Can you add potentials if charge redistributes?

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Discussion Overview

The discussion centers on the potential energy functions of charged conductors when they are brought close together, specifically addressing whether the potential energy functions of isolated conductors can be simply added after charge redistribution occurs. The scope includes theoretical considerations and mathematical reasoning related to electrostatics and potential energy in conductors.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant proposes that it should be possible to add the potential energy functions of two isolated conductors, Vm and Vn, to find the total potential energy when they are brought close together.
  • Another participant argues against this, stating that the potentials change due to charge redistribution and that the new potentials can be added, but they differ from the original potentials.
  • A participant requests a mathematical demonstration or contradiction to support the claim that the potentials cannot simply be added.
  • It is noted that moving the charge distribution alters the potentials created by those charges.
  • One participant emphasizes that the issue is more about physics than mathematics, suggesting that assuming no charge redistribution is a poor assumption for finite-sized conductors.
  • Another participant points out that adding the isolated potentials leads to a non-zero electric field inside the conductor, which would cause a current and further charge redistribution.
  • A later reply references Griffiths' "Introduction to Electrodynamics" for further explanations on the physics and mathematics involved.

Areas of Agreement / Disagreement

Participants express disagreement regarding the addition of potential energy functions after charge redistribution, with some supporting the idea and others contesting it. The discussion remains unresolved with competing views on the validity of the proposed approach.

Contextual Notes

Participants highlight limitations in assumptions regarding charge redistribution and the implications of finite-sized conductors on potential energy calculations. The discussion does not resolve the mathematical steps or the physical principles involved.

amiras
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Let say we have charged conductor M and we know its potential energy function Vm(r) when M is isolated from any charges. We also have charged conductor N with potential energy function Vn(r) when it is isolated.

Now we put objects M and N close together, the charges on their surfaces redistribute. I am interested in potential energy at every point in space, can I still add potential energy functions (Vm + Vn) to find that?

I'd like to think that it is possible to add functions like that, but I can't find a way of proving it mathematically yet. Any ideas of how to show this?
 
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No, you can't do that. When the charges redistribute, the associated potential functions change. The new potentials can be added but they will be different from the original potentials.
 
Last edited:
Could you show that mathematically or find some kind of contradiction, because I am having difficulties finding easy-calculable one.
 
If you move the charge distribution, the potentials created by those charges will change as well.
 
amiras said:
Could you show that mathematically or find some kind of contradiction, because I am having difficulties finding easy-calculable one.

The issue is not about mathematics, it's about physics. Of course if you assume the charge does not redistribute, you can use superposition. But if the charges are distributed over the surface of finite-sized conductors, that is probably a bad assumption.
 
amiras said:
Could you show that mathematically or find some kind of contradiction,
The contradiction is that if you simply add the isolated potentials you will wind up with a non-zero E field inside the conductor. This will lead to a current and therefore a redistribution of charges.
 
The physics and the math for working with potentials and conductors can be found in Griffiths' "Introduction to Electrodynamics", chapters 2 and 3.

The explanations for each of the comments above will be found there as well.
 

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