Re-interpreting the properties of the fields of a uniformly moving hertzian dipole in the vacuum

By briefly revisiting the solution of the potentials of a general electromagnetic source in the vacuum, we propose a clarification to the meanings of the three velocities associated with the electromagnetic waves in the vacuum. The conventional wave velocity c 0 represents the propagation velocity of the electromagnetic pulse generated by a delta source, and is independent on the sources and the observers; the phase velocity represents the propagation velocity of the equi-phase surfaces, and the energy velocity represents the propagation velocity of the field in the direction of the Poynting vector. The Liénard-Wiechert form of the electromagnetic fields of a uniformly moving Hertzian dipole in the vacuum is derived using the two-charge model. Based on the causality principle, the explicit expressions for the phase velocity, the energy velocity, and the Doppler shift in the far fields are derived. The results show that the phase velocity is dependent on the choice of the reference point. The energy velocity is equal to the wave velocity. All the three velocities cannot be added to the moving velocity of the source like vectors. The Doppler effect is also anisotropic. The frequency and the radiation pattern of the Hertzian dipole may change with the moving velocity. Mathematically, when the Hertzian dipole moves faster than the light, the causal solutions of the fields will behave like electromagnetic shock waves.