With use the Hamiltonian form of the Maxwell's equations one biquaternionic model for electro-gravimagnetic (EGM) field is offered. The equations of the interaction of EGM-fields, which are generated by different charge and current, are built. The field analogs of three Newton's laws are offered for free and interacting charge-currents, as well as total field of interaction. The invariance of these equations at Lorentz transformation is investigated, and, in particular, of the charge-current conservation law. It is shown that, by fields interaction, this law differs from the well-known one. The new modification of the Maxwell's equations is offered with entering the scalar resistance field in biquaternion of EGM-field tension. Relativistic formulae of the transformation of density of the masses and charge, current, forces and their powers are built. The solution of the Cauchy problem is given for equation of charge-current transformations.Comment: 15 pages; Physical Mathematics, Vol.1(2009
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