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A new formulation of the Maxwell equations based on two vector and two scalar potentials is proposed. The use of these potentials allows the electromagnetic field equations to be written in the form of a hyperbolic system. In contrast to…
For the system of Maxwell equations of electromagnetism in an $l$-periodic composite medium of overall size $L$ ($0<l<L<\infty$), in the low-frequency quasistatic approximation, we develop an electromagnetic version of strain-gradient…
Teaching electromagnetism by demonstrating a practical application associated with learning content is an important teaching technique. Demonstrations are often performed through video-assisted procedures, and are usually limited to a…
This article contains a digest of the theory of electromagnetism and a review of the transformation between inertial frames, especially under low speed limits. The covariant nature of the Maxwell's equations is explained using the…
We introduce the concept of emergent electric field. This is distinguished from the fundamental one in that the emergent electric field directly appears in observations through the Lorentz force, while the latter enters the phase space as…
We develop some ideas about gauge symmetry in the context of Maxwell's theory of electromagnetism in the Hamiltonian formalism. One great benefit of this formalism is that it pairs momentum and configurational degrees of freedom, so that a…
Maxwell theory is usually treated in the lab frame under the standard time order (light-signal clock synchronization). Particle tracking in the lab frame usually treats time as an independent variable. Then, the evolution of electron beams…
The Lorenz electromagnetic theory of light, published two years after the Maxwell theory, starts by postulating that both scalar and vector potentials are retarded. We show that in spite of this postulate, Lorenz's theory gives a…
Electromagnetic theory is central to physics. An undergraduate major in physics typically takes a semester or a year of electromagnetic theory as a junior or senior, and a graduate student in physics typically takes an additional semester…
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…
The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz's…
This paper summarizes the motivations and results obtained so far in the frame of a particular non-linearization of Classical Electrodynamics, which was called Extended Electrodynamics. The main purpose pursued with this non-linear…
Textbooks frequently use the Helmholtz theorem to derive expressions for the electrostatic and magnetostatic fields but they do not usually apply this theorem to derive expressions for the time-dependent electric and magnetic fields, even…
Lorentz reciprocity establishes a stringent relation between electromagnetic fields and their sources. For static magnetic fields, a relation between magnetic sources and fields can be drawn in analogy to the Green's reciprocity principle…
Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…
Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the…
We explore dynamical features of the maximally symmetric nonlinear extension of classical electromagnetism, recently proposed in the literature as ``ModMax'' electrodynamics. This family of theories is the only one that preserves all the…
The study explores the conformable electromagnetic field theory. The concept of the conformable delta function is introduced. Subsequently, the conformable Maxwell's equations are derived.
We outline a regular way for solving Maxwell's equations. We take, as the starting point, the notion of vector potentials. The rationale for introducing this notion in electrodynamics is that the set of Maxwell's equations is seemingly…
The classical Maxwell--Born--Infeld field equations coupled with a Hamilton--Jacobi law of point charge motion are partially quantized by coupling the Hamilton-Jacobi phase function with an amplitude function, which combines with the phase…