Six charges are placed around a regular hexagon of side length a as shown in the figure. Five of them have charge $q$, and the remaining one has charge $x$. The perpendicular from each charge to the nearest hexagon side passes through the center $O$ of the hexagon and is bisected by the side.
Which of the following statement($s$) is(are) correct in SI units?
$(A)$ When $x=q$, the magnitude of the electric field at $O$ is zero.
$(B)$ When $x=-q$, the magnitude of the electric field at $O$ is $\frac{q}{6 \pi \in_0 a^2}$.
$(C)$ When $x=2 q$, the potential at $O$ is $\frac{7 q}{4 \sqrt{3} \pi \in_0 a}$.
$(D)$ When $x=-3 q$, the potential at $O$ is $\frac{3 q}{4 \sqrt{3} \pi \in_0 a}$.
IIT 2022, Advanced
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