$A$ thin half ring of radius $35 \text{ cm}$ is uniformly charged with a total charge of $Q$ coulomb. If the magnitude of the electric field at the centre of the half ring is $100 \text{ V/m}$, then the value of $Q$ is . . . . . . $\text{nC}$. ($\epsilon_0 = 8.85 \times 10^{-12} \text{ C}^2/\text{Nm}^2$ and $\pi = 3.14$)

$A$ 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 $\mu C$)

Four charges $+q, +2q, +q$ and $-2q$ are placed at the corners $A, B, C$ and $D$ of a square respectively. The force on a unit positive charge kept at the centre $O$ is

The point charges $Q$ and $-2Q$ are placed at a distance $r$ apart. If the electric field at the location of $Q$ (point $A$) due to $-2Q$ is $\vec E$,then the electric field at the location of $-2Q$ (point $B$) due to $Q$ will be:

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

The figure shows a rod $AB$,which is bent in a $120^{\circ}$ circular arc of radius $R$. $A$ charge $(-Q)$ is uniformly distributed over the rod $AB$. What is the electric field $\overrightarrow{E}$ at the centre of curvature $O$?