How Does Charge Distribution Affect Electrostatic Field Dependence?

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SUMMARY

The discussion centers on the electrostatic field dependence in a uniformly charged plane with positive charge density ϱ. The original poster attempted to analyze the problem using cylindrical coordinates, concluding that the field depends on the radial distance r due to observed rotational and translational symmetries. However, the instructor argued that the field depends on the vertical coordinate z, highlighting a misunderstanding of symmetry invariances in electrostatics. This discrepancy emphasizes the importance of correctly identifying the symmetry properties of charge distributions.

PREREQUISITES
  • Understanding of electrostatics and electric fields
  • Familiarity with symmetry concepts in physics
  • Knowledge of cylindrical coordinate systems
  • Basic principles of charge distribution and density
NEXT STEPS
  • Study the principles of electrostatic fields in different coordinate systems
  • Learn about symmetry invariances in electrostatics
  • Explore the mathematical formulation of electric fields from charge distributions
  • Investigate the implications of translational and rotational symmetries on field behavior
USEFUL FOR

Students of physics, particularly those studying electrostatics, educators teaching charge distribution concepts, and anyone interested in the mathematical analysis of electric fields.

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Homework Statement



"Find the direction and the variables which the electrostatic field depends on at all points of the plane (xOy) uniformly charged with the density of positive charges ϱ"

The Attempt at a Solution



So first of all, I have to study the Invariances of symmetry. I tried to switch to the cylindrical coordinate system (Ur, Uθ, Uz) and I observe that there is an Rotational symmetry following Uθ and a Translational symmetry following Uz, which made me conclude that the electrostatic field only depends on r.

2. Homework Equations

However, my teacher found that there is a Rotational symmetry following Uθ and a Translational symmetry following Ur, which means that the field only depends on z.
Shouldn't it be the opposite ?? How did he find so ??

Thank you
 
Physics news on Phys.org
All the charges are in the xOy plane. How does that lead to a translation symmetry in z?
 

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