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?

 

[Nickie]

I can explain this phenomenon using the principles of electrostatics. When a battery is connected to a capacitor, it creates an electric field between the two conductors. This electric field causes electrons to move from one conductor to the other, resulting in a buildup of positive charge on one conductor and an equal amount of negative charge on the other.

The amount of charge that can be stored on a capacitor is determined by its capacitance, which is a property of the materials and geometry of the conductors. This means that regardless of the size or shape of the conductors, the capacitance and therefore the amount of charge that can be stored will remain the same.

Now, according to the principle of conservation of charge, the total amount of charge in a closed system must remain constant. Therefore, as electrons move from one conductor to the other, the total amount of charge on the two conductors must remain the same. This is why each conductor acquires the same amount of charge.

In terms of mathematics, this can be represented by the equation Q = CV, where Q is the charge stored on the capacitor, C is the capacitance, and V is the voltage supplied by the battery. As the capacitance remains constant, the charge stored on each conductor will also remain constant, resulting in the same amount of charge on both conductors.

In summary, the equal charge on both conductors of a capacitor is a result of the principles of electrostatics, specifically the conservation of charge and the relationship between charge, capacitance, and voltage.