For the given figure, find the ratio $\frac{\text{ force on }{\mathrm{q}}_1\text{ due to }{\mathrm{q}}_2}{\text{ force on }{\mathrm{q}}_1\text{ due to }{\mathrm{q}}_3}$

According to coulomb's law force between two charges is given by,

$\mathrm{F}=\frac{{\mathrm{kq}}_1{\mathrm{q}}_2}{{\mathrm{r}}^2}$

Hence,

$\begin{array}{l}{\mathrm{F}}_1=\frac{{\mathrm{kq}}_1{\mathrm{q}}_2}{{\left(\mathrm{lsin}\left({30}^{\circ }\right)\right)}^2}=\frac{12{\mathrm{kQ}}^2}{{\mathrm{l}}^2}\\ {\mathrm{F}}_2=\frac{{\mathrm{kq}}_1{\mathrm{q}}_3}{{\left(\mathrm{lcos}\left({30}^{\circ }\right)\right)}^2}=\frac{8{\mathrm{kQ}}^2}{3{\mathrm{l}}^2}\\ \text{ Now, }\frac{{\mathrm{F}}_1}{{\mathrm{F}}_2}=\frac{12{\mathrm{kQ}}^2}{{\mathrm{l}}^2}\times \frac{3{\mathrm{l}}^2}{8{\mathrm{kQ}}^2}=\frac{9}{2}\end{array}$