# Confusion about fundamental charge vs non-fundamental

I am confused about a basic electric charge concept. The way I see it, when an electron (or other charged particle) is in motion, you define its charge as its elementary/fundamental charge (about $1.6\cdot 10^{19}$ Coulombs). What confuses me about this is that when electrons are stationary (not exactly stationary of course), like on a charged object, (such as a charged plate or capacitor) charge in Coulombs can be defined as the fundamental charge of the electron(s) ($q$) times the voltage of the charged object ($q=CV$ for capacitors).

Does electric charge exist in some way independently from individual electrons? I know that the case I suggested is when electrons are relatively stationary and together, but it still seems slightly confusing.

• The way I see it, when an electron (or other charged particle) is in motion, "you define its charge as its elementary/fundamental charge" - The particle doesn't have to be in motion. The electric charge is an intrinsic property that some particles just have. – Andrei Geanta Nov 4 '17 at 16:13
• Right, but that point I was making was that it seems like charge is something particles can have on their own, but also something they can gain in an electric field. I guess it could just be left as a basic property of electricity. – Tom Nov 4 '17 at 16:35
• The electric field acts upon the charged particles and it accelerates them. But the particles do not gain charge in electric fields. The charge of a particle cannot change, otherwise it will not be that particle anymore. – Andrei Geanta Nov 4 '17 at 16:37
• Yeah, that makes sense. I suppose that these concepts can be a little confusing if you don’t quite understand them. – Tom Nov 4 '17 at 16:50

The electric charge is an intrinsic property that some particles just have. The electric charge of an electron is $q=-e$. The electric charge of a proton or a positron is $q=e$.

In the case that you described, $q$ is the total charge on the capacitor, $C$ is the capacitance and $V$ is the potential difference between the plates. The total charge is given by the number of electrons times the elementary charge that each electron have. $$q=ne$$ So you have two conductive plates separated by a dieletric material. The distance between the plates is $d$. Between the plates there exist an electric field $\vec{E}$. The capacitance is given by the amount of total charge divided by the potential difference: $$C=\frac{q}{E\cdot d}=\frac{q}{V}$$