Coulomb's Law : Force between Two Point-Charges

The mutual electrostatic force of attraction between two small spheres carrying charges $+0.4 \mathrm{\mu C}$ and $-0.8 \mathrm{\mu C}$ in air is $0.2 \mathrm{N}$. What is the separation between the two spheres?   

If the distance between two equal point-charges is halved and their individual charges are doubled, what would happen to the force between them?

Explain the statement ‘Relative permittivity of water is $81$’.   

Is there any lower limit of electric force between two charges $1 \mathrm{m}$ apart in vacuum?

A charge $\mathrm{q}$ is divided into two parts such that they repel each other with a maximum force when placed at a certain distance apart. How has the charge been divided?

How does the force between two point-charges change, if the dielectric constant of the medium in which they are kept, increases?

An attracting-force of $5\mathrm{N}$ is acting between two charges of $+2\mathrm{\mu C}$ and $-2\mathrm{\mu C}$ placed at some distance apart. If the charges are mutually touched and placed again at the same distance, what will be the new force between them?

The force of attraction between two point-charges at a distance $\mathrm{r}$ apart is $\mathrm{F}$. What should be the distance apart in the same medium so that the force becomes $\mathrm{F}/3$? What if force becomes $3\mathrm{F}$?

If the distance between two equal point-charges is doubled and their individual charges are also doubled, what would happen to the force between them?

$\mathrm{A}$,$\mathrm{B}$ and $\mathrm{C}$ are three charged bodies. If $\mathrm{A}$ and $\mathrm{B}$ repel each other and $\mathrm{A}$ attracts $\mathrm{C}$, what is the nature of the force between $\mathrm{B}$ and $\mathrm{C}$?

What is the dimensional formula for $\frac{1}{4\mathrm{\pi } {\mathrm{\epsilon }}_0}$?

Define 'dielectric constant' of a medium in terms of force between electric charges.

Write the relation between relative permittivity ${\mathrm{\epsilon }}_{\mathrm{r}}$ and the absolute permittivity $\mathrm{\epsilon }$ of a dielectric medium.

State the unit of electric permittivity in terms of $\mathrm{SI}$ units.

Is Coulomb's law true for atomic and nuclear distances?

Two conducting spheres $\mathrm{A}$ and $\mathrm{B}$ of the same size are situated at some distance apart. Each has a charge of $+q$ Coulomb and they repel each other with a force of ${10}^{-5} \mathrm{N}$. A third conducting uncharged sphere $\mathrm{C}$ of same size is first touched with $\mathrm{A}$ and then with $\mathrm{B}$ and then placed exactly between $\mathrm{A}$ and $\mathrm{B}$. Calculate the resultant force on $\mathrm{C}$.

Two similarly and equally charged identical metal spheres $\mathrm{A}$ and $\mathrm{B}$ repel each other with a force of $2.0\times {10}^{-5} \mathrm{N}$. A third identical, uncharged sphere $\mathrm{C}$ is touched with $\mathrm{A}$ and then placed at the mid-point between $\mathrm{A}$ and $\mathrm{B}$. What is net electric force on $\mathrm{C}$?

Two identical metallic balls $\mathrm{A}$ and $\mathrm{B}$ have charges $+40$ and $-10 \mathrm{\mu C}$ respectively. The distance between them is $2.0 \mathrm{m}$. What is the magnitude and type of force acting between them? They are touched to each other and again separated by a distance of $2.0 \mathrm{m}$ from each other. Calculate the new force between them. What will be the force if one ball is connected to earth?

Two point-charges of$+2 \mathrm{\mu C}$  and $+6\mathrm{\mu C}$, repel each other with a force of $12 \mathrm{N}$. If each is given an additional charge of$-4 \mathrm{\mu C}$ , then what will be the new force?

The distance between two negatively-charged dust particles is $1 \mathrm{mm}$ and they repel each other with a force of $4.0\times {10}^{-5} \mathrm{N}$. If the charge on one particle is  $4$ times that of the other, then find out the number of electrons charging them separately. The charge on electron is $\left(5/3\right)\times {10}^{-19 }\mathrm{C}$.