Q. A sphere of radius r₀ carries a volume charge density ρ_E. A spherical cavity of radius r₀/2 is then scooped out and left empty, as shown. 

(a) What is the magnitude and direction of the electric field at point A? 

(b) What is the direction and magnitude of the electric field at point B? Points A and C are at the centers of the respective spheres.

Solution: