Using Gauss's theorem,obtain an expression for the force between 2 point charges?

Let the gaussian surface be a sphere and the separation between the charge is r and taking  one charge insde the sphere and the other be at the surface (r)
now  firstly we are interested in finding the magnitude of electric field at a distance r
$\int$E.ds = q_net/∊0
$$\begin{gathered} \int E ds = \frac{q_1}{{\epsilon }_0} \\ E \times 4{\mathrm{\pi r}}^2 =\frac{{\mathrm{q}}_1}{{\mathrm{\epsilon }}_0} \\ \mathrm{E}= \frac{{\mathrm{q}}_1}{ 4{\mathrm{\pi r}}^2{\mathrm{\epsilon }}_0} (\mathrm{this} \mathrm{is} \mathrm{electric} \mathrm{field} \mathrm{due} \mathrm{to} \mathrm{charge} 1 \mathrm{at} \mathrm{a} \mathrm{distance} \mathrm{r}) \end{gathered}$$
now w can find force on due to this electric field on charge q_​2
F = q₂E
    = $$\begin{gathered} q_2 E = \frac{q_1{q}_2}{4{\mathrm{\pi \epsilon }}_0{\mathrm{r}}^2} \\ = \frac{1}{4{\mathrm{\pi \epsilon }}_0}\times \frac{q_1{q}_2}{r^2} \end{gathered}$$
this proves the force of interection between 2 charge particle.