The change of the electromagnetic field in a particular place due to the event of a change in the motion of a charged particle can occur only after the light signal from the event can reach this place. Naive calculations of the electromagnetic energy and the work performed by the electromagnetic fields might lead to paradoxes of apparent non-conservation of energy. A few paradoxes of this type for a simple motion of two charges are presented and resolved in a quantitative way providing deeper insight into various relativistic effects in the classical electromagnetic theory.
We report a new energy conservation law for time-harmonic electromagnetic fields, which is valid for an arbitrary medium. In contrast to the well-established Poynting theorem for time-harmonic fields, the real part of the new energy conservation law gives an equation for the sum of stored electric and magnetic field energies and the imaginary part involves an equation related to the difference between the dissipated electric and magnetic energies. Universally applicable expressions for both the electric and magnetic field energies have been obtained and demonstrated to be valuable in character…
The form of the energy-momentum tensor when a quasimonochromatic field propagates into and through an antireflection-coated, sourceless, transparent, continuous, linear magneto-dielectric medium, initially at rest in the local frame, remains controversial. The Minkowski energy-momentum tensor is the main component of the electromagnetic conservation law. It has been known for over a century that the electromagnetic conservation law is unsound as evidenced by alternative energy-momentum tensors that have been proposed to ameliorate known physical deficiencies (violation of conservation of angul…
The most general expressions of the stored energies for time-harmonic electromagnetic fields are derived from the time-domain Poynting theorem, and are valuable in characterizing the energy storage and transport properties of complex media. A new energy conservation law for the time-harmonic electromagnetic fields, which involves the derived general expressions of the stored energies, is introduced. In contrast to the well-established Poynting theorem for time-harmonic fields, the real part of the new energy conservation law gives an equation for the sum of stored electric and magnetic field e…
The Abraham--Minkowski controversy refers to a long-standing inability to adequately address certain issues involving the conservation of the momentum of an electromagnetic field in a linear dielectric medium. We apply the usual assumption of a material subsystem that couples to the electromagnetic subsystem such that the total energy and total momentum are conserved. We then construct the total energy--momentum tensor from the total energy density and the total momentum density. Applying conservation principles to the total energy--momentum tensor, we construct the tensor energy--momentum con…
It is shown that violation of the Born Rule leads to a breakdown of the correspondence between the quantum electromagnetic field and its classical counterpart. Specifically, the relationship of the quantum coherent state to the classical electromagnetic field turns out to imply that if the Born Rule were violated, this could result in apparent deviations from the energy conservation law applying to the field and its sources (Poynting's Theorem). The result suggests that the Born Rule is just as fundamental a law of Nature as are the conservation laws.
From the energy-momentum tensors of the electromagnetic field and the mechanical energy-momentum, the equations of energy conservation and balance of electromagnetic and mechanical forces are obtained. The equation for the Abraham force in a dielectric medium with losses is obtained
Using classical electrodynamics, this work analyzes the dynamics of a closed microwave cavity as a function of its center of energy. Starting from the principle of momentum conservation, expressions for the maximum electromagnetic momentum stored in a free microwave cavity are obtained. Next, it is shown that, for coherent fields and special shape conditions, this momentum component may not completely average out to zero when the fields change in the transient regime. Non-zero conditions are illustrated for the asymmetric conical frustum whose exact modes can not be calculated analytically. On…
This pedagogical note revisits the concept of electromagnetic helicity in classical systems. In particular, magnetic helicity and its role in mean field dynamo theories is briefly discussed highlighting the major mathematical inconsistency in most of these theories---violation of magnetic helicity conservation. A short review of kinematic dynamo theory and its classic theorems is also presented in the Appendix.
The symmetric tensor energy-impulse of interaction of collective of electric charges with an electromagnetic field is received. A system of covariant energy and momentum conservation equations or a system of equations for the collective motion of charged particles is derived from this tensor. From this system Expressions are derived for collective electrodynamics forces. From the energy-momentum tensor derived the tensor of collective electrodynamics forces is.
A new system of general Navier-Stokes-like equations is proposed to model electromagnetic analogous to hydrodynamic. While most attempts to derive analogues of hydrodynamic to electromagnetic, and vice-versa, start with Navier-Stokes or a Euler approximation, we propose general conservation equations as a starting point. Such equations provide a structured framework from which additional insights into the problem at hand could be obtained. To that end, we propose a system of momentum and mass-energy conservation equations coupled through both momentum density and velocity vectors.
Mechanical angular momentum is not conserved in systems involving electromagnetic fields with non-zero electromagnetic field angular momentum. Conservation is restored only if the total (mechanical and field) angular momentum is considered. Previous studies have investigated this effect, known as "Feynman's Electromagnetic Paradox" or simply "Disk Paradox" in the context of idealized systems (infinite or infinitesimal solenoids and charged cylinders etc). In the present analysis we generalize previous studies by considering more realistic systems with finite components and demonstrating explic…
Challenging the Law of Energy Conservation Through Superposed Waves Based on Spatial Symmetry of Two RF Sources: Theoretical Derivation and Experimental Verification
In electrostatics, we can use either potential energy or field energy to ensure conservation of energy. In electrodynamics, the former option is unavailable. To ensure conservation of energy, we must attribute energy to the electromagnetic field and, in particular, to electromagnetic radiation. If we adopt the standard energy density for the electromagnetic field, then potential energy seems to disappear. However, a closer look at electrodynamics shows that this conclusion actually depends on the kind of matter being considered. Although we cannot get by without attributing energy to the elect…
