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.

 

[Nickie]

I would approach this question by first defining some key terms and concepts. Conductance refers to the ability of a material to allow the flow of electric current, while geometry refers to the shape and size of an object. In this context, the question is asking whether the conductance of two bodies is dependent on their shape and size.

To answer this question, we can look at the equation for conductance, which is given by G = I/V, where G is the conductance, I is the electric current, and V is the voltage. From this equation, we can see that the conductance is dependent on both the current and the voltage. However, in this scenario, the voltage is constant (V1 and V2), so we can focus on the current as the determining factor.

When the two bodies are shorted together, the charges will redistribute themselves until the potential difference between them is zero. This is similar to a capacitor, where the charges on the two plates redistribute themselves until the potential difference between them is equal to the applied voltage.

The amount of charge that flows from one body to the other will depend on the geometry of the conductors. This is because the shape and size of the conductors will affect the distribution of charges and the resulting electric field. For example, if one conductor has a larger surface area, it will be able to hold more charges and therefore, less charge will flow to the other conductor.

In conclusion, the conductance of two bodies is dependent on their geometry, as it affects the distribution of charges and the resulting electric field. This behavior is similar to that of a capacitor, where the capacitance is dependent on the geometry of the plates. Therefore, the amount of charge that flows from one body to the other is also dependent on the geometry of the conductors.