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

When two identical point charges are placed at a distance of $5 \, cm$, they experience a repulsive force of $0.144 \, N$. The value of each charge in microcoulombs $(\mu C)$ is:

Two point charges of $+2 \, \mu \text{C}$ and $+6 \, \mu \text{C}$ repel each other with a force of $12 \, \text{N}$. If a charge of $-4 \, \mu \text{C}$ is added to each,the force will be:

Four point charges $q_{A}=2\; \mu C, q_{B}=-5\; \mu C, q_{C}=2\; \mu C,$ and $q_{D}=-5\; \mu C$ are located at the corners of a square $ABCD$ of side $10\; cm$. What is the force on a charge of $1\; \mu C$ placed at the centre of the square (in $; N$)?

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 $e = 1.6 \times 10^{-19} \, C$).

The unit of permittivity of free space ${\varepsilon _0}$ is