Related papers: Two paths towards circulation time derivative (Max…
Close insight into mathematical and conceptual structure of classical field theories shows serious inconsistencies in their common basis. In other words, we claim in this work to have come across two severe mathematical blunders in the very…
Following Kottler, \'E.Cartan, and van Dantzig, we formulate the Maxwell equations in a metric independent form in terms of the field strength $F=(E,B)$ and the excitation $H=({\cal D}, {\cal H})$. We assume a linear constitutive law…
Experimental validation of the Faraday's law of electromagnetic induction (EMI) is performed when an electromotive force is generated in thin copper turns, located inside a large magnetic coil. It has been established that the electromotive…
The expression for the electromagnetic field of a charge moving along an arbitrary trajectory is obtained in a direct, elegant, and Lorentz invariant manner without resorting to more complicated procedures such as differentiation of the…
An axiomatic approach to electrodynamics reveals that Maxwell electrodynamics is just one instance of a variety of theories for which the name electrodynamics is justified. They all have in common that their fundamental input are Maxwell's…
Maxwell's equations and the equations governing charged particle dynamics are presented for a rotating coordinate system with the global time coordinate of an observer on the rotational axis. Special care is taken in defining the relevant…
In accordance with an old suggestion of Asher Peres (1962), we consider the electromagnetic field as fundamental and the metric as a subsidiary field. In following up this thought, we formulate Maxwell's theory in a diffeomorphism invariant…
A broad class of contour gauges is shown to be determined by admissible contractions of the geometrical region considered and a suitable equivalence class of curves is defined. In the special case of magnetostatics, the relevant…
The induced electric field $\vec{E}(\vec{x})$ during magnetic flux entry in superconductors with arbitrary cross section $\Omega$ and general critical current law, has been evaluated by integration along the vortex penetration paths.…
The force due to electromagnetic induction on a test charge is calculated in different reference frames. The Faraday-Lenz Law and different formulae for the fields of a uniformly moving charge are used. The classical Heaviside formula for…
In this paper, the directional derivatives in accordance with the orthonormal frame {T, N, B} are defined in $M_{q}^{3}(c)$, and the extended Serret-Frenet relations by using Frenet formulas are expressed. Furthermore, we express the…
We investigated how students apply the concept of circulation when faced with problems related to the Ampere-Maxwell law. For this purpose, we designed a metacognitive pencil-and-paper question, presented it to 65 students, and analysed…
It is certain that electrical properties-whether slow (sec) or fast (nsec), even optical (fsec)-are described by Maxwell's equations, and there are terms that depend on the rate of change of the electric and magnetic fields. In particular,…
We investigate the behavior of the time derivatives of the solution to a linear time-fractional, advection-diffusion-reaction equation, allowing space- and time-dependent coefficients as well as initial data that may have low regularity.…
The integral formulation of Maxwell's equations expressed in terms of an arbitrary observer family in a curved spacetime is developed and used to clarify the meaning of the lines of force associated with observer-dependent electric and…
We derive an analytic solution for the electromagnetic vector potential in any gauge directly from Maxwell's equations for potentials for an arbitrary time-dependent charge-current distribution. No gauge condition is used in the derivation.…
The appearance of the time derivative of the acceleration in the equation of motion (EOM) of an electric charge is studied. It is shown that when an electric charge is accelerated, a stress force exists in the curved electric field of the…
Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure…
In a recent publication [Opt. Express 32, 20904 (2024)], the accuracy of the main evolution equation that governs resonator dynamics in the coupled-mode theory (CMT) was questioned. The study concluded that the driving force is proportional…
The Ampere-Maxwell's law and the displacement current constitute one of the most difficult aspects of electromagnetic theory for students in introductory electromagnetics courses. Here we present a set of examples that go beyond the…