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

$\mathrm{ABC}$ is a right angled triangle situated in a uniform electric field $\overrightarrow{\mathrm{E}}$ which is in the plane of the triangle. The points $\mathrm{A}$ and $\mathrm{B}$ are at the same potential of $15 \mathrm{V}$ while the point $\mathrm{C}$ is at a potential of $20 \mathrm{V}.$ $\mathrm{AB}=3 \mathrm{cm}$ and $\mathrm{BC}=4 \mathrm{cm}.$ The magnitude of electric field is (in S.I. Units)

The work which is required to be done to make an arrangement of four particles each having a charge $+q$ such that the particles lie at the four corners of a square of side $a$ is