Consider a fixed uniformly charged insulating sphere with radius R and total charge +Q. A point charge -q (q << Q) with mass m is released from rest at a distance of 3R from the centre of the charged sphere. When the point charge reaches the surface of the sphere, its speed is: ($\varepsilon_0$ is the permittivity of vacuum, neglect gravitational forces).
Explanation
Detailed Solution
Energy conservation: $K_A+U_A=K_B+U_B \Rightarrow -\frac{kQq}{3R}=\frac{1}{2}mv^2-\frac{kQq}{R} \Rightarrow \frac{2}{3}\frac{kQq}{R}=\frac{1}{2}mv^2 \Rightarrow v=\sqrt{\frac{Qq}{3\pi\varepsilon_0mR}}$.