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Electrostatic

# Electric force between charged particles

According to Coulomb's law, the magnitude of attractive or repulsive electric force between two charged particles $q_1$ and $q_2$ is proportional to the product of the magnitude of charges and inversely proportional to the distance squared $r^2$ from each other and is founded by the following formula $F=k\frac{\left|q_1q_2\right|}{r^2}$
Or in vector form as $\vec{F}=k\frac{\left|q_1q_2\right|}{r^2}\hat{r}$

Where $\hat{r}$ is the unit vector along the line joining the particles to one another.

In SI units, $F\to \mathrm{N}$ , $r\to \mathrm{m}$, $q\to \mathrm{C}$ and $k=9\times {10}^9\ \mathrm{N.}{\mathrm{m}}^{\mathrm{2}}\mathrm{/}{\mathrm{C}}^{\mathrm{2}}$

Note 1: the electric forces that two charged particles mutually exert on each other are in opposite directions, along the line joining them, and have the same magnitude (according to Newton's third law)

Note 2: $k$, which called the Coulomb constant, is related to the vacuum permittivity by $k=\frac{1}{4\pi {\epsilon }_0}$