Help calculating the capacitance per meter of a cable?

First you need to calculate the capacitance for a cylindrical capacitor, not parallel plates (the formula you listed). Look at a cross section of the wire so that you see a ring representing the outer radius surrounding a solid circle representing the inner radius of the wire. Then draw a gaussian surface in the empty space between the two pieces of wire and apply Gauss' law.

First: E = electric field at a radial distance R. The wire has length L.

q = ε₀EA = ε₀E(2πRL) where 2πRL is the area of the curved part of the Gaussian surface. Solve this equation for E = q / (2πε₀LR)

Then, you need to take the integral of E from the outer radius to the inner radius along a radial path. This gives you the potential difference between the two pieces of wire.

V = int(E, ds) = -q/(2πε₀L) int(dr/r) where the bounds of integration are a and b, the inner and outer radii. The integral of 1/r is ln(r), subtituting your bounds in you get ln(b/a).

Then, C = q/V

C = 2πε₀L / ln(b/a)

Drop the term L to find the capacitance per unit length.

edit: I assumed no dielectric in this whole derivation, you simply multiply it into the numerator of the above equation.

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