Related papers: Revisiting the charging-capacitor problem
We formulate an existence theorem that states that given localized scalar and vector time-dependent sources satisfying the continuity equation, there exist two retarded fields that satisfy a set of four field equations. If the theorem is…
Electricity plays a special role in our lives and life. Equations of electron dynamics are nearly exact and apply from nuclear particles to stars. These Maxwell equations include a special term the displacement current (of vacuum).…
The decay of the electrical energy in a resistor-vacuum capacitor circuit is shown to involve multiple relaxation processes, with dramatically different time constants. This is measured using a vacuum capacitor to eliminate the effect of a…
Nonlinear elements in a rectifying circuit can be used to harvest energy from thermal fluctuations either steadily or transitorily. We study an energy harvesting system comprising a small variable capacitor (e.g., free standing graphene)…
Electrochemical devices often charge both through Faradaic reactions and electric double layer formation. Here, we study these coupled processes in a model system of a long electrolyte-filled pore subject to a small suddenly-applied…
The notion of a compact object immune to the horizon problem and comprising an anisotropic inhomogeneous fluid with a specific radial pressure behavior, i.e. the gravastar, is extended by introducing an electrically charged component.…
A charged parallel plate capacitor will create particle-antiparticle pairs by the Schwinger process and discharge over time. We consider the full quantum discharge process in 1+1 dimensions including backreaction, when the electric field…
With use the Hamiltonian form of the Maxwell's equations one biquaternionic model for electro-gravimagnetic (EGM) field is offered. The equations of the interaction of EGM-fields, which are generated by different charge and current, are…
Most capacitors do not satisfy the conventional assumption of a constant capacitance. They exhibit memory which is often described by a time-varying capacitance. It is shown that the classical relation, $Q\left(t\right)=CV\left(t\right)$,…
The possibility of an incompletness of the equations of electromagnetism is analyzed using a thought experiment that shows a non-physical behavior according to classical electromagnetism. Basically, from Maxwell equations it is shown that a…
A variational approach is used in order to study the stationary states of Hall devices. Charge accumulation, electric potentials and electric currents are investigated on the basis of the Kirchhoff-Helmholtz principle of least heat…
In this paper we study the Cauchy problem associated to the Maxwell-Schr\"odinger system with a defocusing pure-power non-linearity. This system has many applications in physics, for instance in the description of a charged non-relativistic…
We outline a regular way for solving Maxwell's equations. We take, as the starting point, the notion of vector potentials. The rationale for introducing this notion in electrodynamics is that the set of Maxwell's equations is seemingly…
We propose a generalized London theory that can correctly describe the longitudinal and transverse responses of conventional superconductors to an electromagnetic field. The continuity equation is satisfied by use of a special gauge for the…
Quaternion analysis of time dependent Maxwell's equations in presence of electric and magnetic charges has been developed and the solutions for the classical problem of moving charges (electric and magnetic) are obtained in unique, simple…
We investigate a quantum battery system under both external driving and dissipation. The system consists of a coupled two-level charger and battery immersed in nonequilibrium fermionic reservoirs. By considering the changes in the energy…
In this brief note, we consider a wave equation that has both trapping and a complex potential. For this problem, we prove a uniform bound on the energy and a Morawetz (or integrated local energy decay) estimate. The equation is a model…
A configuration of a test magnetic field in Hayward spacetime is obtained by solving Maxwell's equation with the Hayward metric as the background. The magnetic field lines show a dipole loop-like configuration in the regular Hayward…
In Maxwell's equations, the electric field can be expressed as the sum of the Coulombic field associated with the electric charge and the induced field associated with the time variation of the magnetic field from Faraday's law. The same…
The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we…