I am asking if the permittivity and permeability constants of vacuum space controlling propagation speed of electromagnetic energy, light, through vacuum space:
$$c=\frac{1}{\sqrt{\varepsilon_{0} \mu_{0}}}$$
are somehow correlated or are analogue to the characteristic, capacitance $C_{0}$ and inductance $L_{0}$ values (i.e. values expressed as per-unit length of a transmission line) controlling the signal velocity propagating through a medium (i.e. matter) modeled as a transmission line?
$$V_{s}=\frac{1}{\sqrt{C_{0} L_{0} }}$$
Both $V_{s}$ and $c$ refer to group velocities (i.e. in vacuum space, light phase velocity is the same as its group velocity). $V_{s}$ in $m/s$ units. Characteristic capacitance $C_{0}$ of a specific medium modeled as a transmission line is in $F/m$ units and characteristic inductance of the medium modeled as a transmission line, is $L_{0}$ in $H/m$ units. All units are in SI.
Best Answer
Yes. If the transmission line is surrounded by air then $$ \frac{1}{\sqrt{\mu_0\epsilon_0}}= \frac{1}{\sqrt{LC}}. $$ You can compoute the value of a $L$ and $C$ for a pair of coaxial cylinders, for example, and see that this relation holds. If the transmision line is embedded in a dielectric then the same relation holds, but with $\mu_0$ and $\epsilon_0$ on the LHS replaced by the appropriate magnetic permeability and dielectric constants $\mu$ and $\epsilon$.