Two charges $e$ and $3e$ are placed at a distance $r$ from each other. The distance of the point where the electric field intensity will be zero is .........

The three charges $q/2, q$ and $q/2$ are placed at the corners $A, B$ and $C$ of a square of side '$a$' as shown in the figure. The magnitude of the electric field $(E)$ at the corner $D$ of the square is:

$A$ 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

$A$ 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 $kV \ m^{-1}$)

$A$ thin,positively charged metal ring of radius $R$ is fixed in the $X-Y$ plane with its center at the origin $O$. $A$ negatively charged particle $P$ is released from rest at the point $(0, 0, Z_0)$,where $Z_0 > 0$. Describe the motion of the particle.

Two uniform spherical charge regions $S_1$ and $S_2$ having positive and negative charges overlap each other as shown in the figure. Points $O_1$ and $O_2$ are their centres and points $A, B, C, D$ and $E$ are on the line joining centres $O_1$ and $O_2$. What happens to the electric field from $C$ to $D$?