How to find electric-charge density distribution

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    Density Distribution
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Discussion Overview

The discussion revolves around calculating the electric-charge density distribution, ρ(r), in the context of a uniform electric field represented by unit vectors in the x, y, and z directions. The focus is on theoretical implications and applications of Maxwell's equations.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant suggests using Maxwell's equation, specifically \nabla \cdot \mathbf{E} = \frac {\rho} {\varepsilon_0}, to relate the electric field to charge density.
  • Another participant notes that the divergence of a uniform electric field is zero, implying that there are no charges present in regions where the field is uniform.
  • A participant expresses intent to apply the suggested formula to the problem.

Areas of Agreement / Disagreement

Participants present differing views on the implications of a uniform electric field regarding charge density. One perspective supports the use of Maxwell's equation, while another counters that a uniform field indicates zero charge density.

Contextual Notes

The discussion does not resolve the implications of applying Maxwell's equations to a uniform electric field, nor does it clarify the assumptions regarding the uniformity of the field and its relation to charge distribution.

smantics
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Given only an uniform electric field with unit vectors in the x, y, and z directions, how would you go about calculating the electric-charge density distribution p(r) for that electric field?
 
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One nice formula you might try applying is one of Maxwell's equations: \nabla \cdot \mathbf{E} = \frac {\rho} {\varepsilon_0} The symbol \rho is the charge density that generates the electric field \mathbf{E}, and \varepsilon_0 is a proportionality constant called the permittivity of free space.
 
Thanks, I will try that.
 
The divergence of a uniform field is zero. There are no charges, at least where the field is uniform.
 

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