A hollow spherical conductor, carrying a net charge +Q, has an inner radius
r₁ and an outer radius r₂ = 2r₁. At the center of the sphere is a point charge +Q/2.
(a) Write the electric field strength E in all three regions as a function of r. Then determine the potential as a function of r, the distance from the center, for
(b) r > r₁,
(c) r₁ < r < r₂ and
(d) 0 < r < r₁
(e) Plot both E and V as function of r for r = 0 to r = 2r₂