Two charges of magnitude $5\, nC$ and $-2\, nC$ are placed at points $(2\, cm, 0, 0)$ and $(x\, cm, 0, 0)$ respectively in a region of space where there is no other external field. If the electrostatic potential energy of the system is $-0.5\,\mu J$,find the value of $x$ in $cm$.

Two point charges $+8 \mu C$ and $+12 \mu C$ repel each other with a force of $48 \ N$. When an additional charge of $-10 \mu C$ is given to each of these charges (the distance between the charges is unaltered),then the new force is:

$A$ point charge $q_1 = 4 q_0$ is placed at the origin. Another point charge $q_2 = -q_0$ is placed at $x = 12 \, cm$. The charge of a proton is $q_0$. $A$ proton is placed on the $x$-axis such that the net electrostatic force on it is zero. In this situation,the position of the proton from the origin is $.......... \, cm$.

The force between two point charges $q_1$ and $q_2$ placed in a vacuum at a distance $r \ cm$ apart is $F$. The force between them when placed in a medium having a dielectric constant $K=5$ at a distance $r/5 \ cm$ apart will be:

Two identical spheres,each of mass $1 \, g$,carry an identical charge of $10^{-9} \, C$. They are suspended by strings of equal length. If the distance between the centers of the spheres is $0.3 \, cm$,what is the angle made by the string with the vertical?

Two point charges $+2 \ C$ and $+6 \ C$ separated by a distance '$r$' repel each other with a force of $18 \ N$. If a negative charge of $-4 \ C$ is added to each of these charges,then the force experienced by them is: