Arc in a dipole field

Under the influence of an electrical field that's caused by a dipole made of two opposite charges $q_+=1~\mbox{C}$ and $q_-=-1~\mbox{C}$ that are fixed in space and separated by a distance $l=1~\mbox{mm}$, a test particle of mass $m=1~\mbox{kg}$ and charge $Q=5~\mbox{C}$ can oscillate back and forth with a trajectory that looks like half of a circle of radius $R=1~\mbox{m}$. Find the time period of that oscillation in ms, given that the Coulomb constant is $k=8.99 \times 10^9~\mbox{Nm}^2/\mbox{C}^2$.

Details and assumptions

• Hint: $\int^{\pi/2}_{0} \frac{dx}{\sqrt{\cos{x}}}= 2.622$