Two charged spheres are suspended by strings of equal length. The strings make an angle of $30^{\circ}$ with each other. When suspended in a liquid of density $0.8 \ g/cm^3$,the angle remains the same. The dielectric constant of the liquid is ........ (The density of the material of the sphere is $1.6 \ g/cm^3$.)

The magnitude of the electric force on a $2\, \mu C$ charge placed at the centre $O$ of two equilateral triangles,each of side $10\, cm$,as shown in the figure,is $P$. If the charges at $A, B, C, D, E,$ and $F$ are $2\, \mu C, 2\, \mu C, 2\, \mu C, -2\, \mu C, -2\, \mu C,$ and $-2\, \mu C$ respectively,then $P$ is: ..... $N$

Two point charges $+q_{1}$ and $+q_{2}$ are placed a finite distance '$d$' apart. It is desired to put a third charge $q_{3}$ in between these two charges so that $q_{3}$ is in equilibrium. This is

Coulomb's law for electrostatic force between two point charges and Newton's law for gravitational force between two stationary point masses,both have inverse-square dependence on the distance between the charges and masses respectively.
$(a)$ Compare the strength of these forces by determining the ratio of their magnitudes $(i)$ for an electron and a proton and $(ii)$ for two protons.
$(b)$ Estimate the accelerations of electron and proton due to the electrical force of their mutual attraction when they are $1 \mathring A \left( = 10^{-10} \, m \right)$ apart? $\left( m_{p} = 1.67 \times 10^{-27} \, kg, m_{e} = 9.11 \times 10^{-31} \, kg \right)$

There are two charges $+1 \ \mu C$ and $+5 \ \mu C$. The ratio of the forces acting on them will be

The electrostatic force on a small sphere of charge $0.4 \; \mu C$ due to another small sphere of charge $-0.8 \; \mu C$ in air is $0.2 \; N$.
$(a)$ What is the distance between the two spheres?
$(b)$ What is the force on the second sphere due to the first?