A particle of mass m and carrying charge -q₁ is moving around a charge +q₂ along a circular path of radius r. The period of revolution of the charge -q₁ about +q₂ is

Suppose that the charge -q₁ moves around the charge q₂ along a circular path of radius r with speed v. The necessary centripetal force is provided by the electrostatic force of attraction between the two charges, i.e.,

$$\begin{gathered} \frac{1}{4{\mathrm{\pi \epsilon }}_0}·\frac{{\mathrm{q}}_1\times {\mathrm{q}}_2}{{\mathrm{r}}^2}=\frac{{\mathrm{mv}}^2}{\mathrm{r}} \\ \text{ or } \mathrm{v}={\left(\frac{1}{4{\mathrm{\pi \epsilon }}_0}·\frac{{\mathrm{q}}_1\times {\mathrm{q}}_2}{\mathrm{mr}}\right)}^{1/2} \end{gathered}$$

If T is the period of revolution of the charge -q₁ about q₂, then

$\mathrm{T}=\frac{2\mathrm{\pi r}}{\mathrm{v}}$

Substituting for v, we get $\mathrm{T}=\sqrt{\frac{16{\mathrm{\pi }}^3{\mathrm{\epsilon }}_0{\mathrm{mr}}^3}{{\mathrm{q}}_1{\mathrm{q}}_2}}$