Derivation for capacitance of cylindrical capacitor

Click For 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.
member 731016
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!
 
Physics news on Phys.org
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.
 
  • Like
Likes member 731016
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 !
 
Thread 'Correct statement about size of wire to produce larger extension'
The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...

Similar threads

Replies
2
Views
2K
Replies
6
Views
522
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 14 ·
Replies
14
Views
1K
Replies
4
Views
2K
Replies
3
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
Replies
4
Views
3K