$A$ point charge of $10\,\mu C$ is placed at the origin. At what location on the $X$-axis should a point charge of $40\,\mu C$ be placed so that the net electric field is zero at $x = 2\,cm$ on the $X$-axis?

$A$ metallic ring is uniformly charged as shown in the figure. $AC$ and $BD$ are two mutually perpendicular diameters. The magnitude of the electric field at $O$ due to arc $AB$ is $E$. What would be the magnitude of the electric field at $O$ due to arc $ABC$?

If the net electric field at point $P$ along the $Y$-axis is zero,then the ratio of $\left|\frac{q_2}{q_3}\right|$ is $\frac{8}{5 \sqrt{x}}$,where $x = . . . . . .$

Charges $q$,$2q$,$3q$ and $4q$ are placed at the corners $A$,$B$,$C$ and $D$ of a square as shown in the figure. The direction of the electric field at the centre $O$ of the square is along:

In the figure shown,the distance from point $A$ to the point where the electric field intensity is zero is .......... $cm$.

$A$ circular wire loop of radius $1 \, cm$ carries a total charge $1 \times 10^{-6} \, C$ distributed uniformly over its length. If $0.01 \%$ of its length (circumference) is cut off, then the electric field at the centre of the loop due to the remaining wire is
$(\text{Take} \, \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \, \text{SI unit})$