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Homework Help: 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


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    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


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    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.
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