# Electrostatic Potential

why does electrostatic potential obey superposition?

it's a solution of poisson's equation and solutions of poisson's equation definitely do not obey superposition!

If $$\nabla^2 \varphi_1 = -\rho_1 / \epsilon_0$$ and $$\nabla^2 \varphi_2 = -\rho_2 / \epsilon_0$$, then $$\varphi_1 + \varphi_2$$ satisfies $$\nabla^2 \varphi = -(\rho_1 + \rho_2) / \epsilon_0$$, i.e. the potential of the combined charge distribution $$\rho_1 + \rho_2$$ is the sum of the potentials of the individual distributions.