Ball in a sphere **
We know that if a point charge q is located at radius a in the interior of a sphere with radius R and uniform volume charge density ρ, then the force on the point charge is effectively due only to the charge that is located inside radius a.
(a) Consider instead a uniform ball of charge located entirely inside a larger sphere of radius R. Let the ball's radius be b, and let its center be located at radius a in the larger sphere. Its volume charge density is such that its total charge is q. Assume that the ball is superposed on top of the sphere, so that all of the sphere's charge is still present. Can the force on the ball be obtained by treating it like a point charge and considering only the charge in the larger sphere that is inside radius a?
(b) Would the force change if we instead remove the charge in the larger sphere where the ball is? So now we are looking at the force on the ball due to the sphere with a cavity carved out, which is a more realistic scenario.