flow rate of the electrons is vastly lower than the flow rate of the signal itself!

Of course, but currents here are a result of a field that moves those electrons one way or another, and electrons move, before the field reaches the other end (where a resistor is.. or is not.. or a short circuit is), so in your analogy, marbles move down the tube, before they "realize" that the tube is closed on the other end.

Fair enough. It's an analogy anyway and it is a broken one in more ways than one (for instance: it doesn't deal with propagation of pulses very well because these can be reflected from the end of the tube, you'd have to model it as a tube full of marbles and springs to account for that) but it serves for some discussion purposes.

>regular monopole antennas

There is no real monopole antenna - there's always another "half", like a ground plane, a counterpoise system or even just the body of the person holding a handheld radio.

> how can the conductor conduct when one of the ends is just hanging in the air? AC magic I suppose

I struggled with these matters too. I wouldn't call it "AC magic", but "RF magic".

Notice that you need a different mental model to understand those circuits. In DC and low-freq AC, it's enough to think that voltages and currents manifest themselves instantaneously in a conductor. But that is a (useful) simplification. Roughly speaking, the energy supplied by the power source takes time to propagate over the wire [0].

Having that in mind, take a look at the animated gif in this page: https://en.wikipedia.org/wiki/Dipole_antenna. I believe it's gonna make more sense now.

This mental model also helps to understand why a magnetic loop isn't simply a piece of short-circuited wire -- for a DC or low freq AC circuit, it is indeed a short-circuit; for an RF circuit, it is not. [1]

[0] https://en.wikipedia.org/wiki/Velocity_factor

[1] this mental model is not enough to fully understand any antenna. Many designs also depend on other phenomena, like the electromagnetic interactions between its components, and interactions with its surroundings. But I think that, equipped with this mental model, you'll be able to research further in case you feel interested.

> how can the conductor conduct when one of the ends is just hanging in the air?

At frequencies where the wire radiates, you can't model a wire as an open resistor. You need to model it as a bunch of Rs, Ls and Cs, and there you will see the current flow.

Quick answer: The antenna is like a tube, and the energy stuff is like liquid that sloshes back and forth in the tube generating a kind of wiggle.

This Canadian military video should help: https://www.youtube.com/watch?v=-F7KYLO4Bkg

Also worth mentioning, the US Navy Electricity and Electronics Training Series (NEETS), plus other interesting documentation one can find from the top menu here.

https://maritime.org/doc/#neets

NEETS is a treasure trove of practically.

I liked to play with longwires (sect. 4-22) back in the day ... the longer, the more directional they get. Fun to experiment with (back when copperweld was cheap). But when I did eventually wind up living on a farmstead for a couple of years, I didn't have the time (or the nearby trees) to try out really really long wires.

You can try barbed wire fences! On a dry day they can work very well, obviously you won't have much say in their direction but if you're near a fence it can't hurt to hook up a sensitive receiver to see what you get.

The basics or antenna design have been known for a long time. Any advances have been in the small antennas used in devices, not the large antennas strung up by Marines.

That's not really true though, phased arrays are a fairly recent development and now that we have the computational power to use them more effectively are being used in many more practical applications.

This is really well written and surprisingly accessible! I know nothing about communication systems but was able to read this pretty easily.

Well, it is meant for Marines. Hence also the wide margins, so that even after perfect binding and trimming there's still plenty of space for making notes with a half-eaten crayon.

Joking aside, lots of military manuals share the trait of introducing their subject matter well, in order to ensure that whoever's using the material has at least a reasonably strong basis in the "what" and "why" as well as the "how" - I suppose ideally that's something that'd be covered in training, but also that manual authors don't assume they are writing for an audience that is guaranteed to have been trained. The result is often a supremely useful resource in whatever subject it treats.

Frankly, I can think of worse models for the technical documentation we as software engineers produce...

I started using their template for writing a mini ops manual as a read-only-friday project, and it's still in use and the format became the business's standard for other documentation. feels nice when I see a new hire reading it.

Also, I like the cookies. https://quartermaster.army.mil/jccoe/publications/recipes/se...

Military training stuff has to be accessible. Here's Frank Wilczek:

WHEN I WAS ABOUT TO BEGIN TEACHING at Princeton, my friend and mentor Sam Treiman called me into his office. He had some wisdom to share. Sam pulled a well-worn paperback manual from his desk and told me, "During World War Il the Navy had to train recruits to set up and operate radio communications in a hurry. Many of those recruits were right off the farm, so bringing them up to speed was a big challenge. With the help of this great book, the Navy succeeded. It's a masterpiece of pedagogy. Especially the first chapter. Take a look."

He handed me the book, opened to the first chapter. That chapter was titled "Ohm's Three Laws." I was familiar with one Ohm's law, the famous relation V = IR that connects voltage (V), current (I), and resistance (R) in an electric circuit. That turned out to be Ohm's first law.

I was very curious to find out what Ohm's other two laws were. Turning the fragile, yellowed pages, I soon discovered that Ohm's second law is I = V/R. I conjectured that Ohm's third law might be R = V/I, which turned out to be correct.

