Why Do Both Conductors in a Capacitor Acquire Equal Charge?

[bananabandana]

Homework Statement

A battery is connected to a capacitor made from two conductors. Why do each of the two conductors acquire the same charge,regardless of size or shape?

Homework Equations

The Attempt at a Solution

Well, I can see that this is sensible, intuitively that the charge on one will repel an equal amount of charge on the other. But I have no idea how to prove/represent this mathematically!
Thanks for help! :)

 

[Simon Bridge]

What does a battery do to charge?

 

[bananabandana]

Apply a fixed potential to it, I suppose. But I'm not sure how that helps??

 

[Simon Bridge]

How does it apply the fixed potential?
What does it do to the charge to get that potential?