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    Uniformly charged field: Calculate capacitance of the coaxial cable arrangement

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    According to this book, the electric field outside a uniformly charged,infinite cylindrical conductor is the same as if the cylinder's charge were concentrated in a thin wire along the cylinder's axis. Moreover, the potential inside a uniformly charged infinite cylindrical pipe, like that inside a spherical shell, is a constant. These statements are approximately true for finite cylinders and pipes as long as their lenght is much larger than their radius. Use these facts to calculate the capacitance of the coaxial cable arrangement below:

    C= L/2kln (R0/R2)= 2πâ?¬ L/ln (R0/R2) If L>>>R2
    (a cylindrical wire inside a very long cylindrical shell)

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    Solution Preview

    See attached file.

    Let the charge on conductor is distributed as q C/m.
    The radius of conductor is Ro.
    Take a Gaussian surface of radius r( ...

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