Capacitance of an isolated sphere - solid vs hollow

[elisagroup]

Seems the physics books agree that there is no difference in capacitance whether an isolated sphere is solid or hollow. And the reason mentioned for that always sounds something like the following:

"The reason that the capacitance C, and hence the charge Q, is not affected by whether or not the sphere is hollow or solid is because, in a perfect conductor, like charges are free to take up equilibrium positions in response to the mutual electrostatic (Coulomb) repulsion between them. This means that all of the charges will move to the outer surface of the sphere, and will be distributed uniformly over the surface of the sphere, in order to 'get as far away as possible' from their neighbors. This is the energetically most favorable distribution of the charge. Since the material of which the sphere is made is a conductor, all charges can find their way to the outer surface, whether the interior is hollow or solid. "

But does it account for the scenario where the sphere would be charged to such a degree that the outer surface would get crowded, with charges looking for a more relaxed state and redistributing themselves on the inner layers of the sphere as well. And If that is true, wouldn't that mean that under certain conditions there is a difference in capacitance between solid vs hollow configurations?

 

[Nugatory]

But does it account for the scenario where the sphere would be charged to such a degree that the outer surface would get crowded, with charges looking for a more relaxed state and redistributing themselves on the inner layers of the sphere as well.

It does not, because it is describing a perfect (the word “ideal” is used more often) conductor, and that cannot happen in a perfect conductor. In an ideal conductor the charge density at a point can be arbitrarily high, so the crowding you’re describing never happens. Of course ideal conductors don’t really exist, but many real world conductors come so close that we can calculate capacitance as if they were ideal.

And If that is true, wouldn't that mean that under certain conditions there is a difference in capacitance between solid vs hollow configurations?

Those “certain conditions” would be if we had a sphere made of insulating rather than conductive material - but here it specifically says we’re working with a conductive sphere.