Derivation for capacitance of cylindrical capacitor

AI Thread Summary
The discussion focuses on the derivation of capacitance for a cylindrical capacitor, specifically the transition between steps in the derivation. Participants express confusion about how the radial electric field, denoted as E_r, is substituted in the derivation. The relevant expression for E_r is referenced from equation 23.8 in the textbook. Clarification is provided that this substitution pertains to the electric field outside a very long rod. The conversation emphasizes the importance of understanding this step in the overall derivation process.
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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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