Force between two point charges (interaction force) is directly proportional to the product of magnitude of charges ( $q_1$ and $q_2$ ) and is inversely proportional to the square of the distance between them i.e., $\left ( 1/r^2 \right )$ . This force is conservative in nature. This law is also called inverse square law. The direction of force is always along the line joining the point charges.

$F \propto \dfrac{q_1 q_2}{r^2}$ $F = k \dfrac{q_1 q_2}{r^2}$ $k = \dfrac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 N-m^2/C^2$ $\varepsilon_0 = \mathrm{permittivity \ of \ free \ space} = 10^{-12} C^2/ N-m^2$

Coulomb’s Law in Vector Form

Suppose the position vectors of two charges $q_1$ and $q_2$ are $\bar{r}_1$ and $\bar{r}_2$ , then, electric force on charge $q_1$ due to charge $q_2$ is,

$\bar{F}_{12} = \dfrac{1}{4 \pi \varepsilon_0} \dfrac{q_1 q_2}{|\bar r_1 - \bar r_2 |^3} \left ( \vec {r_1} - \vec{r_2} \right)$

Similarly, electric force on $q_2$ due to charge $q_1$ is

$\vec F_{12} \dfrac{1}{4 \pi \varepsilon_0} \dfrac{q_1 q_2}{|\bar r_2 - \bar r_1|^3} \left ( \bar r_2 - \bar r_1 \right )$

Here $q_1$ and $q_2$ are to be substituted with sign. Position vector of charges $q_1$ and $q_2$ are and respectively where $(x_1 y_1 z_1)$ and $(x_2 y_2 z_2)$ are the coordinates of charges $q_1$ and $q_2$ .

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