General > General Technical Chat
Electroboom: How Right IS Veritasium?! Don't Electrons Push Each Other??
EPAIII:
OK good old OHM's law tells us that the current is inversely proportional to the resistance.
I = E / R
So, with two wires of equal length and all other things also equal (like the path followed or whatever other factors), but with different resistances will carry different currents. Now, how do those currents differ?
The resistance in a conductor is directly proportional to it's length and INVERSELY proportional to it's cross sectional area. Look about 1/4 of the way down the page:
https://en.wikipedia.org/wiki/Electrical_resistance_and_conductance
R = p (l / A)
p is a constant
l is the length of the conductor
A is the cross sectional area of the conductor
A, the cross sectional area is the full area, not just some fraction of it that is near the surface. It does not matter what shape that cross section may be. A round conductor, a square conductor, and a thin but very wide rectangular conductor (like sheet metal or even metal foil), each with the same cross sectional area and the same constant (p) will have the same resistance per unit length and will have the same resistance. So they will all carry the same current - all else being equal, of course. And combining this with Ohm's law, we see that the current is directly proportional to the cross sectional area (A).
A solid, round conductor, like ordinary solid wire, will have far fewer surface charges than a conductor made of thin foil but with the same cross sectional area. But they will carry the same current - all else being equal. If conduction relied on just the surface charges being distributed in a manner from one end of the conductor to the other that produced an E field gradient, then there would be a lot more surface charges on the surface of the foil conductor than on the solid, round one. And those charges would be a lot closer to the electrons inside the conductor so they would exert a lot more force on the interior electrons which would then move faster. And faster moving charges would mean that more charge would pass a given point in a given amount of time - all else being equal again. So the current in the foil conductor would be greater.
BUT, this is NOT the case. The foil conductor has exactly the same current as the round wire conductor. Or as a square one. Or as a triangular one. Or as a star shaped one. Or as one of any other shape. The current is not changed by changes in the amount of surface area the conductor may have, but by the CROSS SECTIONAL AREA.
This seems to argue rather heavily against the idea that it is only the surface gradient that is causing the interior charges (electrons) to move down the conductor.
A further argument and perhaps a better one would be that it will take a finite amount of time, at least 1/c if I am not mistaken, for the initial field to propagate down the wire. So, regardless of weather the force on an internal charge (an electron) is created by only the surface charges or by both surface and interior charges, both the interior and exterior charges (electrons) near the negative battery terminal will start moving BEFORE the ones that are around the half way point in the circuit formed by the wire. Those charges near the negative battery terminal will therefore BUNCH UP. They will become more dense, both on the surface and in the interior. This will create a net negative region both on the surface and in the interior of the conductor. And this net negative region, this net negative charge will exert a force on the charges in front of it.
In the vernacular, it will PUSH those ELECTRONS ahead.
The exact opposite of this also occurs at the same time on the end of the conductor that is connected to the positive battery terminal except in that case a region of net positive charge is created and it will ATTRACT the negatively charged electrons on and IN the wire there. That attraction will then act on the regions of the wire, both surface and interior, in attracting the negative charges ever further down the wire from that positive battery terminal.
Again, in the vernacular, it will PULL those ELECTRONS toward the positive terminal.
In a time (<= l/c), those two effects will meet at the light bulb in the center of the wire loop and it will then have it's maximum current flowing in it so it will light up at full brilliance.
This is not to say that the light bulb may not also have some current flowing in it before that time. But the amount of that current will depend heavily on the exact physical arrangement of the wires between it and the battery terminals and switch.
In this I am assuming that the switch and battery are connected by a length of wire that is negligible.
Sredni:
--- Quote from: EPAIII on June 22, 2022, 11:32:48 am ---A solid, round conductor, like ordinary solid wire, will have far fewer surface charges than a conductor made of thin foil but with the same cross sectional area. But they will carry the same current - all else being equal. If conduction relied on just the surface charges being distributed in a manner
--- End quote ---
I have to stop you here.
You seem to think that the surface charge is the number of free electrons per atoms times the number of atoms that make up the surface of the conductor.
No, it's just a tiny, tiny, tiny, veeeeeeeeeery tiny amount of excess or missing charge that is forced to be there in order to have the whole conductor comply with Ohm's law in local form.
So, no, you can't say a priori what that charge would be by the shape of the cross section of the conductor. It depends on the field estabilished in the whole space by the battery, and the way the conductor is placed in the space around it (and also on the shape of the conductor, that fact that it might become twisted on itself, have sharp bends, kinks...).
The amount of surface charge for 'ordinary circuits' with 'ordinary currents' is so tiny that it sometimes can be equivalent to a handful of electrons. (I also wonder when the classical model will break down with small currents - one can hardly have fractions of electron charge...)
electrodacus:
--- Quote from: Sredni on June 22, 2022, 01:18:28 pm ---
--- Quote from: EPAIII on June 22, 2022, 11:32:48 am ---A solid, round conductor, like ordinary solid wire, will have far fewer surface charges than a conductor made of thin foil but with the same cross sectional area. But they will carry the same current - all else being equal. If conduction relied on just the surface charges being distributed in a manner
--- End quote ---
I have to stop you here.
