Two small conducting spheres of equal radius have charges of $10\ \mu C$ and $-20\ \mu C$ respectively and are placed at a distance $R$ from each other,experiencing a force $F_1$. If they are brought in contact and then separated to the same distance,the new force between them is $F_2$. Find the ratio $F_1 : F_2$.

$A$ point charge $q$ moves from point $P$ to $S$ along the path $PQRS$ in a uniform electric field $E$ directed parallel to the positive $X$-axis. The coordinates of points $P, Q, R,$ and $S$ are $(a, b, 0), (2a, 0, 0), (a, -b, 0),$ and $(0, 0, 0)$ respectively. Calculate the work done by the electric field in this process.

The dimension of $\frac{1}{2} \varepsilon_0 E^2$,where $\varepsilon_0$ is the permittivity of free space and $E$ is the electric field,is:

Four charges $2C, -3C, -4C$ and $5C$ are placed at the corners of a square. Which of the following statements is true for the point of intersection of the diagonals?

Two point charges $Q$ and $-Q/4$ are separated by a distance $x$. Then:

Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges repel each other with a force $F$ when kept apart at some distance. $A$ third spherical conductor $A$ having the same radius as that of $B$ but uncharged,is brought in contact with $B$,then brought in contact with $C$,and finally removed away from both. The new force of repulsion between $B$ and $C$ is-