Four charges equal to $-Q$ are placed at the four corners of a square of side length $a$,and a charge $q$ is at its centre. If the system is in equilibrium,the value of $q$ is:

$A$ force $F$ acts between sodium and chlorine ions of salt (sodium chloride) when placed $1 \ cm$ apart in air. The permittivity of air is $\varepsilon_0$ and the dielectric constant of water is $K$. When a piece of salt is placed in water,the electrical force acting between sodium and chlorine ions $1 \ cm$ apart is:

Three identical charged balls,each of charge $2 \, C$,are suspended from a common point $P$ by silk threads of $2 \, m$ each (as shown in the figure). They form an equilateral triangle of side $1 \, m$. The ratio of the net electrostatic force on one charged ball to the force between any two charged balls is ...........

Two point charges $A$ and $B$ with magnitudes $+4q$ and $-4q$ are placed along a line separated by a distance $r$. The force acting between them is $F$. If $25\%$ of the charge from point $A$ is transferred to point $B$,the force between the charges now becomes:

Two small spheres of masses $M_{1}$ and $M_{2}$ are suspended by weightless insulating threads of lengths $L_{1}$ and $L_{2}$. The spheres carry charges $Q_{1}$ and $Q_{2}$ respectively. The spheres are suspended such that they are in level with one another and the threads are inclined to the vertical at angles of $\theta_{1}$ and $\theta_{2}$ as shown. Which one of the following conditions is essential,if $\theta_{1}=\theta_{2}$?

Positive point charges are placed at the vertices of a star shape as shown in the figure. The direction of the electrostatic force on a negative point charge at the centre $O$ of the star is