Four point charges $-2Q, +q, -2q$ and $+Q$ are placed at four corners of a square A, B, C and D, respectively, as shown in the figure and $OA= OB = a/\sqrt{2}$. If the potential at the center of a square is zero, what is the relation between Q and q?

$Q=-q$

The correct answer is Option (2) → $Q=-q$

Charges: $-2Q$ (A), $+q$ (B), $-2q$ (C), $+Q$ (D)

Distance from centre to each corner: $r=\frac{a}{\sqrt{2}}$

Potential at centre: $V=\frac{k}{r}\big(-2Q+q-2q+Q\big)=\frac{k}{r}(-Q-q)$

Given $V=0\Rightarrow -Q-q=0\Rightarrow Q=-q$

Answer: $Q = -q$