Discussion
A coaxial cable with inner radius 1 mm and outer radius 3 mm, filled with a dielectric of relative permittivity 2.5, has a capacitance per metre of about
Answer: A
Correct answer: 127 pF
For a coaxial line, \[ C = \frac{2\pi\epsilon_0\epsilon_r}{\ln(b/a)} = \frac{2\pi \times 8.854\times10^{-12} \times 2.5}{\ln 3} = \frac{1.391\times10^{-10}}{1.0986} = 127\ \mathrm{pF/m}. \] The logarithm makes the capacitance insensitive to the exact radii - tripling the ratio again would change it by only a third - while the permittivity multiplies it directly.
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