关于麦克斯韦方程组的不带电解与电中性解的区别

Signals induced on electrodes by moving charges, a general theorem for Maxwell's equations based on Lorentz-reciprocity

We discuss a signal theorem for charged particle detectors where the finite propagation time of the electromagnetic waves produced by a moving charge cannot be neglected. While the original Ramo-Shockley theorem and related extensions are all based on electrostatic or quasi-electrostatic approximations, the theorem presented in this report is based on the full extent of Maxwell's equations and does account for all electrodynamic effects. It is therefore applicable to all devices that detect fields and radiation from charged particles.

Can the power Maxwell nonlinear electrodynamics theory remove the singularity of electric field of point-like charges at their locations?

YES! We introduce a variable power Maxwell nonlinear electrodynamics theory which can remove the singularity of electric field of point-like charges at their locations. One of the main problems of Maxwell's electromagnetic field theory is related to the existence of singularity for electric field of point-like charges at their locations. In other words, the electric field of a point-like charge diverges at the charge location which leads to an infinite self-energy. In order to remove this singularity a few nonlinear electrodynamics (NED) theories have been introduced. Born-Infeld (BI) NED theo…

An Alternative to Maxwell's Displacement Current

Though sufficient for local conservation of charge, we show that Maxwells displacement current is not necessary. An alternative to the Ampere Maxwell equation is exhibited and the alternative s electric and magnetic fields and scalar and vector potentials are expressed in terms of the charge and current densities. The alternative describes a theory in which action is instantaneous and so may provide a good approximation to Maxwells equations where and when the finite speed of light can be neglected. The result is reminiscent of the Darwin approximation which arose from the study classical char…

Direct derivation of Lienard Wiechert potentials, Maxwell's equations and Lorentz force from Coulomb's law

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…

如何从continuity equation得到麦克斯韦方程组的协变形式

How to obtain the covariant form of Maxwell's equations from the continuity equation

从电荷的连续性方程出发，导出了协变的麦克斯韦方程组。这一结果提供了一个公理化的方法，麦克斯韦方程组中，电荷守恒被强调为这些方程的基本公理。

从牛顿定律开始，通过狭义相对论的协方差要求推导麦克斯韦方程组

Derivation of Maxwell's equations via the covariance requirements of the special theory of relativity, starting with Newton's laws

麦克斯韦方程组、牛顿定律和狭义相对论之间的联系是从牛顿口头阐述他的前两个定律开始的推导建立起来的。导出的方程需要是协变的，并且简单性准则要求带电粒子上的四矢量力与四矢量速度线性相关。连接张量具有可导出的对称性，并包含电场和磁场矢量。洛伦兹力定律出现了，麦克斯韦方程组的自由空间出现的假设，张量和它的对偶必须都满足一阶偏微分方程。非均匀扩展产生电荷密度和电流密度作为场的源，并且产生电荷的电荷守恒定律。牛顿第三定律被重新解释为一个互易性陈述，它要求源项中的电荷可以被视为与测试粒子相同的物理实体，并且两者可以被分配相同的单位。无论是空间反演还是时间反演都需要协方差，这就排除了磁荷是对电荷施加力的电磁场源。

具有自量子电荷的Maxwell场的奇异源

Singular Sources of Maxwell Fields with Self-Quantized Electric Charge

考虑了真空中齐次麦克斯韦方程组的单值和多值解，其中“源”由场强的（点或弦状）奇异性形成，并且一般不可约为任何δ函数的分布。麦克斯韦方程组本身被视为一个主要的“超势”场的结果（例如，可积性条件），该场受到某些非线性和超定约束（特别是与扭量结构有关）。其结果是，我们得到（在显式或隐式代数形式）的麦克斯韦场的一个杰出的类，与奇异源必然携带一个“自量子化”的电荷整数倍的最小“基本”的。类粒子奇异体服从齐次麦克斯韦方程组的动力学方程，并经历不同类型的嬗变--分叉。所提出的方案源于作者开发的“代数动力学”方法，并在最后一节中进行了审查。附带地，建立了麦克斯韦方程组、复自对偶条件和Weyl "中微子“方程的解之间的基本等价关系，并简要地讨论了磁引力问题。

麦克斯韦猜想是错误的

The Maxwell Conjecture is False

研究构造出存在至少24个非退化临界点的五点电荷构型，证明麦克斯韦关于n个点电荷场最多有(n-1)²个非退化临界点的猜想错误。

狄拉克-麦克斯韦孤子

Dirac--Maxwell Solitons

详细分析了耦合Dirac-麦克斯韦方程组及其解的结构。场方程的数值解的情况下，球对称的引力自相互作用可以忽略不计，揭示了存在的家庭的孤子与电场的优势，完全由所观察到的电荷和质量的基础粒子。发现了一个孤子，它具有电子的电荷和质量以及10^{-23} m的电荷半径。这完全在目前实验确定的~ 10^{-18} m的上限范围内。这些颗粒的性能以及可能的扩展到这里的工作进行了讨论。