Explicit Definitions for the Electromagnetic Energies in Electromagnetic Radiation and Mutual Coupling

In the proposed theory, the total electromagnetic energy of a radiator is separated into three parts: a Coulomb-velocity energy, a radiative energy, and a macroscopic Schott energy. The Coulomb-velocity energy is attached to the sources. It becomes zero as soon as its sources have disappeared. The radiative energy leaves the radiator and propagates to the surrounding space. The macroscopic Schott energy continues to exist for a short time after the sources have disappeared, performing like the Schott energy in the charged particle theory. The Poynting vector describes the total power flux density related to the total electromagnetic energy and should include a real radiative power flow by the radiative energy and a pseudo power flow caused by the fluctuation of the reactive energy. The energies involved in the electromagnetic mutual coupling are separated in a similar way. All energies are defined with explicit expressions in which the vector potential plays an important role. The time domain formulation and the frequency domain formulation of the theory are in consistent with each other. The theory is verified with Hertzian dipole. Numerical examples demonstrate that the theory may provide intuitive interpretation for electromagnetic radiation and mutual coupling problems.