Two point charges $A$ and $B$ of magnitude $+8 \times 10^{-6}\,C$ and $-8 \times 10^{-6}\,C$ respectively are placed at a distance $d$ apart. The electric field at the middle point $O$ between the charges is $6.4 \times 10^{4}\,NC^{-1}$. The distance $d$ between the point charges $A$ and $B$ is ............ $m$. (in $.0$)

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 $x=2q$,the potential at $O$ is $\frac{7q}{4 \sqrt{3} \pi \epsilon_0 a}$.
$(D)$ When $x=-3q$,the potential at $O$ is $\frac{3q}{4 \sqrt{3} \pi \epsilon_0 a}$.

Eleven equal point charges,each of magnitude $+Q$,are placed at all the hour positions of a circular clock of radius $r$,except at the $10$ o'clock position. What is the electric field strength at the centre of the clock?

Two point charges $Q$ and $-3Q$ are placed at a distance $x$ apart. If the electric field at the location of $Q$ is $E$,then the electric field at the location of $-3Q$ is:

For the given figure,the direction of the electric field at point $A$ will be:

$A$ thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net electric field $\vec{E}$ at the centre $O$ is