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:

Two identical charged spheres are suspended by strings of equal length. The strings make an angle of $30^{\circ}$ with each other. When they are immersed in a liquid of density $0.8 \, g \cdot cm^{-3}$,the angle remains the same. If the density of the material of the spheres is $1.6 \, g \cdot cm^{-3}$,find the dielectric constant of the liquid.

Three point charges $+q$,$+2q$,and $+4q$ are placed along a straight line such that the charge $+2q$ is equidistant from the other two charges. The ratio of the net electrostatic force on charges $+q$ and $+4q$ is

The force between two point charges $A$ and $B$ is $F$. If $75\%$ of the charge on $A$ is transferred to $B$,then the new force between $A$ and $B$ is:

The force between two point charges $A$ and $B$ is $F$. If $75\%$ of the charge of $A$ is transferred to $B$,then the new force between $A$ and $B$ is:

Two free positive charges $4q$ and $q$ are at a distance $l$ apart. What charge $Q$ is needed to achieve equilibrium for the entire system and where should it be placed from charge $q$?