A parallel between electro-magnetics in transmission lines and optics.

This highlights a fascinating parallel between electro-magnetics in transmission lines and optics. In coaxial cables, the signal propagation speed is determined by the cable's capacitance (

$CC$) and inductance ($LL$), which are related by the equation:

$$v=\frac{1}{\sqrt{L\cdot C}}v\; =\; \backslash frac\{1\}\{\backslash sqrt\{L\; \backslash cdot\; C\}\}$$

This expression mirrors the relationship found in optics, where the speed of light ($cc$) in a medium is determined by the magnetic permeability ($\mu \backslash mu$) and electric permittivity ($\epsilon \backslash varepsilon$):

$$c=\frac{1}{\sqrt{\mu \cdot \epsilon }}c\; =\; \backslash frac\{1\}\{\backslash sqrt\{\backslash mu\; \backslash cdot\; \backslash varepsilon\}\}$$

Both systems share a core principle: propagation speed is governed by the interplay of fields and their ability to store and transfer energy. In coaxial cables, capacitance stores electric energy and inductance governs magnetic energy, forming a resonant system that dictates signal velocity. In optics, electric permittivity and magnetic permeability perform similar roles at the level of electromagnetic waves.

This parallel highlights the elegant unification of physical principles across scales and systems