Suppose two capacitors are connected in series, I understand that external plates gets equal magnitude because of the batteries terminals, but how does the internal plates also get the charge with same magnitude (opposite in nature). I read some answer saying that because the current flowing in the Series combination is same throughout the circuit. But then i am getting confused as to why current is flowing same throughout? Is there any other reason as to why internal plates gets the same magnitude of charge? I know that the internal plates gets charges because of induction of external plates charges but why in equal magnitude?
Suppose you have two capacitors in series like so:
————————||——————||———————— C1 C2
Consider only the central piece:
|——————| C1 C2
This is a isolated conductor, separated from the rest of the circuit by the insulating dielectric gaps in the capacitors. The total charge of an isolated conductor is a constant. If the initial state is that both capacitors are uncharged, and some external voltage is applied across the total series arrangement, the total charge on the isolated segment must stay at zero. Therefore any charge on the right-hand plate of C1 must be balanced by an equal and opposite charge on the left-hand plate of C2.