Three charges $+Q, q, +Q$ are placed respectively at distances $0, \frac{d}{2},$ and $d$ from the origin on the $x$-axis. If the net force experienced by the charge $+Q$ placed at $x = 0$ is zero,then the value of $q$ is:

Two point charges placed at a certain distance $r$ in air exert a force $F$ on each other. Then the distance $r'$ at which these charges will exert the same force in a medium of dielectric constant $k$ is given by

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 $B$?

$A$ charge $Q$ is divided into two charges $q$ and $Q-q$. The value of $q$ such that the force between them is maximum,is

Four charges are arranged at the corners of a square $ABCD$,as shown in the adjoining figure. The force on the charge kept at the centre $O$ is

Two charges $+q$ and $-3q$ are placed on the $x$-axis separated by a distance $d$. ($-3q$ is to the right of $q$). Where should a third charge $2q$ be placed such that it will not experience any net force?