Answer
The capacitance per meter for the cable is $~~8.1\times 10^{-11}~F/m$
Work Step by Step
We can let the length of the cable be $L = 1.0~m$
We an use Equation (25-14) to find the capacitance if the cable was filled with air:
$C = 2\pi~\epsilon_0~\frac{L}{ln(b/a)}$
$C = (2\pi)~(8.854\times 10^{-13}~C/V~m)~\frac{1.0~m}{ln(0.60~mm/0.10~mm)}$
$C = 3.105\times 10^{-11}~F$
We can find the capacitance if the space is filled with polystyrene:
$C = (2.6)(3.105\times 10^{-11}~F) = 8.1\times 10^{-11}~F$
Since we let the length of the cable be $1.0~m$, the capacitance per meter for the cable is $~~8.1\times 10^{-11}~F/m$
