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Capacitance of coaxial cable

  • Thread starter jumpboy
  • Start date
  • #1
6
0

Homework Statement



http://smg.photobucket.com/albums/v68/jumpboyb/?action=view&current=scan0001.jpg" [Broken]
Pretty much looking for a general equation for capacitance of a coaxial cable per meter length.

given:
-a diagram (click link)
-two radii
-dielectric material
-outer conductor is grounded (V = 0V)

Homework Equations


C = Q/V
C=A/d[tex]\epsilon[/tex]0


The Attempt at a Solution


used the second equation but won't work since its for a parallel plate capacitor.

thats it! I'm lost on this one
 
Last edited by a moderator:

Answers and Replies

  • #2
8
0
I think the best way to approach this problem is with Gauss's law. You need to set an arbitrary charge (it will vanish in the end.). Use a cylinder as your Gaussian surface. Hope this helps
 
  • #3
6
0
Still stuck. Here's what I did with Gauss' Law in mind. (btw, the answer is (2pi[tex]\epsilon[/tex])/ln(R2/R1) and thats not pi to the epsilon not power btw.)

So, with Gauss, you have integral of E dot dA which equals Q/[tex]\epsilon[/tex].

Capacitance - Q=VC...so subsitute that back into the gauss equation so you have....

EA = VC/epsilon [tex]\Rightarrow[/tex] C= EA[epsilon]/V

Electric potential is the negative rate of change of a electric field...ie E = -dV/ds = -V/r where r = R2 - R1

C=-rA[epsilon]=-2pi(r)3[epsilon]

and yea....nothing. I see I need to integrate something, but idk where or what logic to use for it.
 
  • #4
Defennder
Homework Helper
2,591
5
To get V you must integrate the expression for E with respect to dr. You can't just use E = -V/r which is true only for the simplest 1D case.
 
  • #5
8
0
Right, try adding the integral of E dot dl or dr (whatever you guys call it.) into your arsenal.
 
  • #6
the expression you want to integrate is dV = -[Q/(2Pi*R)] with limits from R1 to R2 (inner to outter). This is obtained through gauss's law, saying that EA = Qin/Episilon, solving for E and substituting for the original integral of dV = -[E dot ds]. The area "A" is 2*Pi*r because after the length is taken into acount, it will account for the surface area.
 

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