Charge on two concentric spherical shells

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Discussion Overview

The discussion revolves around the stability of two concentric spherical shells connected to a battery, exploring concepts related to charge distribution, capacitance, and the implications of charge conservation. Participants consider whether the system can reach a stable state and the conditions under which charges on the spheres might remain static.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the stability of the system when connected to a battery, seeking clarification on whether the charges can remain static.
  • Another participant asserts that the system will become stable, interpreting the setup as a capacitor with conducting shells.
  • A participant inquires about the ratio of charges on the two spheres, given their different radii.
  • Concerns are raised about the assumption that the charges on both spheres would be equal, with one participant arguing that this seems unreasonable for stability.
  • Another participant emphasizes that charge conservation implies the charges must be equal, questioning the reasoning behind the stability concern.
  • One participant argues against stability, suggesting that the smaller sphere's sharper edges would lead to a higher concentration of charge, potentially affecting stability.
  • A later reply seeks clarification on the meaning of "stable," distinguishing between electric charge distribution and mechanical stability without supports.

Areas of Agreement / Disagreement

Participants express differing views on the stability of the system and the implications of charge distribution. There is no consensus on whether the charges on the spheres can be equal while maintaining stability, and the meaning of "stable" remains ambiguous.

Contextual Notes

Participants have not fully resolved the implications of charge distribution on stability, nor have they clarified the assumptions regarding the nature of stability being discussed.

brianeyes88677
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There are two spherical shells in different sizes and they are concentric. Now if I connect a battery to the two spheres (connect the negative pole to the smaller sphere and connect the positive pole to the bigger sphere). Will this system become stable? Or is there any situation for the charges on these spheres stay static?
 
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brianeyes88677 said:
Will this system become stable?
Sure. Do you expect something else?
You are connecting a battery to a capacitor (assuming the shells are conducting).
 
If it is a capacitor then what's the ratio of the amount of charges on the both sphere? (the radii are r and R)
 
Is this homework? If yes, please post the full problem statement and your work so far.

What do you think?
 
This is not a homework, it's just a concept that flash through my mind. If it is a capacitor just like you say, the amount of charges on the two spheres should be the same, but I think this isn't reasonable, how can it be stable if the amount of charges are the same?
 
brianeyes88677 said:
This is not a homework, it's just a concept that flash through my mind. If it is a capacitor just like you say, the amount of charges on the two spheres should be the same
Yes, this is given by charge conservation.
brianeyes88677 said:
how can it be stable if the amount of charges are the same?
Where is the problem?
 
No, the system will not become stable because the smaller sphear has shaper edges, charges are more concentrated on sharper surfaces(smaller spheare).
 
Wait, what is meant by "stable" here? In terms of electric charge distribution, or in terms of forces if we don't have supports? I assumed the former one, where the different charge density is not an issue.
 

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