When air is replaced by a dielectric medium of constant $k$, the maximum force of attraction between two charges separated by a distance

Two small spherical balls each carrying a charge $Q = 10\,\mu C$ ($10$ micro-coulomb) are suspended by two insulating threads of equal lengths $1\,m$ each, from a point fixed in the ceiling. It is found that in equilibrium threads are separated by an angle ${60^o}$ between them, as shown in the figure. What is the tension in the threads......$N$ (Given: $\frac{1}{{(4\pi {\varepsilon _0})}} = 9 \times {10^9}\,Nm/{C^2}$)

The ratio of coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is $2.4 \times 10^{39}$. The ratio of the proportionality constant, $K=\frac{1}{4 \pi \varepsilon_0}$ to the Gravitational constant $G$ is nearly (Given that the charge of the proton and electron each $=1.6 \times 10^{-19}\; C$, the mass of the electron $=9.11 \times 10^{-31}\; kg$, the mass of the proton $=1.67 \times 10^{-27}\,kg$ ):

Two identically charged pith balls are suspended from the some point by two massless identical threads density of each ball is $\rho $. If system is immersed in a medium of density $\sigma $, balls remain undeflected, then the dielectric constant of medium is

Two particle of equal mass $m$ and charge $q$ are placed at a distance of $16\, cm$. They do not experience any force. The value of $\frac{q}{m}$ is

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