Related papers: On the Solvability of Maxwell's Equations
The recently re-discovered multipole vector approach to understanding the harmonic decomposition of the cosmic microwave background traces its roots to Maxwell's Treatise on Electricity and Magnetism. Taking Maxwell's directional derivative…
Expectation values of the electromagnetic field and the electric current are introduced at space-time resolution which belongs to the quantum domain. These allow us to approach some key features of classical electrodynamics from the…
The complex form of Maxwell equations has been constructed as one equation for 3-dimensional complex A-vector. The real and imaginary parts of this vector are described with use of electric and magnetic tensions accordingly. With using a…
Gauge transformations are potential transformations that leave only specific Maxwell fields invariant. To reveal more, I develop Lorenz field equations with full Maxwell form for nongauge, sans gauge function, transformations yielding…
The Coulomb force, established in the rest frame of a source-charge $Q$, when transformed to a new frame moving with a velocity $\vec{V}$ has a form $\vec{F}= q\vec{{E}} + q\vec{v} \times \vec{{B}}$, where $\vec{{E}}=\vec{E}'_\parallel +…
Numerical results based on an extended BPM algorithm indicate that, in Marcatili's lossless tapers and bends, through-flowing waves are drastically different from standing waves. The source of this surprising behavior is inherent in…
A long-standing controversy concerning the causes of the magnetic field in and around a parallel-plate capacitor is examined. Three possible sources of contention are noted and detailed. The first is the ambiguous initial impression given…
In this work, the paraxial version of Maxwell equations is derived with the use of two Riemann-Silberstein vectors. Exact solutions of these equations are then obtained representing the paraxial electromagnetic fields. These fields satisfy…
The solution to the wave equation as a Cauchy problem with prescribed fields at an initial time t=0 is purely retarded. Similarly, in the quantum theory of radiation the specification of Heisenberg picture photon annihilation and creation…
The Maxwell equations for an homogeneous medium in which electric currents are composed of Ohmic, diffusive and impressed currents are written in the static approximation in which displacements currents are neglected. Closed exact…
A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive and absorbing dielectric medium is developed. The classical Maxwell equations with spatially…
We begin by reviewing the derivation of generalized Maxwell equations from an operational definition of the electromagnetic field and the most basic notions of what constitutes a dynamical field theory. These equations encompass the…
We consider time-harmonic Maxwell's equations set in an heterogeneous medium with perfectly conducting boundary conditions. Given a divergence-free right-hand side lying in $L^2$, we provide a frequency-explicit approximability estimate…
In his recently discovered handwritten notes on "An alternate way to handle electrodynamics" dated on 1963, Richard P. Feynman speculated with the idea of getting the inhomogeneous Maxwell's equations for the electric and magnetic fields…
A new representation for solutions of Maxwell's equations is derived. Instead of being expanded in plane waves, the solutions are given as linear superpositions of spherical wavelets dynamically adapted to the Maxwell field and…
The multipole expansion for electromagnetic radiation, valid for all wave-lengths and all distances from bounded sources, is presented in Lorentz gauge, rather than the usual Coulomb gauge. This gauge is likely to be preferred in…
We applied an effective approximation into Maxwell's equations with an axion interaction for haloscope searches. A set of Maxwell's equations acquired from this approximation describes just the reacted fields generated by the anomalous…
The Maxwell's electromagnetic equations are isomorphic to the motion equation of a linear elastic continuum which is hard to compression though liable to shear deformation. The Coulomb gauge expresses the medium incompressibility. The…
The stationary Maxwell-Born-Infeld field equations of electromagnetism with integrable regular sources in a Hoelder space are solved using a perturbation series expansion in powers of Born's electromagnetic constant. The convergence of the…
We study the retarded field sourced by a uniformly accelerated particle in a non-local scalar field theory. While the presence of non-locality regularizes the field at the location of the source, we also show that Lorentz-invariant…