Charge doesn't work the same way. All of the charge is on the surface of the sphere (that is how a Van deGraff generator works). Unlike gravity, like charged things inside the sphere are repulsed by the surface just as things outside the sphere are.
The shell theorem holds true for spherically symmetric distributions and inverse-square laws. The electrostatic force within a spherically-symmetric charged object is exactly 0.
As you mention, this assumes a spherically symmetric distribution.
In the case of a charged conductive sphere, the charges are free to move. With no charge present other than that on the sphere they will arrange themselves spherically symmetrically.
But if there is other charge near the sphere (outside or in), shouldn't that cause some rearrangement of the charges on the sphere, breaking in most cases the spherical symmetry?
That's an interesting question! I think the effect would be the opposite of what ChuckMcM imagines: as a (say) positively charged particle inside a positively charged conductive sphere moves from the center toward one side of the sphere, it repels the charges on that side more than it does on the opposite side. It does seem like that would cause those charges to spread out slightly, making that part of the sphere negative relative to the other side, accelerating the particle in the direction it was already going, until it hits the sphere. The minimum energy is thus where all charges within the sphere are on its surface; none are inside. I believe this is consistent with observation.
It has been an interesting conversation so far. Since I have been going through Jackson's text it makes a useful problem to work. I'm working up the field equations for inside the sphere, inside a charged concave surface, and inside a concave depression in a sphere. I suspect that this thread will be dead before I'm done but the next time around I'll be able to post a link to a paper :-).
Coming up with a closed-form solution would be beyond my mathematical abilities at this point, having not done any calculus to speak of in 40 years, but I'll be interested to see if you can.
No, gravity and electrostatic attraction/repulsion are both governed by inverse-square laws, so they act the same.
Also, one of Maxwell's equations (in integral form) says that the total electric field passing through a closed surface is proportional to the amount of charge within the surface. If you consider a spherical surface just inside a uniformly charged sphere, with no charge inside or outside the sphere, there can be no flux passing through this surface (since the total flux must be zero and the field is obviously symmetrical). In fact this is true for any closed surface inside such a sphere.
