Coulomb force ($\mathbf{F}=k_e{q}_1{q}_2\hat{\mathbf{r}}/r^2$)

The Coulomb force is the electrostatic force between electric charges. For point charges in a uniform isotropic medium of permittivity $ϵ$, the force on charge $q_2$ from $q_1$ is ${\mathbf{F}}_{2\leftarrow 1}=q_1{q}_2{\hat{\mathbf{r}}}_{12}/(4\pi ϵr^2)$, where ${\hat{\mathbf{r}}}_{12}$ points from the first charge to the second.

Equal charge signs give repulsion and opposite signs give attraction. The inverse-square dependence allows superposition to construct fields of extended charge distributions. Nearby conductors or spatially varying dielectrics can redistribute charge and alter the field, so the simple uniform-medium pair formula does not automatically solve those boundary problems.

Three identical like point charges, initially at rest at an equilateral triangle's vertices, remain equilateral as they move away from the fixed centroid. Each resultant force is radial by symmetry. If the centroid radius is $r$, its magnitude is $k_e{q}^2/(\sqrt{3}{r}^2)$. In a nonrelativistic model neglecting radiation, energy conservation gives the final speed $v=\sqrt{2k_e{q}^2/(ma)}$ for initial side $a$ and charge mass $m$.