Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $37^{\circ}$ with each other. When suspended in a liquid of density $0.7 \text{ g/cm}^3$,the angle remains the same. If the density of the material of the sphere is $1.4 \text{ g/cm}^3$,the dielectric constant of the liquid is . . . . . . $\left(\tan 37^{\circ} = \frac{3}{4}\right)$.

Electric charges of $1\,\mu C$, $-1\,\mu C$, and $2\,\mu C$ are placed in air at the corners $A$, $B$, and $C$ respectively of an equilateral triangle $ABC$ having a side length of $10\,cm$. The resultant force on the charge at $C$ is......$N$

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

If two charges $q_1$ and $q_2$ are separated by a distance '$d$' and placed in a medium of dielectric constant $K$,what will be the equivalent distance between the charges in air for the same electrostatic force?

Charges $Q$ are placed at the ends of a diagonal of a square and charges $q$ are placed at the other two corners. The condition for the net electric force on $Q$ to be zero is

$A$ particle of mass $M$ and charge $q$ is placed at the midpoint between two fixed charges each of magnitude $Q$, separated by a distance $2d$. The system is collinear as shown in the figure. If the particle is displaced by a small distance $x$ $(x \ll d)$ along the line joining the two charges and released, it will oscillate about the mean position with a time period $T$. ($\varepsilon_{0}$ is the permittivity of free space)