Combined Electromagnetic Energy and Momentum Conservation Equation

We have combined the two fundamental conservation theorems in electromagnetic theory-the energy and the momentum conservation theorems-to derive a vector wave equation for linear and homogeneous media with symmetrical constitutive matrix. We have demonstrated how the relation between the Poynting vector and the momentum density vector affects the electromagnetic quantities. Furthermore, a relation between the Poynting vector, the momentum density vector, and the phase velocity of the Poynting vector has been derived. In addition, what happens if the Poynting vector and the momentum density vector become mutually orthogonal or one of them vanishes has also been discussed. The angle between the above-mentioned vectors has been derived, and a relation between the momentum density vector and the wave vector for plane waves has been obtained. It has been shown that for plane waves, orthogonality of the phase velocity is not feasible.