Charge on two concentric spherical shells

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Connecting a battery to two concentric spherical shells creates a potential difference, leading to charge accumulation on both spheres. The smaller sphere, connected to the negative terminal, will acquire a negative charge, while the larger sphere, connected to the positive terminal, will gain a positive charge. For the system to reach stability, the charges must distribute evenly, resulting in a uniform electric potential across the surfaces of each shell. However, a capacitor requires a voltage difference between its plates to store energy, meaning the spheres cannot maintain the same electric potential while functioning as a capacitor. Thus, the system cannot operate as a capacitor without a voltage difference between the two shells.
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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? Is there any situation for the charges on these spheres stay at the same electric potential? Can this system make a kind of capacitor?
 
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brianeyes88677 said:
s there any situation for the charges on these spheres stay at the same electric potential? Can this system make a kind of capacitor?
I feel these 2 statements are contradicting each other, can the capacitor have no voltage difference between its surfaces when connected to a battery?
 
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