Since a classical charged point particle radiates energy and momentum it is argued that there must be a radiation reaction force. Here we present an action for the Maxwell-Lorentz without self interactions model, where each particle only responds to the fields of the other charged particles. The corresponding stress-energy tensor automatically conserves energy and momentum in Minkowski and other appropriate spacetimes.
In 19th century Maxwell derived Maxwell equations from the knowledge of three experimental physical laws: the Coulomb's law, the Ampere's force law and Faraday's law of induction. However, theoretical basis for Ampere's force law and Faraday's law remains unknown to this day. Furthermore, the Lorentz force is considered as experimental phenomena, the theoretical foundation of this force is still unknown. To answer these fundamental theoretical questions, we derive Lienard Wiechert potentials, Maxwell's equations and Lorentz force from two simple postulates: (a) when all charges are at rest the…
In a brief but brilliant derivation that can be found in Maxwell's Treatise and traced back to his 1861 and 1865 papers, he derives the force on a moving electric charge subject to electromagnetic fields from his mathematical expression of Faraday's law for a moving circuit. Maxwell's derivation in his Treatise of this force, which is usually referred to today as the Lorentz force, is given in detail in the present paper using Maxwell's same procedure but with more modern notation.
This article deals with the study of electromagnetic waves equations and the Lorentz condition, as emergent properties of Maxwell's system in the context of systems theory. To do this, the wave equations and the Helmholtz equation are first deduced. Using the displaced Dirac operator, which is closely related to the main vector calculation operators, it is possible to establish a direct connection between the solutions of the Maxwell time-harmonic system and two quaternion equations. Also, the application of the Lorentz condition to transform the time-harmonic Maxwell system into a simple quat…
This letter reports on a metriplectic formulation of collisional, nonlinear full-$f$ electromagnetic gyrokinetic theory compliant with energy conservation and monotonic entropy production. In an axisymmetric background magnetic field, the toroidal angular momentum is also conserved. Notably, a new collisional current, contributing to the gyrokinetic Maxwell-Ampère equation and the gyrokinetic charge conservation law, is discovered.
Electromagnetic force and torque are typically derived from a stress tensor in conjunction with Maxwell's equations of classical electrodynamics. In some instances, the Principle of Least Action (built around a Lagrangian) can be used to arrive at the same mathematical expressions of force and torque as those derived from a stress tensor. This paper describes some of the underlying arguments for the existence of a Lagrangian in the case of certain simple physical systems. While some formulations of electromagnetic force and torque admit a Lagrangian, there are other formulations for which a La…
We use the method of field decomposition, a technique widely used in relativistic magnetohydrodynamics, to study the small velocity approximation (SVA) of the Lorentz transformation in Maxwell equations for slowly moving media. The "deformed" Maxwell equations derived under the SVA in the lab frame can be put into the conventional form of Maxwell equations in the medium's comoving frame. Our results show that the Lorentz transformation in the SVA up to $O(v/c)$ ($v$ is the speed of the medium and $c$ is the speed of light in vacuum) is essential to derive these equations: the time and charge d…
在这篇文章的第一部分，我们讨论了两个变化的麦克斯韦方程组，已在早期的工作-一类非线性麦克斯韦理论与明确的伽利略限制（和相应的广义杨米尔斯方程），和线性修改的动机耦合的电磁势与一定的非线性薛定谔方程。在最后一节中，我们将重温洛伦兹的一个旧思想，写出麦克斯韦方程组，以证明这样一种理论：同性电荷之间的排斥静电力与异性电荷之间的吸引静电力的大小根本不同。我们详细阐述了洛伦兹的描述，通过电和磁场强度，其控制方程分为两个完全相对论性的麦克斯韦系统-一个描述普通的电磁，和其他描述一个普遍的吸引力或排斥力的长程力。如果这样的力不能被已知的物理原理{ \it a priori}排除，那么它的大小应该通过实验来确定或界定。如果它真的存在，那么有趣的可能性就超出了洛伦兹早期关于它与（牛顿）引力的关系的猜想。
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 containing a temporary singularity and a Maxwellian electrodynamics containing a proposed "topological" axion field. As such, it demonstrates that although "physics breaks down" at a singularity, the physical laws on the spacetime still impose constraints on what can happen. Further, the concepts of transformation optics can be applied to show that our specific mathe…
