Does Electrostatic Potential Obey Superposition?

[latentcorpse]

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!

 

[dx]

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.