Virial theorem for a system of charged particles

Two formulations of the virial theorem are used in practice: one for separate particles and one for a continuous medium. The virial theorem for a system of charged particles which was given by Landau and Lifshitz in their book The Classical Theory of Fields should incorporate both these formulations. However, there is an error there in the derivation of this theorem, which is based on transformation from a discussion in terms of particles to a discussion in terms of a continuous medium. Specifically, the selfeffect force of the charges is not eliminated. As a result, the infinite self-energy of the charges is not eliminated, and the corresponding final equation cannot be satisfied. In the present note, a refined formulation of the virial theorem for a system of charged particles is given. The renormalization of the total electromagnetic field energy is taken into account.