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 of the nearest hexagon side passes through the center \( O \) of the hexagon and is bisected by the side.
\( x \)
Which of the following statements 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
\[
\frac{q}{6 \pi \epsilon_{0} a^{2}}
\]
(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 \( -\frac{3 q}{4 \sqrt{3} \pi \in_{0} a} \)
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