If a charged sphere is said to have a certain self-capacitance, dependent on its radius, then could a single electron also have a specific capacitance value, and since V = Q/C, a specific voltage?
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$\begingroup$ Is it possible to define the radius of an electron? An electron is always in a state of a distribution defined by $\psi$ $\endgroup$– Ghosal_CCommented Oct 2, 2017 at 12:52
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$\begingroup$ Not sure, but I thought ψ was the electron's "location" distribution, not its actual "size". I think it is generally agreed that electrons have a certain diameter, maybe < 10^18 m. Anyway, they are tiny, and so will carry a huge charge density, and therefore, Voltage? $\endgroup$– Leo FreemanCommented Oct 2, 2017 at 13:01
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$\begingroup$ But the charge can also be modelled in a very illiterate way like a distribution like $\iiint\rho\psi{\psi}^{*}\mathrm{d}^3\vec{r}=e$ $\endgroup$– Ghosal_CCommented Oct 2, 2017 at 13:04
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$\begingroup$ If you can assume a radius of an electron, then maybe it is possible to work this out. But, if I may ask, how does one come about to defining the radius of a static electron? $\endgroup$– Ghosal_CCommented Oct 2, 2017 at 13:07
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$\begingroup$ I don't know where the boundary of an electron is, if it even has one. But since the charge stays constant, as we know, and if the radius varied somehow, then the surface "voltage" would also vary with radius. I'm still trying to grasp the significance of a single electron having a "voltage", and at the same time, a collection of electrons on a metal sphere having another voltage. $\endgroup$– Leo FreemanCommented Oct 2, 2017 at 21:53
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2 Answers
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The field around a charged particle (like an electron) is associated with voltages (electric potential) in the familiar 1/R manner. In a sense, all charges are measured by sampling the field (i.e. voltage gradient) they create. So, yes, a single electron does have voltages associated with it, because it induces voltages in its vicinity. It cannot, however, be identified with a particular voltage value, unless 'infinity' were such a value. One cannot remove part of the electron charge, so it cannot be said what energy it takes to do so.
As for capacitance, that is (dimensionally) a distance, and not a property that is directly connected with the charge or mass of an electron. In a sense, a single electron just doesn't have a particle property to derive capacitance from. So, there's no capacitance of an electron. One cannot ADD a new part to the electron charge, so it cannot be said what energy is stored when one does so.
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This is something that has confused me before when I started to think about it. The way that it seems is that when electrons are stationary in a material (an object with static electric charge whether it's a piece of styrofoam or a capacitor), the effective charge is dependent on the number of electrons and their voltage. For an electron effectively alone or in motion, the charge is defined as just the elementary charge of the electron(s). As for single electrons, maybe they could be hypothetically viewed as charged spheres with a constant capacitance and voltage, but that's purely hypothetical as electrons are not shaped like nor do they exist like billiard balls. The arrangement of electrons seems to be just as meaningful for charge calculations as electrons themselves.
