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Coulomb’s Law

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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 .