There exists a uniform electric field $E=4\times {10}^5 \mathrm{V} {\mathrm{m}}^{-1}$ directed along negative $x$-axis such that electric potential at origin is zero. A charge of $-200\mu C$ is placed at origin, and a charge of $+200\mu C$ is placed at $(3 \mathrm{m}, 0).$ The electrostatic potential energy of the system is

Six point charges are placed at the vertices of a regular hexagon of side $a$ as shown. If $E$ represents electric field and $V$ represents electric potential at $\mathrm{O},$ then

Three charges are placed along $x$-axis at $x=-a,$ $x=0$ and $x=a$ as shown in the figure. The potential energy of the system is

A point charge $q$ is held at the centre of a circle of radius $r. B, C$ are two points on the circumference of the circle and $A$ is a point outside the circle. If $W_{AB}$ represents work done by electric field in taking a charge $q_0$ from $A$ to $B$ and $W_{\text{AC }}$ represents the workdone from $A$ to $C,$ then

The charge $\mathrm{q}$ is fired towards another charged particle $\mathrm{Q}$ which is fixed, with a speed $\mathrm{v}$. It approaches $\mathrm{Q}$ up to closest distance $\mathrm{r}$ and then returns. If $\mathrm{q}$ were given a speed $2\mathrm{v}$, the closest distance of approach would be