= Coaxial cable
{title2=$Z_0=(2\pi)^{-1}\sqrt{\mu/\varepsilon}\log(b/a)$}
{wiki}
A <coaxial cable> has an inner conductor surrounded by a concentric outer conductor, with dielectric between them. In the <ideal> homogeneous lossless <Transverse electromagnetic mode>, <electric field> is radial and <magnetic field> circles the axis; the return current flows on the outer conductor. For inner radius $a$ and inner shield radius $b$, its <characteristic impedance> is
$$
Z_0=\frac1{2\pi}\sqrt{\frac\mu\varepsilon}\log\frac ba.
$$
For air dielectric this is approximately $60\log(b/a)$ ohms. A cable's characteristic impedance describes travelling waves, not its DC wire resistance. Finite conductivity, imperfect shielding and higher modes <limit> the <ideal> description.
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