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Homework Help: Coaxial Cable Problem - Finding volume charge density.

  1. Sep 18, 2013 #1
    1. The problem statement, all variables and given/known data

    A long coaxial cable consists of an inner solid cylinder, radius a, and an outer thin coaxial cylindrical shell, radius b. The outer shell carries a uniform surface charge density σ.
    Find the uniform volume charge density ρ that the inner cylinder must have in order that the whole cable (inner + outer) is neutral.

    2. Relevant equations

    Acylinder = 2πbl

    Vcylinder = πa^2l

    Qenc = ∫Vρdτ

    3. The attempt at a solution

    I started by using dq = sigma*dS, and integrating to get Q_b = -2(pi)(sigma)bL. That should be the total charge on the outer cylindrical shell.

    Then I set -Q_b = Q_a, so the net charge of the entire system would be equal to 0.

    Next I used Q_a = row*integral(dVolume) = -Q_b

    to get to (row)(pi)(a^2)(L) = 2(pi)(sigma)(b)(L)

    Solving for row gave me:

    row = [2(sigma)(b)] / a^2

    Does this look like a proper method and correct solution?

    Thank you so much for your time.

  2. jcsd
  3. Sep 18, 2013 #2


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    2017 Award

    Staff: Mentor

    That looks right.
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