I desperately wish there was more awareness of military writing styles in the civilian world.

- They're organizations that have existed for as long as their countries.

- They're incredibly large.

- They have to communicate critical information to a very diverse set of readers.

- They iteratively update their approaches, over decades, often in direct reaction to the most stringent real-world tests.

... how could we not learn something from the systems they're currently using?

My favorite nuggets are (1) the glory of BLUF (bottom-line, up front; or an executive summary of everything to follow), (2) including a formal intent preface to any document (to guide writers and readers in what to include/exclude), (3) thoroughly defining terms (to avoid "we're using the same word with different meanings" problem), and (4) rigorously structuring information into separate sections.

Which isn't to say militaries get everything right all of the time. They do tons of stupid things. But dismissing or ignoring them as a source to cherry-pick best practices is shortsighted.

BLUF is my favorite nugget as well

> ... how could we not learn something from the systems they're currently using?

You haven't noticed the aversion to the military, especially the US military, around here or in "academic" circles?

I wouldn't say I've seen aversion, more lack of awareness.

And what aversion there is seems to be a missing distinction between the military organization and military outcomes.

There are 1.3m active duty US DoD uniformed personnel. And another 1m reserve.

The bulk of those are performing support functions and keeping the whole organization running.

It's difficult for me to form any kind of ethical judgment about support folks, however the military is ultimately employed. And especially when weighed against the large number of tech careers that are in support of advertising/tracking.

>BLUF is my favorite nugget as well

I wonder if the next generation will invent their own version of this. The current 'trendy' one is tl;dr

Because "Abstract" is too abstract of a concept, and "Executive Summary" is too long and presumes the audience.

It's one of these ideas that are universally useful, but get a different name in each context.

I will often do "TL;DR:" at the top when realize I've written rather more than I'd expected.

>But dismissing or ignoring them as a source to cherry-pick best practices is shortsighted.

No truer statement about humanity has been spoken

BLUF is great but is kind of like the MVP in that execution highly varies from author to author

Antennas and communications systems are two very different disciplines, by the way. The two ARE linked together in a single larger system quite often, so you’ll have people who have got their hands in both areas, but aside from the baseline knowledge of calculus involved, having ability in one area won’t make it easier to understand the other.

Pretty surreal to see this trending on HN!

"The NVIS loop: so easy, a marine could do it"

For those with some fundamental undergrad math background, check out the gold standard book on antennas

    Antenna Theory: Analysis and Design, Constantine Balanis

https://www.amazon.com/Antenna-Theory-Analysis-Constantine-B...

The ARRL antenna book is also worth your while: https://www.arrl.org/arrl-antenna-book

radio is probably one of my all time fav concepts. thanks for this

Say what you will about American militarism... but the branches put out some exceptionally thorough, clear, and practical training documents... in most cases. (Same goes for the FAA from personal experience)

Two observations, one mundane, one serious.

Funny how even in reference textbooks on radio/EM/etc, for some reason people cannot help but use half circles on a plot about a sine function, instead of the proper function shape. Don't know why that is! See Figure 1-2.

And more seriously, I think that all of our useful military education texts date from pre-1990s, when the military was one part an able research and development (and educational) and contracting institution. Now today most all of that capability has been outsourced to the military contractors and anyone who could write such a text (or properly design an aircraft on the military side) has long left.

At least in terms of aircraft I think you have some camp tinted glasses on. Aircraft, vehicles, ships, and equipment of all sorts has always been developed by private industry. Often in very close partnership with the military, of course. Any manufacturing capacity directly owned by the US Government has always been extremely specialized. Think Los Alamos and Oakridge vs Boeing.

Of course they were developed largely by industry in putting designs into execution and production, but decades ago, the in-house knowledge to spec and actively participate in the detailed technical/engineering design stages still existed in large measure within the military.

Think of most aircraft types up to the 70s -- people in the military (engineers, designers) worked side by side with Grumman, Northrop, etc. in the designs and saying what kind of technical envelope was possible. Actually drawing up designs.

In large part (generalization of course, except for some pockets of expertise) the Pentagon is a bunch of project managers. Skilled I'm sure, but the depth of technical knowledge that used to exist has largely moved to the contractors. And this migration/dispersal of responsibility -- which notably caused a loss of single-minded direction in creating aircraft/ships that meet a specific desired need, driven by deep expertise -- has led to the hugely expensive but bland/mediocre/too many chefs in the kitchen projects that you often think of today. Just my opinion of course.

Ya but what's that 'f' (or lamba) term doing in the path loss equation? I'm pretty sure Einstein or Feynman would cast a jaundiced eye at that.

where?

During my time in the Navy doing radio comms and intelligence, I quickly learned a mastery of Maxwells equations, information theory, Fourier series etc. was much less important than learning and applying practical knowledge from manuals like this. For the folks discussing transmission lines I think the telegraphers equation is a useful tool.

Reminds me, the other day I came upon this article that was written about military planes using 5 mile long antennas to communicate with submarines.

https://www.thedrive.com/the-war-zone/31477/heres-why-an-e-6...