In a 1911, Ernest Rutherford modeled an atom as being a point of positive charge Ze surrounded by a negative charge - Ze uniformly distributed in a sphere of radius R centered on the point. At distance r within the sphere, the electric fleld is E = Ze/4πε0 (1/r2 – r(R3). He also gave the electric potential as V = Ze/4πε0 (1/r – 3/2R + r2(2R3) .

(a) Show how the expression for the electric fleld follows from the expression for V.

(b) Why does this expression for V not go to zero as r → ∞?