Two charges $+4e$ and $+e$ are at a distance $x$ apart. At what distance must a charge $q$ be placed from charge $+e$ so that it is in equilibrium?

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:

$A$ ring of radius $R$ is charged with a charge $Q$. The electric field at a point on its axis at a distance $r$ from the circumference of the ring is:

Three charges $2q, -q, -q$ are located at the vertices of an equilateral triangle. At the centre of the triangle:

$A$ uniformly charged rod of length $4\,cm$ and linear charge density $\lambda = 30\,\mu C/m$ is placed as shown in the figure. Calculate the $x-$ component of the electric field at point $P$.

$A$ point charge of $50 \mu C$ is placed in the $XY$ plane at a location with radius vector $\vec{r}_0 = 2 \hat{i} + 3 \hat{j} \ m$. The electric field strength magnitude at a point with radius vector $\vec{r} = 8 \hat{i} - 5 \hat{j} \ m$ is (Given: $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \ N \ m^2 \ C^{-2}$). (in $kV \ m^{-1}$)