When do you use R or r for Gauss' Law

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    Gauss Gauss' law Law
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Discussion Overview

The discussion revolves around the application of Gauss' Law, specifically the use of the variables r and R in the equation E A = 1/4piEo * Qenc. Participants explore the conditions under which to use each variable based on the position of the Gaussian surface relative to the charged object, examining both theoretical and conceptual aspects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants express confusion about when to use r or R in the context of Gauss' Law, noting that different examples yield different results.
  • One participant suggests that r should be treated the same on both sides of the equation if the Gaussian surface is outside the original surface, but questions this based on conflicting examples.
  • Another participant proposes a pattern: using R on the right side of the equation when the Gaussian surface is outside the original surface (r > R), and using r on both sides when the Gaussian surface is inside or on the surface (r ≤ R), but seeks a deeper understanding of the physical reasoning behind this.
  • A later reply attempts to clarify that the right side of the equation represents the charge enclosed, indicating that if the Gaussian surface is outside, it accounts for the total charge, while if it is inside, it only accounts for the charge within that Gaussian surface, assuming uniform charge density.
  • One participant mentions rewriting Q enclosed in terms of surface charge density (sigma) and volume charge density (ro), indicating a focus on the mathematical representation of charge distribution.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the use of r versus R, with multiple competing views and interpretations of Gauss' Law remaining unresolved.

Contextual Notes

Limitations include potential misunderstandings of the physical implications of charge distribution and the conditions under which different variables apply, as well as unresolved mathematical steps in the application of Gauss' Law.

Who May Find This Useful

This discussion may be useful for students and educators in physics, particularly those studying electromagnetism and Gauss' Law, as well as individuals seeking clarification on the application of mathematical concepts in physical contexts.

Fjolvar
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I've seen many examples of spheres, cylinders, and planes and I'm trying to understand when to use r or R in the equation E A = 1/4piEo * Qenc. I've seen examples where the r's will cancel giving a simplified answer and then others where you have something like R^2 / r^2.

So my question is how do you know what type of r to write on the left side of the equation AND the right side of the equation. Thank you.
 
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I thought you treated r the same on both sides of the eqn if the Gaussian surface was outside of the original surface, but that doesn't seem correct based on the examples I've seen in Griffiths.
 
I think I've noticed a pattern but I still don't understand the physical meaning behind it. It seems if the Gaussian is written outside of the original surface (r>R) then you use R on the right side of the equation. If (r< or equal to R) then you can use r on both sides of the equation, which will result in some cancellation when you bring over A to the right side and calculate E. But physically I would like to understand why this is. Any help would be greatly appreciated, thanks.
 
I'll attempt to answer my own question. The right side of the equation is Q enclosed which means the charge inside of the Gaussian surface.. so if your Gaussian is outside the surface, the charge enclosed is the total charge of the surface, but if your Gaussian is within the original surface, the charge enclosed is only equal to the charge within that Gaussian and not the total... as long as the charge density is uniform and we have charge inside. Right?
 
I'm referring to rewriting Q enclosed in terms of the surface charge (sigma) and volume charge density (ro)..
 

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