Physics - Electrostatics Question with Solution | TestHub

It is given that ${\vec{F}}_A+{\vec{F}}_B+{\vec{F}}_D=0$ Where ${\vec{F}}_A,{\vec{F}}_B$ and ${\vec{F}}_D$ are the forces applied by charges placed at $A,B$ and $D$ on the charge placed at $C$. $\begin{array}{l}\Rightarrow {\overrightarrow{\mathrm{F}}}_{\mathrm{B}}+{\overrightarrow{\mathrm{F}}}_{\mathrm{D}}=-{\overrightarrow{\mathrm{F}}}_{\mathrm{A}}\\ \left|{\overrightarrow{\mathrm{F}}}_{\mathrm{B}}+{\overrightarrow{\mathrm{F}}}_{\mathrm{D}}\right|=\sqrt{2}\frac{\mathrm{KqQ}}{{\mathrm{a}}^2}\\ \Rightarrow \left|{\overrightarrow{\mathrm{F}}}_{\mathrm{A}}\right|=\frac{{\mathrm{KQ}}^2}{2a^2}\\ \therefore \sqrt{2}\frac{\mathrm{KqQ}}{a^2}=-\frac{{\mathrm{KQ}}^2}{2a^2}\\ \Rightarrow \frac{\mathrm{Q}}{q}=-2\sqrt{2}\end{array}$