Related papers: Can Maxwell's equations be obtained from the conti…
In a calculation that directly parallels the derivation of the Thomas precession, the first time derivative of the retarded potentials is derived. The solutions have to be integrated in time to obtain the potential solution. The Thomas…
For smooth solutions to Maxwell's equations sourced by a smooth charge-current distribution $j_a$ in stationary, asymptotically flat spacetimes, one can prove an energy conservation theorem which asserts the vanishing of the sum of (i) the…
The differential form of the Maxwell's equations was first derived based on an assumption that the media are stationary, which is the foundation for describing the electro-magnetic coupling behavior of a system. For a general case in which…
The paper studies the validity of Maxwell equation in the case for coexistence of electromagnetic field and gravitational field. With the algebra of quaternions, the Newton's law of gravitation is the same as that in classical theory of…
The form of Maxwell's theory is well known in the framework of general relativity, a fact that is related to the applicability of the principle of equivalence to electromagnetic phenomena. We pose the question whether this form changes if…
The origin of galactic and extra-galactic magnetic fields is an unsolved problem in modern cosmology. A possible scenario comes from the idea of these fields emerged from a small field, a seed, which was produced in the early universe…
In this paper we express the retarded fields of Maxwell's theory in terms of the instantaneous fields of a Galilei-invariant electromagnetic and we find the vector function whose spatial and temporal derivatives transform the instantaneous…
The Lorentz force equations provide a partial description of the geodesic motion of a charged particle on a four-manifold. Under the hypothesis that Maxwell's equations express symmetry properties of the Ricci tensor, the full…
We give a concise axiomatic introduction into the fundamental structure of classical electrodynamics: It is based on electric charge conservation, the Lorentz force, magnetic flux conservation, and the existence of local and linear…
Maxwell's equations hold in inertial reference frames in uniform translational motion relative to one another. In conjunction with the Lorentz coordinate transformation equations, the transformation equations for the electric and magnetic…
We propose a new propagation formula for the Maxwell field in de Sitter space which exploit the conformal invariance of this field together with a conformal gauge condition. This formula allows to determine the classical electromagnetic…
For explicitly time depending mass density, which satisfies a continuity equation, it is shown that Maxwell-like equations for gravitational field follow naturally without any need of General Relativity Theory approximation or related…
The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we…
In an exact quantum-mechanical framework, we show that expectation values of the second-quantized electro-magnetic fields in the Coulomb gauge, and in the presence of classical sources, automatically lead to causal and retarded…
Analysis of the original Feynman's formula for a moving point charge leads to the notion of a retarded time, which has to be treated as a field. The Lorentzian frame, the trajectory, and the retarded time field uniquely determine a system…
The concept of electromagnetic field can be neatly formulated by recognizing that the simplest form of the four-force is indeed feasible. We show that Maxwell's equations almost entirely stem from the properties of spacetime, notably from…
The purpose of this paper is to explore, in a space of four-dimensions, the possible forms that second-order, bi-scalar-vector-tensor field equations derivable from a variational principle can assume. In order to restrict this enormous…
We construct an analytic solution to Maxwell's equations that violates global charge conservation, by building on the possibilities demonstrated in [Foundations of Physics 49, 330 (2019)]. The construction is valid for a spacetime…
Local continuity equations involving background fields and variantions of the fields, are obtained for a restricted class of solutions of the Einstein-Maxwell and Einstein-Weyl theories using a new approach based on the concept of the…
Extended guiding-center Vlasov-Maxwell equations are derived under the assumption of time-dependent and inhomogeneous electric and magnetic fields that obey the standard guiding-center space-time-scale orderings. The guiding-center…