Two equal point charges each of charge 'q' are placed at a distance of 2a from each other and a third charge -2q in placed at the mid point between them. The potential energy of the system is:

$\frac{-7 q^2}{8 \pi \varepsilon_0 a}$

The correct answer is Option (3) → $\frac{-7 q^2}{8 \pi \varepsilon_0 a}$

The total potential energy (U) is -

$U=U_{12}+U_{23}+U_{13}$

$=\frac{q^2}{8πε_0a}+\left(\frac{-2q^2}{4πε_0a}+\frac{-2q^2}{4πε_0a}\right)$

$=\frac{1}{4πε_0}\left(\frac{q^2}{2a}-\frac{4q^2}{a}\right)$

$=\frac{1}{4πε_0}\left(-\frac{7q^2}{2a}\right)$

$=-\frac{7q^2}{8πε_0a}$