Halliday, Resnick & Walker — Gauss' Law: Problem 46

46 Assume that a ball of charged particles has a uniformly distributed negative charge density except for a narrow radial tunnel through its center, from the surface on one side to the surface on the opposite side. Also assume that we can position a proton anywhere along the tunnel or outside the ball. Let $F_R$ be the magnitude of the electrostatic force on the proton when it is located at the ball's surface, at radius $R$. As a multiple of $R$, how far from the surface is there a point where the force magnitude is $0.70F_R$ if we move the proton (a) away from the ball and (b) into the tunnel?