Show that \(\frac{1}{\sqrt{\mu_0 \varepsilon_0}}\) gives the velocity of an electromagnetic wave in free space.
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You can also verify this using dimensional analysis. The dimensions of \(\varepsilon_0\) are \([\text{M}^{-1}\text{L}^{-3}\text{T}^4\text{A}^2]\) and for \(\mu_0\) they are \([\text{M L T}^{-2}\text{A}^{-2}]\). Multiplying them gives \([\text{L}^{-2}\text{T}^2]\). Taking the reciprocal square root yields \([\text{L T}^{-1}]\), which matches the dimensions of velocity.