I have made some revisions according to the advices of other researchers and submitted a new version of the theory (v4). I also have added a supplementary material for the the new version, including some detailed explanations and derivations.

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 considered to be attached to the sources as the same in the charged particle theory. 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. It is a kind of oscillating energy and is considered to be responsible for energy exchange between the reactive energy and the radiative energy, performing like the Schott energy in the charged particle theory. As the Poynting vector describes the total power flux density related to the total electromagnetic energy, it should include the contributions of the real radiative power and a pseudo power flow caused by the fluctuation of the reactive energy. The energies involved in the electromagnetic mutual coupling are interpreted in a similar way. In the theory, 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 also verified with Hertzian dipole. Numerical examples demonstrate that the theory may provide insightful interpretation for electromagnetic radiation and mutual coupling problems.