Question

Two equal charges $q$ are placed at a distance of $2a$ and a third charge $-2q$ is placed at the midpoint. The potential energy of the system is

• A. $\frac{8q^2}{7\pi {\epsilon }_{0}a}$
• B. $\frac{7q^2}{8\pi {\epsilon }_{0}a}$
• C. $\frac{-7q^2}{8\pi {\epsilon }_{0}a}$
• D. None

Answer 1

Answer: (C)

$U=U_1+U_2+U_3$
$U=\frac{K(q)(-2q)}{a}+\frac{K(-2q)(q)}{a}+\frac{K(q)(q)}{2a}$
$U=\frac{-4K{q}^2}{a}+\frac{K{q}^2}{2a}$
$U=\frac{K{q}^2}{a}\left[-4+\frac{1}{2}\right]$
$U=\frac{K{q}^2}{a}\left(\frac{-7}{2}\right)$
$\Rightarrow U=\frac{-7K{q}^2}{2a}$
$U=\frac{-7q^2}{8\pi {\epsilon }_0}a$