Dimensional Analysis Poisson Equation

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SUMMARY

The discussion focuses on the application of dimensional analysis to Poisson's equation in one dimension, expressed as d²φ/dx² = ρ(x)/ε. Participants explore how to determine the order of magnitude of the electrostatic potential φ based on a given charge density profile ρ(x). It is established that the electrostatic potential can be shifted by a constant without violating the conditions of the Poisson equation, indicating its arbitrary nature.

PREREQUISITES
  • Understanding of Poisson's equation in electrostatics
  • Familiarity with dimensional analysis techniques
  • Knowledge of charge density profiles and their implications
  • Basic concepts of electrostatic potential and its properties
NEXT STEPS
  • Study the derivation and applications of Poisson's equation in various dimensions
  • Explore advanced dimensional analysis methods in physics
  • Investigate the implications of arbitrary constants in electrostatic potential
  • Learn about charge density profiles and their effects on electrostatic fields
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Physicists, electrical engineers, and students studying electrostatics or dimensional analysis in physics.

aaaa202
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Suppose I am given some charge density profile ρ(x). Poisson's equation in 1D reads

d2φ/dx2 = ρ(x)/ε

Is there a simple way to see what the order of magnitude of the electrostatic potential should be from a dimensional analysis?
 
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aaaa202 said:
Suppose I am given some charge density profile ρ(x). Poisson's equation in 1D reads

d2φ/dx2 = ρ(x)/ε

Is there a simple way to see what the order of magnitude of the electrostatic potential should be from a dimensional analysis?
The potential is arbitrary. You can shift it by a constant and still satisfy the Poisson equation.
 

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