Charge on two concentric spherical shells

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SUMMARY

The discussion centers on the stability of two concentric spherical shells connected to a battery, with the smaller shell negatively charged and the larger shell positively charged. It is established that this configuration behaves like a capacitor, where charge conservation dictates that the charges on both spheres must be equal. However, the system is deemed unstable due to the higher charge density on the smaller sphere, which has sharper edges that concentrate charges. The conversation highlights the importance of understanding electric charge distribution and stability in electrostatic systems.

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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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