Four point charges -Q , -q , 2q and 3Q are placed at corners of the...

Let the side length of the square be $a$. The distance of the centre from each corner is $r = \dfrac{a}{\sqrt{2}}$.

The electric potential at the centre of the square is the algebraic sum of the potentials due to all four charges.

$V = \dfrac{1}{4\pi\epsilon_0} \left( \dfrac{-Q}{r} + \dfrac{-q}{r} + \dfrac{2q}{r} + \dfrac{3Q}{r} \right)<br><br>Given that$V = 0$, we have:<br><br>$-Q - q + 2q + 3Q = 0$<br><br>2Q + q = 0$

$Q = -\dfrac{q}{2}<br><br>Answer:$ Q = -q/2