The main topic of research in this contribution is about the propagation of electromagnetic waves in homogeneous isotropic media discretized by the finite element method. Both the nondispersive free space and the dispersive unmagnetized cold plasma are address. The twenty-nodes hexahedral finite element HE20 is selected for the analysis. This element is formulated in energy-orthogonal form. It means that the element stiffness matrix is split into basic and higher order components. This decomposition is applied to the magnetic energy of the finite element assemblage. By a dispersion analysis, the higher order magnetic energy is related to the indicators of numerical dispersion for the phase and group velocities, the energy error introduced by the finite element discretization, and the number of elements per wavelength. The effect of the finite element discretization over the dielectric constant of the plasma is taken into account. As application, by energy arguments based on the dispersion analysis, a criterion to identify spurious eigenmodes in isotropic electromagnetic cavities discretized by energy-orthogonal HE20 elements emerge.