Derivation for capacitance of cylindrical capacitor

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SUMMARY

The discussion focuses on the derivation of capacitance for a cylindrical capacitor, specifically addressing the transition between steps in the derivation. Participants clarify that the radial electric field, denoted as ##E_r##, is replaced with the expression for the electric field outside a very long rod, as referenced in equation 23.8 of the relevant textbook. This substitution is crucial for understanding the capacitance calculation in cylindrical geometries.

PREREQUISITES
  • Understanding of electric fields, particularly radial electric fields.
  • Familiarity with cylindrical capacitor concepts.
  • Knowledge of mathematical derivation techniques in electromagnetism.
  • Access to the textbook containing equation 23.8 for reference.
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  • Review the derivation of capacitance for cylindrical capacitors in textbooks.
  • Study the application of Gauss's Law to cylindrical symmetry.
  • Examine the implications of electric field equations in capacitor design.
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Students and professionals in electrical engineering, physicists, and anyone involved in the study of capacitors and electric fields, particularly those focusing on cylindrical geometries.

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Homework Statement
Please see below
Relevant Equations
Please see below
I don't understand how they got from the previous step to the next step of the derivation circled in red:
1675053075013.png

Many thanks!
 
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They replaced ##E_r## with the expression for the radial electric field for a very long rod in the region outside the rod. See equation 23.8 in the textbook that they quote.
 
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kuruman said:
They replaced ##E_r## with the expression for the radial electric field for a very long rod in the region outside the rod. See equation 23.8 in the textbook that they quote.
Thank you @kuruman !
 

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