Clarification on an electric fields solution

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Homework Help Overview

The discussion revolves around the conversion of electric field components into cylindrical coordinates, specifically questioning the treatment of the radius "a" in the context of an electric field expression.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster questions why the radius "a" loses its exponent during the conversion to cylindrical coordinates, indicating a potential misunderstanding of the underlying mathematics.
  • Some participants explore the relationship between the differential length element and the angle in cylindrical coordinates.

Discussion Status

Participants are engaged in clarifying the mathematical reasoning behind the conversion process. A connection to the arc length formula has been acknowledged, suggesting a productive direction in the discussion.

Contextual Notes

The original poster emphasizes that this inquiry is not part of a homework problem, but rather a question about a solution provided in a solutions manual.

Allenman
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This isn't actually a homework problem. I just had a question about the solution they provided.

Homework Statement


physprob96.png



2. Solution given in solutions manual
physsol96.png



3. My question

When they convert dE into cylindrical coordinates why does the radius "a" lose its exponent?

dE = [itex]\frac{\kappa\lambda\delta l}{a^{2}}[/itex] = [itex]\frac{\kappa\lambda\delta\theta}{a}[/itex]

I have to be missing something simple, I just know it...
 
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Allenman said:
This isn't actually a homework problem. I just had a question about the solution they provided.

Homework Statement


physprob96.png


2. Solution given in solutions manual
physsol96.png


3. My question

When they convert dE into cylindrical coordinates why does the radius "a" lose its exponent?

dE = [itex]\frac{\kappa\lambda\delta l}{a^{2}}[/itex] = [itex]\frac{\kappa\lambda\delta\theta}{a}[/itex]

I have to be missing something simple, I just know it...
It's because [itex]d\ell=a\cdot d\theta\,.[/itex]
 
Does that come from the arc length formula?

Thank you
 
Yes it does.
 

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