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