Tiered Structure of Maxwell's Equations

The electric and magnetic fields can be written in terms of two vector potentials A and C with the corresponding scalar potentials ϕA and ϕC. It will be shown, that with the appropriate definitions, the relationship between the vector potentials A and C is equivalent to the relations between the E and B fields. These potentials can in turn be described in terms of other potpotentials A (2) and C(2) and the process can be carried out ad infinitum. The tiered structure is first shown in the temporal gauge where the scalar potentials are zero. Thereafter, the procedure is recreated in the Lorenz gauge. In this gauge, the potpotentials A (2) and C(2) are equal to scaled Hertz vectors. This procedure is a novel and simple derivation of the Hertz polarization potentials. The continuity equation of the rotational content of the EM field is evaluated in the second tier. These results are compared with the well known helicity density and flux definitions. The assessed density and its flow can be mapped from one tier to the next, by evaluation of the time derivative of each of the field functions involved prior to taking the products.