Physics

The key insight is that $\mu$ and $\epsilon$ appear together in the wave equation for electromagnetic waves, where their product determines the speed of light: $c = 1/\sqrt{\mu\epsilon}$. By rearranging this relationship and using the fact that resistance has dimensions of $[ML^2T^{-3}I^{-2}]$ and speed has dimensions of $[LT^{-1}]$, you can express the ratio $\mu/\epsilon$ in terms of $R$ and $T$. The trick is recognizing that impedance (which has dimensions of resistance) naturally connects electromagnetic properties to mechanical quantities.

The key insight is that $\mu$ and $\epsilon$ appear together in the wave equation for electromagnetic waves, where their product determines the speed of light: $c = 1/\sqrt{\mu\epsilon}$. By rearranging this relationship and using the fact that resistance has dimensions of $[ML^2T^{-3}I^{-2}]$ and speed has dimensions of $[LT^{-1}]$, you can express the ratio $\mu/\epsilon$ in terms of $R$ and $T$. The trick is recognizing that impedance (which has dimensions of resistance) naturally connects electromagnetic properties to mechanical quantities.