You seem to think that the surface charge is the number of free electrons per atoms times the number of atoms that make up the surface of the conductor.
No, it's just a tiny, tiny, tiny, veeeeeeeeeery tiny amount of excess or missing charge that is forced to be there in order to have the whole conductor comply with Ohm's law in local form.
So, no, you can't say a priori what that charge would be by the shape of the cross section of the conductor. It depends on the field estabilished in the whole space by the battery, and the way the conductor is placed in the space around it (and also on the shape of the conductor, that fact that it might become twisted on itself, have sharp bends, kinks...).
The amount of surface charge for 'ordinary circuits' with 'ordinary currents' is so tiny that it sometimes can be equivalent to a handful of electrons. (I also wonder when the classical model will break down with small currents - one can hardly have fractions of electron charge...)
--- End quote ---
EPAIII is correct and I mentioned this in one of the other threads.
With DC current the charges will be distributed basically equal on the entire cross section of the wire.
With AC a lot more of the charges will be on the side of the conductor facing the return conductor so not equally distributed since the conductor forms a capacitor with the return wire. With high frequency most of the charges will be close to the surface (still inside the conductor) so resistance of the same conductor will increase as you do not take advantage of the entire conductor.
This image is probably what is shown in schools and it is correct except for the fact that it is valid for a coaxial cable so the return path of that current is through the cylindrical shield around the wire drawn in the photo. If return wire is like in Derek's example on the side then density of charged particles will be higher on the side facing the return conductor with which it forms a capacitor.
This asymmetric charge distribution is only for the first few nanoseconds during transient in Derek's experiment and at steady state DC charges will basically be uniformly distributed.
Sredni:
--- Quote from: electrodacus on June 22, 2022, 03:41:42 pm ---
--- Quote from: Sredni on June 22, 2022, 01:18:28 pm ---...
You seem to think that the surface charge is the number of free electrons per atoms times the number of atoms that make up the surface of the conductor.
No, it's just a tiny, tiny, tiny, veeeeeeeeeery tiny amount of excess or missing charge that is forced to be there in order to have the whole conductor comply with Ohm's law in local form.
...
The amount of surface charge for 'ordinary circuits' with 'ordinary currents' is so tiny that it sometimes can be equivalent to a handful of electrons. (I also wonder when the classical model will break down with small currents - one can hardly have fractions of electron charge...)
--- End quote ---
EPAIII is correct and I mentioned this in one of the other threads.
With DC current the charges will be distributed basically equal on the entire cross section of the wire.
With AC a lot more of the charges will be on the side of the conductor facing the return conductor so not equally distributed since the conductor forms a capacitor with the return wire. With high frequency most of the charges will be close to the surface (still inside the conductor) so resistance of the same conductor will increase as you do not take advantage of the entire conductor.
--- End quote ---
I was not talking about the electrons that make up the current.
I was talking about the surface charge: the excess electrons or lack thereof that - along with the original external field generated by the battery - shape the electric field inside the conductor in such a way that it be directed along the conductor axis and will have a magnitude that satisfies Ohm's law in its local form.
Read Chabay and Sherwood. Or Jackson's paper "Surface charges on circuit wires and resistors play three different roles" (American Journal of Physics 64 (7), July 1996), or one of the other references I have put in this answer: https://electronics.stackexchange.com/questions/532541/is-the-electric-field-in-a-wire-constant
rfeecs:
--- Quote from: Sredni on June 22, 2022, 04:53:29 pm ---I was not talking about the electrons that make up the current.
I was talking about the surface charge: the excess electrons or lack thereof that - along with the original external field generated by the battery - shape the electric field inside the conductor in such a way that it be directed along the conductor axis and will have a magnitude that satisfies Ohm's law in its local form.
Read Chabay and Sherwood. Or Jackson's paper "Surface charges on circuit wires and resistors play three different roles" (American Journal of Physics 64 (7), July 1996), or one of the other references I have put in this answer: https://electronics.stackexchange.com/questions/532541/is-the-electric-field-in-a-wire-constant
--- End quote ---
That's the steady state condition. But how did the surface charges get there? Maybe they "pushed" each other?
And what would happen if the electrons in the wire at some random instantaneous time ended up bunched up a little bit at one spot? Maybe they would "push" each other apart? (Of course the positive lattice atoms have a role, too, in "pulling" the electrons.) Is the continuity equation and conservation of charge maintained by "pushing" and "pulling"?
It seems like the whole arrangement of surface charges and constant current at every point along the wire is created and maintained by charges "pushing" and "pulling" each other.
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