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A new simplified approach for teaching electromagnetism is presented using the formalism of geometric algebra (GA) which does not require vector calculus or tensor index notation, thus producing a much more accessible presentation for…
We construct a number of explicit examples of hyperbolic monopoles, with various charges and often with some platonic symmetry. The fields are obtained from instanton data in four-dimensional Euclidean space that are invariant under a…
We investigate the evolution of geometric invariants, as defined by Michel \cite{Michel}, in the context of asymptotically hyperboloidal initial data sets. Our focus lies on the charges of energy and linear momentum, and we study their…
Inhomogeneous charge distributions have important repercussions on electrostatic interactions in systems of charged particles but are often difficult to examine theoretically. We investigate how electrostatic interactions are influenced by…
We reveal a new way in which the Lorenz gauge condition is related to the electric charge conservation, in a universe where electrically charged point particles are created and annihilated. We derive our results using time symmetric…
The problem concerning the form of the electrostatic field potential of the infinite charged metallic plane contacting with the metallic sphere is solved. The distributions of the surface charge densities both on the plane and the sphere…
Geometric phases play a crucial role in diverse fields. In chemistry they appear when a reaction path encircles an intersection between adiabatic potential energy surfaces and the molecular wavefunction experiences quantum-mechanical…
The problem of the `infinite energy' of a point charge is well known in connection with the Lorentz--Abraham--Dirac equation and, more significantly, in quantum electrodynamics. Though it is not stated usually, this is strongly related to…
We obtain a two-parameter set of solutions, which represents a spherically symmetric space-time with a superposition of a neutral fluid and an electric field. The electromagnetic four-potential of this Einstein-Maxwell space-time is taken…
We solve for the motion of charged particles in a helical time-periodic ABC (Arnold-Beltrami-Childress) magnetic field. The magnetic field lines of a stationary ABC field with coefficients $A=B=C=1$ are chaotic, and we show that the motion…
In this work we analyze the motion of charged particles in the background of the Kiselev geometry, which is considered here as an exact solution in the context of power-Maxwell electrodynamics. As it is well known, one can use either an…
We show that it is possible to obtain self-consistent and physically acceptable relativistic classical equations of motion for a point-like spin-half particle possessing an electric charge and a magnetic dipole moment, directly from a…
Electromagnetic quantities at a spacetime point have tensor Lorentz transformations between relatively-moving inertial frames. However, since the Lorentz transformation of time between inertial frames depends upon both the time and space…
A relativistic version of the correspondence principle, a limit in which classical electrodynamics may be derived from QED, has never been clear, especially when including gravitational mass. Here we introduce a novel classical field theory…
Modern advances in transformation optics and electromagnetic metamaterials made possible experimental demonstrations of highly unusual curvilinear optical spaces, such as various geometries necessary for electromagnetic cloaking. Recently…
Charged fluids rotating around compact objects can form unique equilibrium structures when ambient large-scale electromagnetic fields combine with strong gravity. Equatorial as well as off-equatorial toroidal structures are among such…
In nonlinear electrodynamics, QED included, we find a static solution to the field equations with an electric charge as its source, which is comprised of homogeneous parallel magnetic and electric fields, and a radial…
A new finite-range electromagnetic (EM) theory containing both electric and magnetic charges constructed using two vector potentials A^{} and Z^{} is formulated in the spacetime algebra (STA) and in the algebra of the three-dimensional…
In Klein geometric model of space the mass is manifestation of the quantized charges oscillations in additional compactified dimension. We analyze model in which common in four-dimensional space-time for mass and electric charge of the…
We consider several geometric inequalities in general relativity involving mass, area, charge, and angular momentum for asymptotically hyperboloidal initial data. We show how to reduce each one to the known maximal (or time symmetric) case…