1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solving Spherical and Cylindrical Capacitors for Inner Radii

  1. Feb 25, 2009 #1
    1. The problem statement, all variables and given/known data
    I have two homework problems, both of which require me to solve the equation for the capacitance of a capacitor for the inner radius of the capacitor (one cylindrical, one spherical). This shouldn't be a problem, but I think my algebra is screwy.
    a = inner radius
    b = outer radius
    C = capacitance
    h = height of capacitor

    2. Relevant equations
    Capacitance of a Spherical Capacitor:
    (i) C=4[tex]\pi[/tex][tex]\epsilon_{0}[/tex]ab / (b-a)

    Capacitance of a Cylindrical Capacitor:
    (ii) C=2[tex]\pi[/tex][tex]\epsilon_{0}[/tex]h / ln(b/a)

    3. The attempt at a solution
    My attempts at solving these for a are as follows:
    (i) a = b*C / (C + 4*[tex]\pi[/tex]*[tex]\epsilon[/tex]*b)
    (ii) a = b / e[tex]^{(2*\pi*\epsilon*h / C)}[/tex]
     
    Last edited: Feb 26, 2009
  2. jcsd
  3. Feb 25, 2009 #2

    Delphi51

    User Avatar
    Homework Helper

    Both are correctly derived!
    What is the h in the spherical formula?
     
  4. Feb 25, 2009 #3
    The equations are solved for a correctly?

    There is no h in the spherical formula.
     
  5. Feb 25, 2009 #4

    Delphi51

    User Avatar
    Homework Helper

    An h is showing in each formula on my screen. Just before "/ ln(b/a)" in the first formula.
     
  6. Feb 25, 2009 #5
    whoops, i had them labeled wrong. (i) is the capacitance of a spherical capacitor, and (ii) is the capacitance of a cylindrical capacitor. h is the height of the capacitor. Hm, I must be entering values into my calculator incorrectly... rechecking now.
     
  7. Feb 26, 2009 #6
    Yeah, I solved the cylindrical one (ii) correctly, I just just plugging values in incorrectly.

    The spherical one is still giving me issues though, I'm getting

    a = b + (C / (4 * Pi * E)), which means that a will always be greater than b, an impossible situation when a is the inner radius. So I think that somewhere I've got my algebra wrong, specifically a minus sign missing somewhere.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Solving Spherical and Cylindrical Capacitors for Inner Radii
  1. Cylindrical capacitor (Replies: 8)

  2. Cylindrical Capacitor (Replies: 1)

  3. Cylindrical Capacitor (Replies: 3)

  4. Spherical Capacitors (Replies: 1)

Loading...