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## OT- physics question

For some reason today I was thinking about charge, electrons, and close encounters- and I started wondering about how dense a charge could become. We all know that in a capacitor the two plates support a charge. An excess of electrons gather on one plate. Just how many can gather- or another way to ask the question is how closely can electrons pack together and co-exist? By what means or material can they be coerced to amass to the greatest extent? Is there a theoretical limit involved?

We know we can force a large number of electrons to flow through a conductor, based on voltage applied and resistance. And we know that we can arrange a very high current to flow based on a chemical conversion process in a cell or battery. The closest thing to answering my question could be the super capacitor.

Should there be or is there a limit to how closely electrons can pack?

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I imagine that there is a practical limit but in theory would it not be a question of static voltage?

Consider what happens with a Van der Graf (sp?) machine. It is not possible to run the machine forever piling more and more electrons on the capacitor ball as eventually discharge takes place by corona discharge or by leaping to something (or someone!).
Last edited by The Artful Bodger; 12-07-2017 at 04:15 AM.

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That is an interesting question. Since electrons have a negative charge, there will be forces that increase as they are packed more densely. I think a magnetic field and/or electrostatic field may be required to keep them from dissipating. In a capacitor, energy is stored as positive and negative charge separated by an insulating material (including vacuum). It makes sense that having an oppositely charged plate in close proximity would exert an attractive force counteracting the repulsive force of the electrons. So a thinner dielectric increases capacitance, but also reduces the maximum voltage according to its breakdown in volts/unit thickness.

The answer may be in the following, but I don't understand it:
http://physics.ucsc.edu/~peter/231/m...eld/node2.html

This discusses electron density which may help with understanding:
http://hyperphysics.phy-astr.gsu.edu...ic/ohmmic.html

Here is a paper that refers to electron density per unit area, regarding the Hall effect;
http://www.phys.columbia.edu/~w3081/...s/qhenotes.pdf

Discussion of charge density:
https://en.wikipedia.org/wiki/Charge_density

It seems the maximum number of electrons per square meter would depend on its diameter, which is not fully determinate. However, it appears to be in the order of 10e-15 meters. Thus there could be no more than 10E30 electrons per square meter.

http://hypertextbook.com/facts/2000/DannyDonohue.shtml

The charge of an electron is about 1.6E-19 coulombs. Thus one square meter of tightly packed electrons would have a charge of about 1.6E11 coulombs. Charge of a capacitor (Q) = C * V. So the maximum charge would correspond to a 100,000 volt 1.6 million farad capacitor!
Last edited by PStechPaul; 12-07-2017 at 04:55 AM.

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Surface are is also involved. In Electrolytic capacitors for instance, the foil is not flat, it is treated so that it's "pitted" to increase the surface area. I think that's why new super capacitors use graphene and uther materials because of the real surface area.

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I'm no rocket scientist, but as I understand, thinking of electrons "packing" is off a bit. I believe they are added to the orbits? of atoms so there is probably a limit to how many can be there related to the material the electrode is made of?

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Capacitance is in coulombs per volt.

More coulombs, more voltage. The voltage is the limit. To stand the volts the insulator is thicker, which decreases the capacitance, which means you need more volts to cram the same charge in, which needs more insulation. Or a larger area of plates, which needs more volume, will maintain the capacitance.

No free lunch.

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Not an expert, but temperature may play some role in how many electrons can be packed within a given area or volume. Atoms and subatomic particles' movement and kinetic energy is related to temperature. Put a certain quantity of hydrogen inside a sealed balloon at 50 deg F and then raise the balloon's temperature to 100 deg F and you'll find the balloon expands because the hydrogen atoms are bouncing around inside more rapidly. Not sure if it's quite a 1 to 1 comparison to electrons onto a rigid (non-expanding) conducting surface, but there may be a similar relationship. Most known superconductors will not super-conduct without being dropped to very low temperatures. This may be related to this effect.

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Originally Posted by darryl
For some reason today I was thinking about charge, electrons, and close encounters- and I started wondering about how dense a charge could become. We all know that in a capacitor the two plates support a charge. An excess of electrons gather on one plate. Just how many can gather- or another way to ask the question is how closely can electrons pack together and co-exist? By what means or material can they be coerced to amass to the greatest extent? Is there a theoretical limit involved?

.....

Should there be or is there a limit to how closely electrons can pack?
In a conductor, there are electrons which are not bound to any particular atom. So there is no direct number that will "fit".

Yes, it takes voltage to cram them in. Any voltage is possible, although there is a limit to what is practical. 1 Farad stores 1 coulomb of electrons (6.24 x 10^18) when one volt is applied across it. 2 coulombs for 2 volts, etc. A coulomb is also the charge that is transferred when one ampere flows for one second.

Capacitance goes UP when the insulator between plates is made thinner. That also tends to make the allowable voltage less. Most super capacitors can only withstand about 2.5V or so without breaking down, so they are generally used in series to get to usable voltages.

The limit on packing electrons is voltage. Negative voltage applied repels electrons into the capacitor and causes them to pack closer together in a capacitor. They will only STAY packed if there is no path for them to get away from each other that has a lower voltage than the voltage used to "pack them together".

If you push electrons onto one plate of a capacitor, they are driven away off the other plate. That is a "higher energy condition" than when they are evenly spread out, so a charged capacitor stores energy. That means you have to use energy to force electrons to pack together, but you can get a lot of it back when you let them flow away from each other again.

Insulators have a "dielectric constant", which represents the degree to which their molecules are "polarized" (having a negative and positive end), and how easy it is to have their molecules turned to align with an electric field. A high dielectric constant, meaning the molecules turn readily, and have a definite negative and positive end, means that the insulator will, at a given thickness, give a larger capacitance than others.

So, thinner dielectric, higher dielectric constant, higher applied voltage, and more total plate area, all make a capacitor that stores more charge (more electrons).

I suppose that when you could not REMOVE any more electrons from one plate, when you "run out of electrons", that would be a sort of limit on the charge storage. But there are an awful lot of electrons, and the voltage would get rather high before you managed to do that, I believe.

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Originally Posted by Juiceclone
I'm no rocket scientist, but as I understand, thinking of electrons "packing" is off a bit. I believe they are added to the orbits? of atoms so there is probably a limit to how many can be there related to the material the electrode is made of?

Exactly correct

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Originally Posted by Juiceclone
I'm no rocket scientist, but as I understand, thinking of electrons "packing" is off a bit. I believe they are added to the orbits? of atoms so there is probably a limit to how many can be there related to the material the electrode is made of?
In metals, there are electrons which are not bound to atoms...... That's HOW conduction can occur. If they were bound, they would have to be broken loose before conduction could occur. There would be a minimum voltage, and large energy requirements.

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