Two pith balls carrying equal charges are suspended from a common point by strings of equal length. The equilibrium separation between them is $r$. Now,the strings are rigidly clamped at half the height. The equilibrium separation between the balls now becomes:

In the given figure,if $O$ is the midpoint of $AB$,calculate the net force on charge $Q$.

What are the units of $K = 1/(4\pi \varepsilon_0)$?

$A$ particle of mass $M$ and charge $q$ is placed at the midpoint between two fixed charges each of magnitude $Q$,separated by a distance $2d$. The system is collinear as shown in the figure. If the particle is displaced by a small distance $x$ $(x \ll d)$ along the line joining the two charges and released,it will oscillate about the mean position with a time period $T$. ($\varepsilon_{0}$ is the permittivity of free space)

If $\varepsilon_0$ and $\varepsilon$ represent the permittivity of free space and absolute permittivity of a medium,then the relative permittivity of the medium is:

Two equally charged metal spheres $A$ and $B$ repel each other with a force of $4 \times 10^{-5} \ N$. Another identical uncharged sphere $C$ is touched to $A$ and then placed at the midpoint of the line joining the spheres $A$ and $B$. The net electric force on the sphere $C$ is