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?
Select ALL correct options:
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 $\frac{7 q}{4 \sqrt{3} \pi \epsilon_0 a}$
D
When $x=-3 q$, the potential at $O$ is $-\frac{3 q}{4 \sqrt{3} \pi \epsilon_0 a}$
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