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Capacitance per unit length - two cylindrical conductors

  1. Aug 14, 2015 #1
    1. The problem statement, all variables and given/known data
    Two cylindrical conductors, of distance between them d and radius a (a<<d), have dielectric layer of relative permitivitty εr and thickness a. Calculate capacitance per unit length of this system.

    2. Relevant equations
    Capacitance per unit length, C'=Q'/U
    Gauss law, cylindrical symmetry, E=Q'/(2πεr2)

    3. The attempt at a solution
    I have started with the equation C'=Q'/U.
    Voltage integration limits: (a - 2a) + (2a - (d-2a)) + ((d-2a) - (d-a))
    After calculating the partial integrals, voltage U is:

    Applying voltage in the expression for capacitance per unit length gives

    In my books solution, in the numerator there is πε0 for C'.

    Are my limits of integration for voltage correct? Maybe it is a mistake in books solution.
    Thanks for replies.
  2. jcsd
  3. Aug 14, 2015 #2


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    Staff: Mentor

    I don't understand that part.

    As far as I understand the problem statement, you have two separate "cables"? Then the problem does not have a cylinder symmetry. Otherwise: do you have a sketch of the layout?
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