Given information
A battery is connected to a capacitor.
Step-by-step explanation
The battery pumps the charge from one plate to another. every electron pushed out of the battery negative terminal is matched by an electron being pulled in from the positive terminal. As a consequence, every electron added to the capacitor negative plate is matched by an electron removed from the positive plate. Electrons repel each other, so they move to be far apart from each other as possible. the repulsion acts across the dielectric of the capacitor. this allows a current to flow, but once the charge is fully distributed an equilibrium is reached where no more current flows and everything is in balance.
the balance of charge is that neither the battery nor the capacitor can create or destroy charge. Since they were neutral before they were connected, they must be neutral after they are connected. The charge removed from one plate appears as excess on the other plate. This is true regardless of the conductor size or shape.