The time period of revolution of a charge q₁ and of mass m moving in a circular path of radius r is due to coulomb force of attraction with another charge q₂ at its centre is:

find the force between the two charges using coulumb force formula.see that force is attracting. also charge -q1 is revolvingthus it is the case of circular motion with that force acting as centripital force.equate it to mw2r (centripital force on body of mass m and revolving with w angular speed)find w.