Write the value of the Coulombian constant $k$ in $SI$ units.

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 charges $+10 \mu C$ and $-10 \mu C$ are separated by $10 \text{ cm}$. The magnitude of the force acting on another charge $5 \mu C$ placed at the midpoint of the line joining the two charges will be: [Use $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ N m}^2 \text{ C}^{-2}$] (in $\text{ N}$)

Assume that you have $10^{23}$ carbon atoms. All the nuclei are placed at the North Pole of the Earth and all the electrons are placed at the South Pole of the Earth. (Radius of Earth = $6400 \ km$). The force between the charges is approximately:

$A$ certain charge $2Q$ is divided at first into two parts $q_{1}$ and $q_{2}$. Later,the charges are placed at a certain distance. If the force of interaction between the two charges is maximum,then find the value of $\frac{Q}{q_{1}}$.

$A$ charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium if $q$ is equal to: