Question

How much work will be done in placing the charges $+q,+2q,$ and $+4q$ at the corners of the equilateral triangle of side a metre?

Answer 1

$\begin{array}{cc}W& =W_{12}+W_{13}+W_{23}\\ W& =\frac{k\left(q\right)\left(2q\right)}{a}+\frac{k\left(q\right)\left(4q\right)}{a}+\frac{k\left(4q\right)\left(2q\right)}{a}\\ W& =\frac{k{q}^2}{a}[2+4+8]\text{where}k=\frac{1}{4\pi {\epsilon }_0}\\ W& =\frac{1}{4\pi {\epsilon }_0}\frac{14q^2}{a}\text{Joule}\end{array}$