$\frac{E^2}{{\mu }_0}$ has the dimensions (E = electric field, ${\mu }_0=$  permeability of free space)

$\left[\frac{E^2}{{\mu }_0}\right]=\left[\frac{{\epsilon }_0{E}^2}{{\epsilon }_0{\mu }_0}\right]=\left[\frac{energy/volume}{{(1/speedoflight)}^2}\right]$

$=\left[\frac{energy{\left(speed\right)}^2}{volume}\right]$

$=\left[\frac{M{L}^2{T}^{-2}{L}^2{T}^{-2}}{L^3}\right]=\left[ML{T}^{-4}\right]$