Question

Three point charges q are placed at three vertices of an equilateral triangle of side a. The magnitude of electric force on any charge due to the other two is equal to $\frac{\sqrt{x}}{4\pi {\epsilon }_0}{\left(\frac{q}{a}\right)}^2$ where $x$ is:

Answer 1

Force due to charge on corner B= $\frac{1}{4\pi ϵ}\frac{q^2}{a^2}\overrightarrow{BA}$
Force due to charge on corner C= $\frac{1}{4\pi ϵ}\frac{q^2}{a^2}\overrightarrow{CA}$
Total force= $2\frac{1}{4\pi ϵ}\frac{q^2}{a^2}cos\left({30}^{\circ }\right)\overrightarrow{OA}=2\frac{1}{4\pi ϵ}\frac{q^2}{a^2}\frac{\sqrt{3}}{2}$