Chapter 23, Problem 46P

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 0.50 f _r if we move the proton (a) away from the ball and (b) into the tunnel?