= Lossless coaxial line parameters
{title2=$C'=2\pi\epsilon/\ln(b/a),\quad L'=\mu\ln(b/a)/(2\pi)$}
For ideal coaxial conductors of radii $a<b$ filled with a homogeneous <permittivity> $\epsilon$ and <magnetic permeability> $\mu$, <Gauss's law> gives $E_r=\lambda/(2\pi\epsilon r)$ and hence $C'=2\pi\epsilon/\ln(b/a)$. The magnetic field $H_\varphi=I/(2\pi r)$ has energy per unit length $L'I^2/2$, giving $L'=\mu\ln(b/a)/(2\pi)$. These are the external-field parameters when internal magnetic penetration into the conductors is neglected. Their product is $L'C'=\mu\epsilon$, and the <characteristic impedance> is $\sqrt{L'/C'}=\sqrt{\mu/\epsilon}\ln(b/a)/(2\pi)$.
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