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A new formulation of electromagnetism based on linear differential commutator brackets is developed. Maxwell equations are derived, using these commutator brackets, from the vector potential $\vec{A}$, the scalar potential $\phi$ and the…
The fallacies associated with the gauge concept in electromagnetism are illustrated. A clearer and more valid formulation of the basics of classical electromagnetism is provided by recognizing existing physical constraints as well as the…
We consider the electrodynamics of electric charges and currents in vacuum and then generalise our results to the description of a dielectric and magnetic material medium : first in spatial algebra (SA) and then in space-time algebra (STA).…
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…
Theoretical comment for the registration of longitudinal electric waves in interacting laser beams is given. Recent information on longitudinal electric and scalar waves in plasma, plasmons, waveguides, antennas and nano-structures is…
In the present paper it is shown that the Maxwell theory can be finely represented in the matrix form of Dirac's equation, if the Dirac wave function is identified with the electromagnetic wave by defined way. It seems to us, that such…
Causality in electrodynamics is a subject of some confusion, especially regarding the application of Faraday's law and the Ampere-Maxwell law. This has led to the suggestion that we should not teach students that electric and magnetic…
Using geometric algebra and calculus to express the laws of electromagnetism we are able to present magnitudes and relations in a gradual way, escalating the number of dimensions. In the one-dimensional case, charge and current densities,…
Although relativistic electrodynamics is more than 100 year old, there is one neglected topic in its presentation and application: relativistic transformations of electromagnetic integrals. Whereas in theoretical and applied electrodynamics…
Learning to use math in physics involves combining (blending) our everyday experiences and the conceptual ideas of physics with symbolic mathematical representations. Graphs are one of the best ways to learn to build the blend. They are a…
The Physics Education Group at the University of Washington is examining the extent to which students are able to use graphs of potential energy vs. position to infer kinematic and dynamic quantities for a system. The findings indicate that…
The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which…
We study differential equations, describing interaction of electromagnetic field with moving sidebars and surfaces, coming from integral electrodynamics laws. It is shown that differential equations contain but the such features of…
The governing equations of Maxwell electrodynamics in multi-dimensional spaces are derived from the variational principle of least action which is applied to the action function of the electromagnetic field. The Hamiltonian approach for the…
We describe a study on the conceptual difficulties faced by college students in understanding hydrodynamics of ideal fluids. This study was based on responses obtained in hundreds of written exams and oral interviews, which were held with…
Throughout introductory physics, students create and interpret free body diagrams in which multiple forces act on an object, typically at a single location (the object's center of mass). The situation increases in difficulty when multiple…
We discuss the great importance of using mathematical software in solving problems in today's society. In particular, we show how to use Mathematica software to solve ordinary differential equations exactly and numerically. We also show how…
Symbolic equations are one of the many representations used in physics. Understanding these representations is important for students because they are how students access knowledge in physics. In this paper I build off of the work by Redish…
Upper-division physics students spend much of their time solving problems. In addition to their basic skills and background, their epistemic framing can form an important part of their ability to learn physics from these problems.…
Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired at the introductory and intermediate levels.…