Title: A contradiction in the experimental and mathematical validation of Maxwell's equations
Abstract: The Liénard-Wiechert (LW) equations are used to numerically evaluate the electric and magnetic fields of a constant current of discrete point charges including a section, where the charge carriers are first accelerated and then decelerated. The total fields are shown to satisfy the laws of Ampere-Maxwell (AM) and Gauss. The far-field part of this solution is coherent with approximately static E and B fields. This is in conflict with comparable theoretical treatments, where the total far-field is assumed to be incoherent, and the predicted radiation is oscillating. Further, the study shows that energy is not conserved internally in the total LW far-field. In conclusion, these findings suggest that the total LW far-field, that is used to validate Maxwell's equations mathematically, is non-physical. Consequently, AM's and Gauss's law may not be generally valid in the case of accelerated charges.