I'm trying to better understand the process of charging a capacitor with a battery. My textbook (the Halliday's Fundamental of Physics) describes this process in these terms:
When the circuit [...] is completed, electrons are driven through the wires by an electric field that the battery sets up in the wires. The field drives electrons from capacitor plate h to the positive terminal of the battery; thus, plate h, losing electrons, becomes positively charged. The field drives just as many electrons from the negative terminal of the battery to capacitor plate l; thus, plate l, gaining electrons, becomes negatively charged just as much as plate h, losing electrons, becomes positively charged.
So, if I understand correctly: because of a potential difference between the positive terminal + and plate h, an electric field appears and moves the electrons from h to +, then the battery does work to move these electrons from its positive to its negative terminal, and finally because of a potential difference between the negative terminal - and plate l, an electric field appears and moves these electrons from - to l.
The textbook goes on by saying:
Initially, when the plates are uncharged, the potential difference between them is zero.
If the plates, which are isolated conductors, are uncharged, that is, there is no net charge on them, is it correct to assume that their electric potential is zero?
Vh = 0V,
Vl = 0V, then
Vh - Vl = 0V.
As the plates become oppositely charged, that potential difference increases until it equals the potential difference V between the terminals of the battery. Then plate h and the positive terminal of the battery are at the same potential, and there is no longer an electric field in the wire between them. Similarly, plate l and the negative terminal reach the same potential, and there is then no electric field in the wire between them. Thus, with the field zero, there is no further drive of electrons.
I'm ok with this, but if my previous assumption is correct (
Vh = Vl = 0V), the negative terminal of the battery must have a negative potential, otherwise in the wire connecting it to plate l we would have:
- no electric field if
V- = 0V;
- a reversed electric field if
V- > 0V.
The problem is that nowhere is said that the negative terminal of a battery must have a negative potential, the book says that it has a lower potential than the other terminal, so it could be zero or even positive.
So my assumption is incorrect? Why?