Conductance of 2 bodies: Is it dependent on geometry?

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Homework Help Overview

The discussion centers around the conductance of two arbitrarily shaped conductors with specified charges and potentials. The original poster seeks to demonstrate that the charge transfer between these conductors, when connected, is solely dependent on their geometry.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between charge transfer and geometry, questioning how to prove that this relationship exists independently of other factors. There is a suggestion to consider the behavior of capacitors in this context.

Discussion Status

The discussion is ongoing, with participants offering insights into the relationship between geometry and charge transfer. Some guidance has been provided regarding the relevance of capacitor equations, but no consensus has been reached on the proof itself.

Contextual Notes

Participants note that the voltages are relative to a reference point, indicating that capacitance may play a role in the discussion. The original poster's question implies a need to clarify assumptions about the system's setup and the factors influencing charge transfer.

Arkavo
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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?
 
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The voltages are with respect to something. There is capacitance between themselves and that something.
 
yes but how do i prove the original question? that charge transferred is independent of all factors except geometry and potential difference?
 
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.
 

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