Electrodynamics regarding volume charge density behavior

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SUMMARY

This discussion focuses on the behavior of volume charge density in electrodynamics, particularly the distinction between constant and non-constant charge densities. The Dirac delta function is mentioned as a potential tool for modeling isolated charge densities, although it is not essential for electrostatics. The conversation references Griffiths' work, emphasizing the limitations of applying Gauss's law at the surface of a dielectric due to the divergence of the electric field. Understanding these concepts is crucial for grasping the fundamentals of electrostatics and charge distribution.

PREREQUISITES
  • Understanding of electrostatics principles
  • Familiarity with Gauss's law
  • Knowledge of Dirac delta functions
  • Basic concepts of dielectric materials
NEXT STEPS
  • Study Griffiths' "Introduction to Electrodynamics" for detailed explanations
  • Learn about the application of Gauss's law in different charge distributions
  • Explore the mathematical properties of Dirac delta functions in physics
  • Investigate the behavior of electric fields at dielectric boundaries
USEFUL FOR

Students of physics, educators teaching electrodynamics, and researchers interested in charge density behavior and electrostatic principles.

AHSAN MUJTABA
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In this explanation we need to involve the Dirac delta functions(maybe) but I clearly have a difficulty in understanding it can some one explain me the whole concept of constant or non constant volume charge density.
 
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If this is a constant charge density, then technically we are discussing electrostatics. In some ways the simplest model for an isolated "small {in physical extent) charge density uses the Dirac ##\delta ## function but it is not essential for the electrostatics.
A static charge density is typically a continuum of finite total charge in a finite space that is constant is time.
 
Would you please elaborate a bit please?
 
Your question needs to be more specific. There are very large books on this subject!
 
Okay being specific I want to quote the following paragraph from Griffiths,
"We cannot apply Gauss’s law precisely at the surface of a dielectric, for here ##\rho_b## blows up, taking the divergence of E with it."
I don't really understand the meaning of it an explanation is needed.
 

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