When air is replaced by a dielectric medium of constant $k$,the maximum force of attraction between two charges separated by a distance $r$:

Two charges each of charge $+10 \mu C$ are kept on $Y$-axis at $y=-a$ and $y=+a$, respectively. Another point charge $-20 \mu C$ is placed at the origin and given a small displacement $x$ $(x \ll a)$ along $X$-axis. The force acting on the point charge is ($x$ and $a$ are in metres, $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \text{ N m}^2 \text{ C}^{-2}$)

Two identical spheres are charged with equal charges and the force between them is $F$. If $50\%$ of the charge from one sphere is transferred to the other sphere,then the new force will be ........ $F$.

Two small spheres each having the charge $+Q$ are suspended by insulating threads of length $L$ from a hook. This arrangement is taken into space where there is no gravitational effect. Then the angle between the two suspensions and the tension in each will be:

Two similar tiny balls of mass $m$,each carrying charge $q$,are hung from silk threads of length $l$ as shown in the figure. These are separated by a distance $x$ and the angle $2\theta$ is small. Then,for equilibrium:

For the system shown in the figure,find $Q$ such that the resultant force on $q$ is zero.