Why Do Both Conductors in a Capacitor Acquire Equal Charge?

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When a battery is connected to a capacitor, it establishes a fixed potential difference across the two conductors. This potential difference causes equal but opposite charges to accumulate on each conductor, regardless of their size or shape. The repulsion between like charges ensures that both conductors acquire the same magnitude of charge. Mathematically, this can be understood through the relationship between charge, capacitance, and voltage, where the charge on each conductor is directly proportional to the voltage applied by the battery. Understanding the role of the battery in maintaining this fixed potential is key to grasping why both conductors have equal charge.
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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! :)
 
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What does a battery do to charge?
 
Apply a fixed potential to it, I suppose. But I'm not sure how that helps??
 
How does it apply the fixed potential?
What does it do to the charge to get that potential?
 

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