Conductance of 2 bodies: Is it dependent on geometry?

[Arkavo]

Homework Statement

I have 2 arbitrarily shaped conductors with charge Q₁ and Q₂ with potetials V₁ and V₂ respectively. I then short them (connect with a thin metallic thread) now i have to prove that the amount of charge that flows from one to the other is: Only dependent on the geometry of the conductors.

Homework Equations

Does this behave like a capacitor, if so how?

 

[CWatters]

The voltages are with respect to something. There is capacitance between themselves and that something.

 

[Arkavo]

yes but how do i prove the original question? that charge transferred is independent of all factors except geometry and potential difference?

 

[CWatters]

Perhaps look at the equation for a parallel plate capacitor. In particular the units. If the current depends only on quantities measured in meters or square meters then you've proved it depends on geometry.