A point particle $P$ of charge $Ze$ is fixed at the origin in 3-dimensions, while a point particle $E$ of mass $m$ and charge $-e$ moves in the electric field of $P$.
I have the Newtonian equation of motion as $- \frac{Ze^2}{4 \pi \epsilon_{0}} \frac{\vec{r}}{r^3} = m \ddot{\vec{r}}$ I derived this from Newton's law and Coulomb's law.
I then went on to show that the particle moves in a plane by showing it has a constant normal vector.
Can anyone help me find this if the orbit is circular about $P$ what it's orbital frequency is -in terms of the constants we have? I would be extremely grateful.
I have attempted this by parameterizing the orbit, differentiating with respect to time and substituting into the equation of motion, however all I get are two unsolvable differentials equations.