A charged particle with charge q and mass m is given an initial kinetic energy K_{0} at the middle of a uniformly charged spherical region of total charge Q and radius R . q and Q have opposite signs. The spherically charged region is not free to move. Throughout this problem consider electrostatic forces only.
a. Find the value of K_{0} such that the particle will just reach the boundary of the spherically charged region.
b. How much time does it take for the particle to reach the boundary of the region if it starts with the kinetic energy K_{0} found in part (a)?