How Does Charge Distribution Affect Electrostatic Field Dependence?

AI Thread Summary
The discussion centers on determining how charge distribution affects the electrostatic field in a uniformly charged plane. The original analysis identified rotational symmetry in the angular direction and translational symmetry in the vertical direction, suggesting the field depends only on the radial distance. However, the teacher argued that the field should depend solely on the vertical coordinate, leading to confusion about the symmetry interpretations. The key question raised is how the charge distribution in the xOy plane results in translational symmetry in the z-direction. Clarification on these symmetry principles is essential for understanding the electrostatic field's dependence.
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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
 
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All the charges are in the xOy plane. How does that lead to a translation symmetry in z?
 
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