Two identical spheres have charges $+q$ and $-q$ and are placed at a certain distance. The force between them is $F$. If a third identical sphere with charge $+q$ is placed exactly between the two spheres, what is the magnitude and direction of the force experienced by it?

$A$ charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium if $q$ is equal to:

Three charges $q, Q$ and $+4q$ are placed in a straight line of length $d$ at positions $0, d/3$ and $2d/3$ respectively. In order to make the net force on $q$ be zero, the value of $Q$ should be

Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges $Q$ repel each other with a force $F$ when kept apart at a distance $r$. $A$ third spherical conductor 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

Two insulated charged copper spheres $A$ and $B$ have their centres separated by a distance of $50 \; cm$. The charge on each is $6.5 \times 10^{-7} \; C$. Suppose the spheres $A$ and $B$ have identical sizes. $A$ third sphere of the same size but uncharged is brought in contact with the first,then brought in contact with the second,and finally removed from both. What is the new force of repulsion between $A$ and $B$?

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: