Electrostatic Potential

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

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latentcorpse	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!

dx Blog Entries: 1 Recognitions: Gold Member Homework Help	If [tex] \nabla^2 \varphi_1 = -\rho_1 / \epsilon_0 [/tex] and [tex] \nabla^2 \varphi_2 = -\rho_2 / \epsilon_0 [/tex], then [tex] \varphi_1 + \varphi_2 [/tex] satisfies [tex] \nabla^2 \varphi = -(\rho_1 + \rho_2) / \epsilon_0 [/tex], i.e. the potential of the combined charge distribution [tex] \rho_1 + \rho_2 [/tex] is the sum of the potentials of the individual distributions.