Answer
See answers.
Work Step by Step
The situation provides feedback that quickly balances the charges.
Imagine that the positive plate momentarily had more charge than the negative plate. This would attract negative charges, which would flow from the battery to the negative plate, and this would continue until the magnitudes of the 2 charges were equal.
Another proof relies on the fact that the battery and capacitor were neutral beforehand, and remain so after they’re connected. Any charge removed from one plate must be on the other plate.
Neither argument depends on the conductors’ sizes or shapes.
