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Capacitance per length unit of coaxial cable

  1. Aug 14, 2015 #1
    1. The problem statement, all variables and given/known data
    Coaxial cable has double layered dielectric.
    a=2mm, b=4mm, c=8mm, εr1=3, εr2=4.5, Uab=1000V
    1. Calculate capacitance per unit length of a cable.
    2. Calculate inner and outer charge densities of a cable.
    2. Relevant equations

    Gauss law
    C'=Q'/U
    σ = nD
    σp = nP

    3. The attempt at a solution

    After applying Gauss law for dielectrics, I get electric field:
    E=Q'/(2πε0r1r2r)).
    Limits of integration for voltage: (a - b) + (b - c)
    U=(Q'(ln(b/a)+ln(c/b)))/(2πε0r1r2))


    Then, C'=(2πε0r1r2))/(ln(b/a)+ln(c/b))
    This gives me C'=288pF/m but in my books solution it is C'=144pF/m.

    Could someone check this.
    Thanks for replies.
     

    Attached Files:

  2. jcsd
  3. Aug 14, 2015 #2

    mfb

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    2016 Award

    Staff: Mentor

    E shouldn't have the same formula in both parts, it has to include the local ε somehow. Also, in the way you wrote it the units do not match.
    I'm surprised that your answer seems to be exactly a factor of 2 off with this, however.
     
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