[Physics] Is it possible to determine how many electrons there are in a plate from its voltage

electronspotential energyvoltage

We've just stared doing voltage in school, and so I wondered if this is possible 🙂

If I charge an insulated metal plate using an EHT to something like 5kV, then I've added electrons to the plate. My guess is that the extra electrons 'push more' than what can be countered by the protons, causing a voltage, almost like a spring compressing I guess. (Correct me if I'm wrong!).

So, if I know the voltage of the plate, and I know how many atoms there are in the plate, is it possible to calculate how many extra electrons have been added to cause the voltage?


Best Answer

If voltage is all that you know, then the answer is No.

If you know how much charge $Q$ in Coulombs is added, you only have to divide by the charge $e$ on each electron (in Coulombs). Otherwise, if you have a parallel plate capacitor and you know the capacitance $C$, you can work it out from $Q = CV$.

Your suggestion that the extra electrons 'push more' like a spring is interesting because a capacitor stores energy as a spring does. In a spring the elastic energy stored is $\frac 12 kx^2$ where $k$ is the spring constant (how stiff it is) and $x$ is what distance it is stretched or compressed, whereas in a capacitor the electrical energy stored is $\frac 12 CV^2$. So the formulas are similar.