Poisson's equation in electrostatics

Summary

Poisson's equation in electrostatics is the equation $\Delta \varphi = -\rho / \varepsilon_0$ for the electric potential $\varphi$ of a charge density $\rho$. It is the case of Poisson's equation that comes from physics. It packs Coulomb's law and Gauss's law into one second-order partial differential equation. With boundary conditions, it is the main tool to find potentials near conductors.