Related papers: Image Charges Re-Imagined
The geometry of the elementary charge is studied in the framework of the concept of space considered as a tessellation lattice ('tessellattice'), which has recently been developed by M. Bounias and the author. The descriptive-geometric…
A classical problem in acoustic (and electromagnetic) scattering concerns the evaluation of the Green's function for the Helmholtz equation subject to impedance boundary conditions on a half-space. The two principal approaches used for…
Two-dimensional Born-Infeld electrostatic fields behaving as the superposition of two point-like charges in the linearized (Maxwellian) limit are worked out by means of a non-holomorphic mapping of the complex plane. The changes underwent…
We derive analytical expressions for external fields of a relativistic bunch of charged particles with a circular and an elliptical cross section under different boundary conditions and interaction of the fields with an accelerator…
We evaluate the electrostatic potential and the electrostatic field created by a point charge and an arbitrarly oriented electrical dipole placed near a grounded perfectly conducting sphere. Induced surface charge distributions as well as…
We develop a systematic approach to calculating the electrostatic force between point charges in an arbitrary geometry with arbitrary boundary conditions. When the boundary is present, the simple expression for the force acting on a charge…
This letter announces and summarizes results obtained in arXiv:1111.5051 and considers several natural extensions. The aforementioned paper proposes a procedure to reconstruct coefficients in a second-order, scalar, elliptic equation from…
We show that in the grounded conducting sphere image problem, all the necessary information about the image charge can be found from a mirror equation and a magnification formula. Then, we propose a method to solve the image problem for an…
I derive formulas for the electrostatic potential of a charge in or near a membrane modeled as one or more dielectric slabs lying between two semi-infinite dielectrics. One can use these formulas in Monte Carlo codes to compute the…
We analytically examine the pair interaction for parallel, discrete helices of charge. Symmetry arguments allow for the energy to be decomposed into a sum of terms, each of which has an intuitive geometric interpretation. Truncated Fourier…
In the study of colloidal, biological and electrochemical systems, it is customary to treat surfaces, macromolecules and electrodes as homogeneously charged. This simplified approach is proven successful in most cases, but fails to describe…
Two-dimensional (2D) electronic materials are of significant technological interest due to their exceptional properties and broad applicability in engineering. The transition from nanoscale physics, that dictates their stable…
The third named author has been developing a theory of "higher" symplectic capacities. These capacities are invariant under taking products, and so are well-suited for studying the stabilized embedding problem. The aim of this note is to…
The issue of electric charges in interaction with partially reflective surfaces is addressed by means of field theoretic methods. It is proposed an enlarged Maxwell lagrangian, describing the electromagnetic field in the presence of a…
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…
Mobile charge in an electrolytic solution can in principle be represented as the divergence of ionic polarization. After adding explicit solvent polarization a finite volume of electrolyte can then be treated as a composite non-uniform…
In article the following tasks on computer modeling of electric fields are analyzed: 1) calculation of distribution of potential for the field created by two parallel plates and charged bodies in the non-uniform environment; 2) calculation…
Using techniques from geometry and complex analysis in their simplest form, we present a derivation of electric fields on surfaces with non-trivial topology. A byproduct of this analysis is an intuitive visualization of elliptic functions…
Image charge effect is a fundamental problem in electrostatics. However, a proper treatment at the continuum level for many-ion systems, such as electrolyte solutions or ionic liquids, remains an open theoretical question. Here, we…
A new class of exact solutions of the Einstein-Maxwell system is found in closed form. This is achieved by choosing a generalised form for one of the gravitational potentials and a particular form for the electric field intensity. For…