A nonconducting solid sphere has a uniform volume charge density p. Let r be the vector from the center of the sphere to a general point P within the sphere.

(a) Show that the electric field at P is given by E = ρr/3ε₀. 

(b) A spherical cavity is hollowed out of the sphere, as shown in Figure. Using superposition concepts, show that the electric field at all points within the cavity is uniform and equal to E = ρa/3ε₀, where a is the position vector from the center of the sphere to the center of the cavity.