# Is there a maximum possible voltage?

This question got me to wondering if there is a maximum theoretical voltage. It seems to me there's a limit to how much positive or negative charge you could have--say, a container full of electrons and a container full of protons.

Edit, since it seems I'm not being understood: Voltage is caused by a difference in potential between two points. It seems to me that this potential is inherently limited by the fact that it requires particles to carry it. I am NOT talking about a failure due to arcing.

• This question requires careful interpretation. "maximum theoretical" means is there is some theory which puts an upper cap on the phenomenon of voltage. In the absence of such a theory, voltage is theoretically unlimited (though not practically). – Kaz May 24 '14 at 2:06
• The number of atoms in the entire observable universe is estimated to be within the range of 10^78 to 10^82. It's probably not possible (due to relativistic limits) to move all the electrons to one side, but you could do some absolutely pointless/meaningless sums using these numbers. – RedGrittyBrick May 24 '14 at 8:27
• I suspect that the Schwinger limit is salient to this question. en.wikipedia.org/wiki/Schwinger_limit – Alfred Centauri May 24 '14 at 10:31

First of all: voltage has nothing to do with distance as some people say. Electrical field has to do with distance, but voltage is simply a potential difference. The highest voltages can be reached with so-called bulk charge, i.e. the amount of electrons in a certain mass of matter divided by the mass of the object.

Yes, there is a theoretical maximum potential difference. It is the potential difference as dictated by the Pauli exclusion principle; i.e. no two particles may exist in the same state at the same time. This limits the density of electrons that you can have in the universe and, conversely, the maximum potential difference. It may be possible to construct such an electron-dense cloud synthetically for an infinitesimal amount of time even, although it would obviously never be stable. Protons are a suboptimal way of (theoretically) constructing a potential like this, as their charge density is many orders of magnitude lower. Bare electrons are the way to go as the lowest-mass charge carrying particle in matter**.

Now, this says absolutely nothing about the upper limit on a practical, (pseudo)stable voltage. There is no such thing as a maximum density electron cloud and more importantly, it's very hard to produce a perfectly neutral counterpart close enough to do anything with. We know that neutron stars are essentially the densest 'usable' matter in the universe, but it is electrically neutral for the most part (although it probably has a soup of charged particles living on quantum degeneracy pressure in the core). It's probably a bad candidate for a really electron-dense piece of material.

Black holes are another big problem for the practicality of things. We simply don't know what actually is a black hole. If it's a true singularity (i.e. all matter concentrated into one point), it is an exception or extension to Pauli's exclusion principle and when viewed just in the three dimensions of space it can be regarded as an infinitely dense object. But we also know that it probably has no charge at all, and even if it did, the electromagnetic force cannot interact with anything over the apparent horizon. So this is probably also not a candidate.

The next and probably 'best' candidate is most likely radiation-stripped hydrogen gas clouds. It's not dense at all, but hydrogen clouds around highly active star-forming regions are constantly being stripped of their electrons by the intense x-ray and ultraviolet (ionizing) radiation from young, blue, bright stars. This means we're dealing essentially with a big cloud of protons. Downside is: electrical interaction is hard, so you can't do anything with that potential, but it's there.

** I forgot quarks.. I guess you can be even a bit more efficient with those.

• Q=CV. Pull the plates apart, C goes down, V goes up. I have seen the demonstration. – gbarry May 24 '14 at 8:45
• Indeed, for a finite charge, voltage is limited by minimum capacitance,and thus by distance to other matter. Even if the universe is unbounded, if the density of matter has a lower bound then capacitance will not decrease to an arbitrarily low value with increasing distance. – Spehro Pefhany 25 mins ago – Spehro Pefhany May 24 '14 at 10:13
• Ah yes, I understand where you are coming from then. That is just a linear effect though, I was thinking in terms of how to get charge density up many orders of magnitude. – user36129 May 26 '14 at 9:06
• AFAIK, black holes do carry electric charge. Otherwise you could drop gazillions of electrons into one of them and end up with a universe having positive net charge. For practical matters (and the problem at hand) they should however be viewed as opaque balls of Schwarzschild size carrying a homogenuous charge. – Hagen von Eitzen Jan 5 '15 at 15:42
• I didn't mean to come across like I meant black holes can't have charge; they can, just that as far as I know most scientists think that they don't have an appreciable charge as it's mostly being fed charge-neutral matter. Although this is beyond what I should be talking about so don't ask me too hard of questions about this :P – user36129 Jan 5 '15 at 16:06

The potential difference between two bodies is directly proportional to the charge accumulated on it. And that charge is proportional to the free electrons (or ions) in it. The maximum value of which is decided by the number of particles (atoms) in it. So if this is bounded hence the maximum potential difference.

If universe is bounded or the number of atoms in it are bounded, then there is a maximum theoretical voltage. But since we don't know about the existence of boundary of universe, we have to consider the theoretical maximum of voltage as infinity.

• According to current theory the universe has no bounds, but its size is finite but expanding, most probably without limit. Hence the charge at any one time would be finite, but in the long run any charge value can be reached. – Wouter van Ooijen May 24 '14 at 7:13
• @WoutervanOoijen if charge and space are bounded, so does the voltage. But we still don't have a measure of it. If we do also, that number would be too large that we may have to classify that as infinity. :) – nidhin May 24 '14 at 7:24
• Space is not bounded! It is finite, that's something completely different. And 'classifying' a very large number as infinity is nonsense. The essence of infinity (take alph-0, the lowest infinity) is that it is larger than any number. – Wouter van Ooijen May 24 '14 at 10:16
• Sorry for the words used. I meant the same. – nidhin May 24 '14 at 10:48

No. You can put upper limits on what voltages can exist in the observed universe, but there's no theoretical limit in voltage between two objects that are arbitrarily far apart.

• I'm not talking about whether it will arc over, but how much potential can exist. – Loren Pechtel May 24 '14 at 4:26