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Say we have a hollow conducting sphere (with some finite thickness). If this object has an excess charge amounting to +Q coulomb, and there is no extra electric field in the surroundings (due to other charges), how will the charge be distributed?

Intuitively it seems that the charge will be symmetrically distributed..(all other cases seem too ugly), but in this case how is charge inside the conducting surface zero? Does this have something to do with solid angle and the fact that two cones with vertex at a point in the conductor will have a special relation of the (charge/distance^2) factors? (more charge is distance is more...)

If this is the case can someone please prove that the effect of the two corresponding cones will cancel each other out?

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Same charges repulse each other. So when they are confined in a system, they try to have stable distance among them as much as possible. For a hollow conducting sphere this stable maximum distance is equal distribution of charges in the outer surface. If any charge try to go the inside conducting surface it automatically decrease distance which increase repulsion. That's why charge inside the conducting surface zero.

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