The dimension of \(\sqrt{\frac{{\mu }_{0}}{{ϵ}_{0}}}\) is equal to that of : ( \({\mu }_{0}=\) Vacuum permeability and \…

$$
\begin{aligned}
& L=\frac{\mu_0 N A}{\ell} \\
& C=\frac{A \epsilon_0}{d} \\
& \frac{L}{C} \propto \frac{\mu_0}{\epsilon_0} \\
& \sqrt{\frac{\mu_0}{\epsilon_0}} \propto \sqrt{\frac{L}{C}} \\
& \frac{L}{C}=\frac{\tau R}{(\tau / R)}=R^2 \\
& \sqrt{\frac{\mu_0}{\epsilon_0}}=R
\end{aligned}
$$