AbstractThis study investigates the curved worldline of a charged particle accelerated by an electromagnetic field in flat spacetime. A new metric, which dependes on the charge-to-mass ratio and electromagnetic potential, is proposed to describe the curve characteristic of the world-line. The main result of this paper is that an equivalent equation of the Lorentz equation of motion is put forward based on a 4-dimensional Riemannian manifold defined by the metric. Using the Ricci rotation coefficients, the equivalent equation is self-consistently constructed. Additionally, the Lorentz equation of motion in the non-inertial reference frames is studied with the local Lorentz covariance of the equivalent equation. The model attempts to geometrize classical electromagnetism in the absence of the other interactions, and it is conducive to the establishment of the unified theory between electromagnetism and gravitation.

Apart from an introductory chapter which focuses mainly on some important mathematical concepts and analytical techniques, this book consists entirely of questions and solutions on topics in classical electromagnetism. The questions are divided into three categories according to their ‘level of difficulty’, and the book should appeal to students who are at different stages in their respective degrees. A wide range of topics are treated which include: the basic experimental laws of electricity and magnetism, Maxwell’s equations, electric and magnetic fields in vacuum and in matter, electromagnetic waves with applications to waveguides and antennas, the electromagnetic potentials, multipole expansions and multipole moments, gauge transformations, electric circuits, electromagnetic radiation, the electromagnetic field tensor and covariance. The solutions are usually followed by a set of comments intended to stimulate inductive reasoning and provide additional information of interest (including points of historical significance). Both analytical and numerical techniques are used to obtain and analyse solutions. The computer calculations use Mathematica (version 10), and the relevant code is given in the text. The book will be useful to students and lecturers in undergraduate and graduate-level courses on classical electromagnetism and in computational physics.

If the interior of a conducting cavity (such as a capacitor or a coaxial cable) is supplied with a very high-frequency electric signal, the information between the walls propagates with an appreciable delay, due to the _niteness of the speed of light. The con_guration is typical of cavities having size larger than the wavelength of the injected signal. Such a non rare situation, in practice, may cause a break down of the performances of the device. We show that the classical Coulomb's law and Maxwell's equations do not correctly predict this behavior. Therefore, we provide an extension of the modeling equations that allows for a more reliable determination of the electromagnetic _eld during the evolution process. The main issue is that, even in vacuum (no dielectric inside the device), the fast variation of the signal produces sinks and sources in the electric _eld, giving rise to zones where the divergence is not zero. These regions are well balanced, so that their average in the domain is zero. However, this behavior escapes the usual treatment with classical electromagnetism.

A tensorial method was used in computing the intensity of Ultra High Frequency(UHF) radiation within 2D and 3D geometrical structures. This was done based on the theoretical concepts of classical electromagnetism. Using a software program, “power estimator” the intensities at various distances from the source of radiation were obtained and it was found that shapes which are less geometrically homogenous exhibits high intensity values and that the maximum intensity value was observed within a cylinder to be 1534.70w/m² at 0.02m away from the source of radiation, while the minimum intensity value was observed in a circle at 0.10m away from the source to be 2.49w/m².

The formulation of a complete theory of classical electromagnetism by Maxwell is one of the milestones of science. The capacity of many-body systems to provide emergent mini-universes with vacua quite distinct from the one we inhabit was only recognized much later. Here, we provide an account of how simple systems of localized spins manage to emulate Maxwell electromagnetism in their low-energy behaviour. They are much less constrained by symmetry considerations than the relativistically invariant electromagnetic vacuum, as their substrate provides a non-relativistic background with even translational invariance broken. They can exhibit rich behaviour not encountered in conventional electromagnetism. This includes the existence of magnetic monopole excitations arising from fractionalization of magnetic dipoles; as well as the capacity of disorder, by generating defects on the lattice scale, to produce novel physics, as exemplified by topological spin glassiness or random Coulomb magnetism. This article is part of the themed issue ‘Unifying physics and technology in light of Maxwell's equations’.