Two identical spheres are charged with equal charges and the force between them is $F$. If $50\%$ of the charge from one sphere is transferred to the other sphere,then the new force will be ........ $F$.

$A$ charge $Q$ is divided into two parts $q$ and $Q - q$. If the Coulomb repulsion between them when they are separated by a distance $r$ is to be maximum,the ratio of $\frac{Q}{q}$ should be:

The value of the electric permittivity of free space $(\varepsilon_0)$ is ........

Two equal point charges exert a force $F$ on each other when they are placed distance $d$ apart in air. When they are placed distance $D$ apart in a medium of dielectric constant $K$, they exert the same force. The distance $D$ is equal to

Two identical balls having like charges $Q_1$ and $Q_2$ are placed at a distance $r$ apart and repel each other with a force $F$. They are brought in contact and then moved apart to a distance equal to half their initial separation. The force of repulsion between them increases $4.5$ times in comparison with the initial value. The ratio of the initial charges of the balls, $\frac{Q_1}{Q_2}$, is:

$A$ particle of mass $1 \, mg$ and charge $q$ is placed at the midpoint of two stationary particles,each carrying the same charge $q$,kept at a distance of $2 \, m$. If the free charged particle is displaced from its equilibrium position by a small distance $x$ $(x \ll 1 \, m)$,it executes $SHM$. Its angular frequency of oscillation will be $.... \times 10^{8} \, rad/s$ if $q^{2} = 10 \, C^{2}$.