A point charge $q=-2\mu \mathrm{C}$ is kept at the origin of a co-ordinate system. Another charge $Q=1\mu \mathrm{C}$ is kept at a point having co-ordinates $(0.6,0.8)\mathrm{m}$. Find force on $q$ due to $Q$.

$\vec{F}=k\frac{qQ}{|\vec{r}{|}^2}\hat{r}$. In this equation $|\vec{r}|=r$ is nothing but distance between the two charges. You must be careful in writing $\hat{r}$. It is a unit vector from source $(Q)$ towards the test charge $(q)$. Put $q$ and $Q$ with sign in the above equation. In Short (i) Coulomb's law gives force between two point charges. We can use it directly to get force between two small charged bodies kept at large separation. (ii) Magnitude of force between two charges is $F=\frac{1}{4\pi {\epsilon }_0{\epsilon }_r}\frac{|q_1{q}_2|}{r^2}$ where ${\epsilon }_r=1$ for vacuum and air. For all other $\mathrm{medium}{\epsilon }_r>1$ (iii) $k=\frac{1}{4\pi {\epsilon }_0}=9\times 10^9\frac{\mathrm{N}-{\mathrm{m}}^2}{{\mathrm{C}}^2}$ and ${\epsilon }_0=8.85\times 10^{-12}\frac{{\mathrm{C}}^2}{\mathrm{N}-{\mathrm{m}}^2}$ (iv) Force due to source charge $(q)$ on a test charge $(Q)$ can be written in vector form as $\vec{F}=\left(k\frac{qQ}{r^2}\right)\hat{r}$ where $r$ is distance between the two charges and $\hat{r}$ is a unit vector directed from the source charge to the test charge. While using this equation we must put $q$ and $Q$ with their respective signs. (v) Electrostatic force is far stronger than the gravitational force. (vi) 1 coulomb is a large charge.