Electrostatics - Charge Density

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Discussion Overview

The discussion revolves around the calculation of charge density from a given electrostatic potential. Participants explore the relevant equations and concepts, specifically focusing on the relationship between electrostatic potential and charge density.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about the method to calculate charge density from electrostatic potential, referencing Maxwell's equations but expressing uncertainty about specific details.
  • Another participant suggests using Laplace's equation, linking it to Gauss's Law and providing a formula involving charge density and permittivity.
  • A third participant corrects the previous suggestion, stating that the appropriate equation is Poisson's equation rather than Laplace's equation.
  • The initial poster acknowledges the correction and expresses gratitude for the clarification regarding Poisson's equation.

Areas of Agreement / Disagreement

The discussion contains a correction regarding the appropriate equation to use, indicating some disagreement on the initial suggestion of Laplace's equation. However, there is no consensus on the broader topic of calculating charge density from electrostatic potential.

Contextual Notes

Participants reference specific equations without fully detailing the assumptions or conditions under which they apply, such as the nature of the electrostatic potential or the context of the charge distribution.

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):

[tex]-\nabla^2 \Phi = \rho / \epsilon_0[/tex]
 
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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