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 $\frac{q}{6 \pi \epsilon_0 a^2}$.

$(C)$ 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 $\frac{3 q}{4 \sqrt{3} \pi \epsilon_0 a}$.

Four charges $2C, -3C, -4C$ and $5C$ respectively are placed at all the corners of a square. Which of the following statements is true for the point of intersection of the diagonals ?

An electric charge $10^{-6} \mu \mathrm{C}$ is placed at origin $(0,0)$ $\mathrm{m}$ of $\mathrm{X}-\mathrm{Y}$ co-ordinate system. Two points $\mathrm{P}$ and $\mathrm{Q}$ are situated at $(\sqrt{3}, \sqrt{3}) \mathrm{m}$ and $(\sqrt{6}, 0) \mathrm{m}$ respectively. The potential difference between the points $P$ and $Q$ will be :

The electric potential at the surface of an atomic nucleus $(Z = 50)$ of radius $9.0×{10^{ - 13}}\, cm$ is

A table tennis ball which has been covered with conducting paint is suspended by a silk thread so that it hang between two plates, out of which one is earthed and other is connected to a high voltage generator. This ball

Charges are placed on the vertices of a square as shown Let $\vec E$ be the electric field and $V$ the potential at the centre. If the charges on $A$ and $B$ are interchanged with those on $D$ and $C$ respectively, then