\(\frac{m v^2}{r}=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{q_1 q_2}{r^2}\)

\(v=\left[\frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_2}{r m}\right]^{\frac{1}{2}}\)

For \(1\) trip

\(T=\frac{2 \pi r}{v}=2 \pi r\left[4 \pi \varepsilon_0 m r\right]\left[q_1 q_2\right]^{\frac{1}{2}}\)

\(T=\sqrt{\frac{16 \pi^3 \varepsilon_0 m r^3}{q_1 q_2}}\)