$A$ 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 $q^{2} = 10 \, C^{2}$.

Two point charges $+q_1$ and $+q_2$ repel each other with a force of $100 \ N$. $q_1$ is increased by $10 \%$ and $q_2$ is decreased by $10 \%$. If they are kept at their original positions, the change in the force of repulsion between them is:

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

Why is Coulomb's law associated with Newton's $3^{rd}$ law?

$A$ certain charge $Q$ is divided into two parts $q$ and $(Q-q)$. How should the charges $Q$ and $q$ be divided so that $q$ and $(Q-q)$ placed at a certain distance apart experience maximum electrostatic repulsion?

As shown in the figure,a configuration of two equal point charges $(q_0 = +2 \mu C)$ is placed on an inclined plane. The mass of each point charge is $20 \, g$. Assume that there is no friction between the charge and the plane. For the system of two point charges to be in equilibrium (at rest),the height $h = x \times 10^{-3} \, m$. The value of $x$ is $..........$. (Take $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, Nm^2 C^{-2}, g = 10 \, ms^{-2}$)