In this paper, the solution to long standing problem of deriving Maxwell’s equations and Lorentz force from first principles, i.e., from Coulomb’s law, is presented. This problem was studied by many authors throughout history but it was never satisfactorily solved, and it was never solved for charges in arbitrary motion. In this paper, relativistically correct Liénard–Wiechert potentials for charges in arbitrary motion and Maxwell equations are both derived directly from Coulomb’s law by careful mathematical analysis of the moment just before the charge in motion stops. In the second part of this paper, the electrodynamic energy conservation principle is derived directly from Coulomb’s law by using similar approach. From this energy conservation principle the Lorentz force is derived. To make these derivations possible, the generalized Helmholtz theorem was derived along with two novel vector identities. The special relativity was not used in our derivations, and the results show that electromagnetism as a whole is not the consequence of special relativity, but it is rather the consequence of time retardation.
The paper presents the numerical results for the induced electric field in the various models of the human eye and the head. The comparison between the extracted or the single organ models and the compound organ models placed inside realistic head models obtained from the magnetic resonance imaging scans is presented. The numerical results for several frequencies and polarizations of the incident electromagnetic (EM) plane wave are obtained using the hybrid finite element method/boundary element method (FEM/BEM) formulation and the surface integral equation (SIE) based formulation featuring the use of method of moments, respectively. Although some previous analysis showed the similar distribution of the induced electric field along the pupillary axis obtained in both eye models, this study showed this not to be the case in general. The analysis showed that the compound eye model is much more suitable when taking into account the polarization of the incident EM wave. The numerical results for the brain models showed much better agreement in the maximum values and distributions of the induced surface field between detailed models, while homogeneous brain model showed better agreement with the compound model in the distribution along selected sagittal axis points. The analysis could provide some helpful insights when carrying out the dosimetric analysis of the human eye and the head/brain exposed to high frequency EM radiation.
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