Question

Four charges +q,+q,+q and +q are placed at the corners A,B,C and D of a square. What is the resultant force on the charge at D?

Answer 1

$$\begin{gathered} TheresultantforceatthecornerDwhenfourcharges+qeach \\ areplacedatcorneraA,B,C,andDodasquareofsideaisgivenby; \\ F=\frac{1}{4\pi {\epsilon }_0}\times \frac{q^2}{2a^2}+\frac{1}{4\pi {\epsilon }_0}\times \frac{\sqrt{2}{q}^2}{a^2} \\ F=\frac{1}{4\pi {\epsilon }_0}\times \frac{q^2}{a^2}\left(\frac{1}{2}+\sqrt{2}\right)=\frac{1}{4\pi {\epsilon }_0}\times \frac{q^2}{2a^2}\left(1+2\sqrt{2}\right)=\frac{1}{4\pi {\epsilon }_0}\times \frac{3.828q^2}{2a^2} \\ orF=\frac{1.914}{4\pi {\epsilon }_0}\times \frac{q^2}{a^2} \end{gathered}$$