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The Maxwell integral equations expressing Ampere's and Faraday's laws are shown to be affected by heavy physical approximations. The usual deduction from them, moreover, of the corresponding set of differential Maxwell equations is based,…
Quantum mechanics is challenging even for advanced undergraduate and graduate students. Dirac notation is a convenient notation used extensively in quantum mechanics. We have been investigating the difficulties that the advanced…
We consider time-harmonic electromagnetic wave equations in composites of a dispersive material surrounded by a classical material. In certain frequency ranges this leads to sign-changing permittivity and/or permeability. Previously meshing…
High-stakes exams play a large role in determining an introductory physics student's final grade. These exams have been shown to be inequitable, often to the detriment of students identifying with groups historically marginalized in…
Even if students can make the blend, interpret physics correctly in mathematical symbology and graphs, they still need to be able to apply that knowledge in productive and coherent ways. As instructors, we can show our solutions to complex…
The physics community explores and explains the physical world through a blend of theoretical and experimental studies. The future of physics as a discipline depends on training of students in both the theoretical and experimental aspects…
In this paper, we discuss the Maxwell equations in terms of differential forms, both in the 3-dimensional space and in the 4-dimensional space-time manifold. Further, we view the classical electrodynamics as the curvature of a line bundle,…
We present data from a between-student study on student response to questions on Newton's Third Law given throughout the academic year. The study, conducted at Rochester Institute of Technology, involved students from the first and third of…
We investigate possible evidence from Extended Theories of Electro-Magnetism by looking for deviations from the Amp\`ere-Maxwell law. The photon, main messenger for interpreting the universe, is the only free massless particle in the…
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…
We deal with the problem of assigning electromagnetic moments to a quasi-stable particle (i.e., a particle with mass located at particle's decay threshold). In this case, an application of a small external electromagnetic field changes the…
The expectation value of an observable is an important concept in quantum mechanics. However, upper-level undergraduate and graduate students in physics have both conceptual and procedural difficulties when determining the expectation value…
The modern physics course is a crucial gateway for physics majors, introducing concepts beyond the scope of K-12 education. Despite its significance, content varies widely among institutions. This study analyzes 167 modern physics syllabi…
We investigate the space-time dependence of electromagnetic fields produced by charged participants in an expanding fluid. To address this problem, we need to solve the Maxwell's equations coupled to the hydrodynamics conservation equation,…
Maxwell's macroscopic equations combined with a generalized form of the Lorentz law of force are a complete and consistent set of equations. Not only are these five equations fully compatible with special relativity, they also conform with…
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…
This paper examines the theory of electron magnetic dipole moment interactions with magnetic fields or other electrons in classical and quantum electrodynamics. We show that these interactions may be described by a version of the Poynting…
That static electric and magnetic fields can store momentum may be perplexing, but is necessary to ensure total conservation of momentum. Simple situations in which such field momentum is transferred to nearby bodies and point charges have…
The lock-in amplifier is a versatile instrument frequently used in physics research. However, many students struggle with the basic operating principles of a lock-in amplifier which can lead to a variety of difficulties. To improve…
The 100-year-long problem concerning the correct form of the electromagnetic energy-momentum tensor in continuous media (usually called the Abraham-Minkowski problem) continues to attract interest. We provide a critical analysis of…