The given diagram shows two semi-infinite lines of charge having equal (in magnitude) linear charge density but with opposite signs. The electric field at any point on the $x$-axis for $(x > 0)$ is along the unit vector:

$A$ spherical conductor of diameter $6 \ mm$ is kept in a uniform electric field of intensity $2 \times 10^7 \ N/C$. The maximum charge on the conductor is $\left[\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ SI units}\right]$. (in $\mu C$)

$A$ semi-infinite non-conducting rod lies along the $+x$-axis with its left end at the origin. The rod has a uniform linear charge density $\lambda$. The magnitude of the electric field $|\vec{E}|$ at a point on the $y$-axis at a distance $L$ from the origin will be:

The number of electrons to be put on a spherical conductor of radius $0.1\,m$ to produce an electric field of $0.036\,N/C$ just above its surface is:

The figures below show regular hexagons with charges at the vertices. In which of the following cases is the electric field at the centre not zero?

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