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.
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. A coil or a capacitor (or even a piece of wire, but there the effects are very small) are components that do not follow Ohm's laws, you need to add more parameters than just current, voltage and resistance to work out what's happening.
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.
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.
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.
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.
No. DC energy also flows around the wire. And I mean around, entirely outside of the conductor, not in the skin or anything like that. 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 movement of electrons, and thus the deposition of the energy via "resistance", may indeed be limited to just the surface of the conductor; this is what that calculator shows)
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.
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.
@H8crilA is talking about energy, you are describing 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.
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
Of course it isn't, as any transformer or transmitter/radio 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 circuit 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. But when you are designing satellites you should.
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, fact by then you'll be pretty intimately familiar with the underlying electromagnetic theory, it's unavoidable.
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. (Outside, as in -- through the void between power sources and sinks. Not the skin.) 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.
It's not a matter of "circuit theory vs. Maxwell's equations" (and I don't know why @H8crilA is framing the argument like that). Circuit theory simply doesn't say anything about the flow of energy. It deals with current flow and voltage potentials, but not energy flow (except in the cases of transmission lines and transformers). It's not "wrong" or an "approximation" in this sense -- but there's nowhere in a circuit diagram you can point to and say "this is the path the energy is following". (Unless you start decorating the diagram with arrows between power sources and sinks, which then starts to look a heck of a lot like the Poynting vector.) But if you say instead, "the energy flows through this wire" (which again, circuit theory does not claim), this is mathematically inconsistent in even the simplest circuit, since, after all -- energy does not flow in circles!
I suppose one could augment circuit theory with a notion of "energy flow through a wire" by equating that to product of the current through the wire and the potential between that wire and some fixed reference (e.g. ground). This would be mathematically consistent but not give meaningful physical results -- the battery-light bulb circuit above, if tied to an arbitrary potential high above the reference, would indicate a proportionally arbitrary massive amount of power flowing "out" of the battery, and slightly less than that amount flowing back "in" to the battery. Maybe some EEs conceptualize circuits this way (maybe even I do unconsciously?) but I'm not aware of this being standard pedagogy.
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.
"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.
edit: thinking about this some more: essentially the two wires you are talking about have some of the properties of a charged capacitor, and the electric field is passing between those two 'plates'. That makes me wonder if the field is mostly concentrated between the 'plane' (it can be quite a complex shape) between the two conductors rather than that most of it is in free space radiating outward. After all an electric field normally does the same thing for a charged capacitor, the bulk of the field sits between the plates with only a small fraction moving outside of the envelope of the plates.
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). It also would explain the 'single electron' issue outlined above, that wouldn't apply, you get a magnetic fieldline or you don't and if you do that single photon can do useful work.
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:
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 single wire, which doesn't make any sense at all (and it 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 shows that there definitely is 'work' being done inside a wire. So there is a non-zero length Poynting vector pointing (heh) to the inside of the wire! (as a result of the resistance of the wire), and that energy is subtracted from the amount of energy available for the load.
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 (it's circulating 'virtual photons' for a bit of physics weirdness), 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. Its presence gives rise to the 'Hall effect', which shows up as a voltage induced in a conductor placed across the field lines.
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 field of the free electrons in a conductor also doesn't do any work. But when you start moving those electrons using an electric field their magnetic field is doing work in the medium that they are moving through. The electrons themselves only move a fraction (on the order of a millimeter per second) 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.
[This also neatly explains why electrical signals propagate at the speed of light: the electrons themselves may move slowly but their magnetic fields propagate at the speed of light, and if you think about it a bit longer it also explains why voltage and current in an AC circuit can be different than the real power drawn by the load because the load itself can temporarily store energy (power factor!). This can even cause zero apparent power while real work is done in the load. This shows up as the angle of phase difference between current and voltage, and is why the electrical company really doesn't like you if you use large inductive loads because they have a very low power factor, all the way down to zero for 'perfect' inductors.]
In a pure DC setup the interactions between the moving electrons and the stationary material 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. The current in such a setup would be mostly limited by the internal resistance of the source (the wire loop is essentially a short). 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.
Adding a load is then a slight modification of that circuit, a localized increase in resistance relative to the resistance of the wires, but work is done in all parts of the circuit (including the source!) proportional to the resistance (and hence the voltage drop) across that fraction of the circuit.
In an AC setup some of the radiated energy would 'escape' from the wire because the changing magnetic fields radiated by the wire would induce currents elsewhere, and if you engineer your AC setup carefully (resonance) to maximize such loss you have an antenna. Conversely, that loop 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), such as in an AM radio (which uses a coil of wire across a ferrite core, essentially an electromagnet).
If you carefully engineer this to transfer energy using magnetic fields between two such circuits with minimal losses you end up with a closely coupled set of two loops of wire aka a transformer.
In each of these cases the part that you try to engineer away shows up as loss, imperfect transfer in a transformer warms up the transformer (eddy currents in the laminations for instance) and imperfect transfer for an antenna system shows up as heat due to reflected power (to the point where a very simple way to blow up a radio transmitter of any serious power is to disconnect the antenna).
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 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 mostly 'inside' the wire (say: a standard powercord where the conductors are close to each other, but they definitely do not have to be, in fact the wires could be of unequal length all the way down to zero). All the Poynting vector does is to show how strong the cross product of electrical and magnetic fields are at any given point of a system 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 physical lay-out of the system, the interior resistance of the source and the interior resistance of the wire and if you don't take these 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, radiated EM field), each of which would require their own miniature Poynting vector to account for all of the imperfections.
So by switching from one wire to two wires and a load the picture became needlessly complicated, and technically incorrect. You don't actually need a separate load to demonstrate any 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 does not depend on in which direction the current flows and doesn't even care about the direction of the field itself, it will simply excite the atoms of the material that the carrier is made out of by virtue of moving the free electrons around and it will do so proportionally to the resistance of the carrier resulting in heating the material up (which in turn shows up as excited atoms with electrons in a higher oribit, and gives rise to new photons when they fall back, 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 moving 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. If the energy really did flow 'mostly outside of the wire' then the wire wouldn't heat up, it heats up because of the fields of all of those electrons interacting with the fields of the captive electrons in the material just like a mirror absorbs light and then spits out brand new photons (the basis for the photo electric effect, think of a solar panel as a 'one way' mirror that turns those absorbed photons into free electrons which are then captured by a diode resulting in a potential difference across that diode). It also explains superconductivity: in a superconductor the current flows unimpeded because the number of interactions between the fields of the electrons moving through the material and the fields of the atoms of the material itself is extremely low, so there is no 'work' done in the conductor itself and hence no potential across the superconductor. If you use a superconductor to short a power source then all of the energy will go into the magnetic field, rather than that it gets converted into heat (which creates all kinds of interesting complications, the fields are so strong that if the electromagnet isn't constructed very carefully it will tear itself apart).
Interesting discussion. Main takeaway: precision matters.
> 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).
I think a big part of the confusion stems from separating the wires from the load: they are all the same thing, wires are load too and there is no 'privileged' reference frame for any particular chunk of wire (or load, or internal resistance in the battery) that deserves special consideration or that needs to be paired with something else to make it work, as long as the circuit is whole current will flow and the moving electromagnetic field is sufficient to explain all of the observed phenomena. The only part where the electric field figures in is as the accelerating force for the free electrons in the circuit, the higher the voltage the more of those electrons that will partake in the movement (which is effectively how you can derive Ohms law).
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.
