Assume that a ball of charged particles has a uniformly distributednegative charge density except for a narrow radial tunnel throughits center, from t

Assume that a ball of charged particles has a uniformly distributednegative charge density except for a narrow radial tunnel throughits center, from the surface on one side to the surface on the opposite side. Also assume that we can position a proton any where along the tunnel or outside the ball. Let ${F}_{R}$ be the magnitude of the electrostatic force on the proton when it islocated at the ball's surface, at radius R. As a multiple ofR, how far from the surface is there a point where the forcemagnitude is 0.44FR if we move the proton(a) away from the ball and (b) into the tunnel?
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yagombyeR
Jeffrey Jordon

(a) The flux is still $-750N{m}^{2}/{C}^{2}$ , since it depends only on the amount of charge enclosed.

(b) We use  $\varphi =\frac{q}{{ϵ}_{0}}$​ to obtain the charge q :

$-6.64×{10}^{-9}C$