Two electric charges are arranged as shown in the figure. Where should a third charge be placed so that it remains in equilibrium?

Three charges,each $+Q$,are placed at the vertices of an equilateral triangle of side $a$. What is the net electrostatic force on any one charge? $\left( k = \frac{1}{4\pi \varepsilon _0} \right)$

In a medium,the force of attraction between two point charges,distance $d$ apart,is $F$. What distance apart should these point charges be kept in the same medium,so that the force between them becomes $16F$?

Two equally charged,identical metal spheres $A$ and $B$ repel each other with a force '$F$'. The spheres are kept fixed with a distance '$r$' between them. $A$ third identical,but uncharged sphere $C$ is brought in contact with $A$ and then placed at the mid-point of the line joining $A$ and $B$. The magnitude of the net electric force on $C$ is

$A$ proton of mass $m$ and charge $e$ is projected from a very large distance towards an $\alpha$-particle with velocity $v$. Initially,the $\alpha$-particle is at rest,but it is free to move. If gravity is neglected,then the minimum separation along the straight line of their motion will be:

$A$ charge of $1 \mu C$ is divided into two parts such that their charges are in the ratio of $2: 3$. These two charges are kept at a distance of $1 \ m$ apart in vacuum. Then,the electric force between them (in $N$) is