# What is the “positive charge” on a capacitor if only electrons and not protons flow through a circuit?

Speaking in non-conventional current terminology, electrons should build up from the positive terminal of power supply to the top plate of a capacitor. What I don't get is, from an atomic perspective, how an electric field is created since the capacitor is given no "positive" charge from protons.

• Are you referring to the atoms in the power source? – Mahmoud Maarouf Oct 7 '20 at 3:59
• You can get positive charge by pushing out electrons. You don't need to move protons, which is why you can have both positive and negative currents down a wire even though only electrons move through metal. – user1850479 Oct 7 '20 at 4:13
• Electrons get pushed in on one side and pushed out on the other side so that the capacitor as a whole maintains net neutral charge. Protons don't come into it. Electrons in the dielectric (insulator) material move slightly without actually coming loose and moving through the electrodes. – mkeith Oct 7 '20 at 6:25
• @mkeith So the positive charges in the dielectric move to one side of the capacitor and the negative charges on the other? – Mahmoud Maarouf Oct 7 '20 at 6:31
• @MahmoudMaarouf the negative charges move a little bit, leaving one side more positive and one side more negative. Polar molecules rotate or shift to align themselves in the electric field, basically. – mkeith Oct 7 '20 at 14:05

## 2 Answers

Consider a parallel metal plate capacitor.

An excess of electrons on any plate gives a negative charge.

A Scaricity of electrons on any plate gives a positive charge.

When we talk about a capacitor, the overall charge on the capacitor is zero (if you consider both plates). What happens is - some electrons of one plate move to the second plate thereby giving you a positively charged plate and a negatively charged plate.

When you discharge the capacitor, those excess electrons from the negative plate return back to the positive plate and both plates become neutral.

• "Only electrons flow in a circuit ..." That's true for metallic conductors but positive ions can flow in batteries and electrolysis, etc. – Transistor Oct 7 '20 at 7:12
• @transistor - yeah. sorry, I didn't think of that case. I will edit. Thanks for pointing it out. – Whiskeyjack Oct 7 '20 at 7:18

In metals, where the only mobile charge carriers are electrons (other materials use other charge carriers), the positive charge is the excess of nuclear protons, whose charge is now no longer being neutralised by the electrons in the shell.

To put some numbers on this, consider a capacitor whose plates are 1 square metre, and with a separation of 10 um. The standard capacitance formula of C=Ae/d gives a capacitance of about 1 uF, assuming a vacuum dielectric.

Let's say the metalisation is aluminium, with a unit cell dimension of 0.4 nm. If we count the number of atoms on the surface layer of the electrodes, it comes to 1/(0.4 n)2 = 6.3e18. There are many more atoms in the film, but let's only consider the surface monolayer. As each atom has 13 electrons and 13 neutrons, that's a total charge of (surprisingly, I picked 1 m2 and Al first) 13 Coulombs each of proton and electron charge. However, only the outermost electron is freely available to move in the conduction band, so that's 1 C of mobile charge.

Let's charge the capacitor to 1 kV. As Q = CV, that's 1 mC. So 0.1% of the mobile electronic charge has left the positive plate, which stops it neutralising 1 mC of the total 13 C nuclear charge. Meanwhile, 1 mC of electrons have arrived on the negative plate, leaving the capacitor overall neutral.