Coulomb's law

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The force exerted on a test charge q_1\, with position \mathbf{r}_1\, due to a second charge q_2\, with position \mathbf{r}_2\, is given by

\mathbf{F} = \frac{1}{4\pi \epsilon_0} \frac{q_1 q_2}{r_{12}^2} \hat \mathbf{r}_{12}\,,

where \mathbf{r}_{12} = \mathbf{r}_2 - \mathbf{r}_1\,. It has magnitude \frac{1}{4\pi \epsilon_0} \frac{q_1 q_2}{r_{12}^2}\, and is directed along the vector \mathbf{r}_{12}\, connecting q_1\, and q_2\,.

The constant

k = \frac{1}{4\pi \epsilon_0} \approx 8.987\ 551\ 787\times 10^{9} N m^2 /C^2\,,

is known as Coulomb's constant, where \epsilon_0\, is the permittivity of the vacuum.

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