Two balls with equal charges are in a vessel with ice at $-10^{\circ} C$ at a distance of $25 \ cm$ from each other. On forming water at $0^{\circ} C$,the balls are brought nearer to $5 \ cm$ for the interaction between them to be same. If the dielectric constant of water at $0^{\circ} C$ is $80$,the dielectric constant of ice at $-10^{\circ} C$ is:

Two balls of same mass and carrying equal charge are hung from a fixed support of length $l$. At electrostatic equilibrium,assuming that the angle made by each thread is small,the separation $x$ between the balls is proportional to

The ratio of gravitational force and electrostatic repulsive force between two electrons is approximately (gravitational constant $= 6.7 \times 10^{-11} \, Nm^2/kg^2$,mass of an electron $= 9.1 \times 10^{-31} \, kg$,charge on an electron $= 1.6 \times 10^{-19} \, C$).

Two spheres having the same radius and mass are suspended by two strings of equal length from the same point in such a way that their surfaces touch each other. On depositing a charge of $2 \times 10^{-6} \ C$ on them,they repel each other such that in equilibrium,the angle between their strings becomes $60^{\circ}$. If the distance from the point of suspension to the center of the sphere is $10 \ cm$,find the mass of each sphere. $(k = 9 \times 10^9 \ SI, g = 10 \ ms^{-2})$. (in $kg$)

In one model of the electron,the electron of mass $m_e$ is thought to be a uniformly charged shell of radius $R$ and total charge $e$,whose electrostatic energy $E$ is equivalent to its mass $m_e$ via Einstein's mass-energy relation $E = m_e c^2$. In this model,$R$ is approximately ($m_e = 9.1 \times 10^{-31} \, kg$,$c = 3 \times 10^8 \, ms^{-1}$,$1 / 4 \pi \varepsilon_0 = 9 \times 10^9 \, Nm^2C^{-2}$,magnitude of the electron charge $e = 1.6 \times 10^{-19} \, C$).

$A$ point charge $q_1$ exerts an electric force on a second point charge $q_2$. If a third charge $q_3$ is brought near,the electric force of $q_1$ exerted on $q_2$: