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 Cq_+=1~\mbox{C} and q=1 Cq_-=-1~\mbox{C} that are fixed in space and separated by a distance l=1 mml=1~\mbox{mm}, a test particle of mass m=1 kgm=1~\mbox{kg} and charge Q=5 CQ=5~\mbox{C} can oscillate back and forth with a trajectory that looks like half of a circle of radius R=1 mR=1~\mbox{m}. Find the time period of that oscillation in ms, given that the Coulomb constant is k=8.99×109 Nm2/C2k=8.99 \times 10^9~\mbox{Nm}^2/\mbox{C}^2.

Details and assumptions

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