Electrostatics - Charge Density

AI Thread Summary
To calculate charge density from an electrostatic potential, Poisson's equation is used, expressed as -∇²Φ = ρ/ε₀. This equation relates the electrostatic potential (Φ) to charge density (ρ) in a static electric field. The discussion clarifies the distinction between Poisson's equation and Laplace's equation, emphasizing the importance of remembering the correct formulation. The user expresses gratitude for the reminder about Poisson's equation. Understanding these equations is crucial for analyzing electrostatic systems.
Herbststurm
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Hi,

if we only have an electrostatic potential given. How to calculate the charge density?

I know of course Maxwell equation, here without any time dependence, but I missed always some further specifications, or I forget something important :confused: :redface:

thanks
greetings
 
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Use Laplace's equation (derived from Gauss's Law):

-\nabla^2 \Phi = \rho / \epsilon_0
 
That's Poisson, not Laplace.
 
Thanks, that helps a lot. :smile:

I knew Poissons equation, but I forgot it. :redface: Damn...

Greetings
 
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