# Electrostatic Potential

by latentcorpse
Tags: electrostatic, potential
 P: 1,431 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!
 HW Helper PF Gold P: 1,962 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.

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