Related papers: When negative is not "less than zero": Electric ch…
The present tutorial aims at covering the fundamentals of electromagnetism, in a condensed and clear manner. Some solved and proposed exercises have been included. The reader is assumed to have knowledge of basic electricity, partial…
Negative and complex numbers are so familiar in modern mathematics, physics, and engineering that it is easy to forget how uncertain their status once was. They did not become established through a single route. This article follows four…
Electromagnetic field together with zero-mass charges moving in this field form a well-behaved semi-dissipative dynamical system -- Electrodynamics of Massless Charges (EMC). We give equations of EMC, argue that EMC is an adequate theory…
In gauge theories like the standard model, the electric charges of the fermions can be heavily constrained from the classical structure of the theory and from the cancellation of anomalies. We argue that the anomaly conditions are not quite…
We have been investigating the difficulties that students in upper-level undergraduate courses have in determining the probability distribution for measuring energy and position as a function of time when the initial wave function is…
Electromagnetic particle is considered as appropriate particle solution of nonlinear electrodynamics. Mass, spin, charge, and dipole moment for the electromagnetic particle are defined. Classical motion equations for massive charged…
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…
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…
The performance of over 2000 students in introductory calculus-based electromagnetism (E&M) courses at four large research universities was measured using the Brief Electricity and Magnetism Assessment (BEMA). Two different curricula were…
A theory containing both electric and magnetic charges is formulated using two vector potentials, $A_{\mu}$ and $C_{\mu}$. This has the aesthetic advantage of treating electric and magnetic charges both as gauge charges, but it has the…
We analyze the motion of an electric charge in the field of a magnetically charged event in three-dimensional spacetime. We start by exhibiting a first integral of the equations of motion in terms of the three conserved components of the…
The notion that the electromagnetic field is quantised is usually inferred from observations such as the photoelectric effect and the black-body spectrum. However accounts of the quantisation of this field are usually mathematically…
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…
Electromagnetism becomes a nonlinear theory having (effective) photon-photon interactions due at least to electron-positron fluctuations in the vacuum. We discuss the consequences of the nonlinearity for the force felt by a charge probe…
The Dirac approach to include magnetic charge in Maxwell's equations places the magnetic charge at the end of a string on which the the fields of the theory develop a singularity. In this paper an alternative formulation of classical…
We discuss the clusters of resources that emerge when upper-division students write about electromagnetic fields in linear materials. The data analyzed for this paper comes from students' written tests in an upper-division electricity and…
From non-linear theory of electromagnetism, suggested in (physics/9801031), follows that non-relativistic equation for scalar potential of electron in the field of nuclei is equivalent to respective Schr\"odinger equation. For mass and…
The charge on an atom at a metallic surface in an electric field is defined as the field-derivative of the force on the atom, and this is consistent with definitions of effective charge and screening charge. This charge can be found from…
In this work, we present an explanation of the electric charge quantization based on a semi-classical model of electrostatic fields. We claim that in electrostatics, an electric charge must be equal to a rational multiple of the elementary…
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…