1.2 Coulomb's Law

1.2 Coulomb's Law

The electrostatic force between two point charges $q_1$ and $q_2$ separated by distance $r$:

$$F = \frac{1}{4\pi\varepsilon_0} \cdot \frac{q_1 q_2}{r^2}$$

where $\dfrac{1}{4\pi\varepsilon_0} = k = 9 \times 10^9\,\text{N m}^2\text{C}^{-2}$.

In vector form:

$$\vec{F}_{12} = \frac{1}{4\pi\varepsilon_0} \cdot \frac{q_1 q_2}{r^2}\,\hat{r}_{12}$$

Superposition Principle

The net force on a charge $q_1$ due to multiple charges is the vector sum:

$$\vec{F}_1 = \vec{F}_{12} + \vec{F}_{13} + \cdots + \vec{F}_{1n}$$