A positive charge Q is uniformly distributed throughout the volume of a dielectric sphere of radius R. A point mass having charge +q and mass m is fired toward the center of the sphere with velocity v from a point at distance `r (r gt R)` from the center of the sphere. Find the minimum velocity v so that it can penetrate `(R//2)` distance of the sphere. Neglect any resistance other than electric interaction. Charge on the small mass remains constant throughout the motion.

Answer

`sqrt((2KQq)/(mR)((r-R)/r+3/8))`

Explanation

From the energy conservation
`(KQq)/r+1/2 mv(2)=11/8(KQq)/R+0`
`v=sqrt((2KQq)/(mR)[11/8-R/r])`