Three charges $Q,+q$ and $+q$ are placed at the vertices of right-angle triangle as shown. The net…
Three charges $Q,+q$ and $+q$ are placed at the vertices of right-angle triangle as shown. The net electrostatic energy of the configuration is zero. The value of $Q$ is
$-2 q$
$-\frac{q}{1+\sqrt{2}}$
$+q$
$\frac{-\sqrt{2} q}{\sqrt{2}+1}$
Solution
The potential energy of the system can be written pair-wise as follows:
$\begin{aligned}
& U=\frac{k Q q}{l}+\frac{k q q}{l}+\frac{k Q q}{\sqrt{2} l}=0 \\
& Q=-\frac{\sqrt{2} q}{\sqrt{2}+1}
\end{aligned}$
