相关论文: Biot-Savart-like law in electrostatics

We present an alternative formulation of the magnetostatic boundary value problem which is useful for calculating the magnetic field around a magnetic material placed in the vicinity of steady currents. The formulation differs from the…

A numerical model for simulating electro-vortical flows in OpenFOAM is developed. Electric potential and current are solved in coupled solid-liquid conductors by a parent-child mesh technique. The magnetic field is computed using a…

The non-linear second order Born-Infeld equation is reduced to a simpler first order complex equation, which can be trivially solved for the coordinates as functions of the field. Each solution is determined by the choice of a holomorphic…

In the first part of this work we apply Bohr (old or naive quantum atomic) theory for analysis of the remarkable electro-dynamical problem of magnetic monopoles. We reproduce formally exactly some basic elements of the Dirac magnetic…

Based on the ideal gas model, the dielectric polarization of mantle is achieved, the physical-mathematical model is constructed and the estimate calculation of a dipole of Earth's magnetic field with the considering of rotation, parameters…

The equations of electrostatics are presented in pre-metric form, and it is pointed out that if the origin of the nonlinearity is the constitutive law for the medium then the differential equations themselves remain linear, while the…

Using the mathematical theory of shape calculus as tool, we perform a rigorous investigation of the virtual work principle for the computation of electromagnetic forces in static settings. The main goal is to shed light on the widely held…

A gradient of a single salt in a solution generates an electric field, but not a current. Recent theoretical work by one of us [Phys. Rev. Lett. 24, 248004 (2020)] showed that the Nernst-Planck equations imply that crossed gradients of two…

In the absence of wave propagation, transient electromagnetic fields are governed by a composite scalar/vector potential formulation for the quasistatic Darwin field model. Darwin-type field models are capable of capturing inductive,…

We investigate possible shapes of the electric field, which oscillating dipoles in a certain region of biological tissue can produce in a neighboring region, or outside the tissue boundaries. We find that a wide range of shapes, including…

Multiscale finite element methods for 2D/1D problems have been studied in this work to demonstrate their excellent ability to solve real-world problems. These methods are much more efficient than conventional 3D finite element methods and…

As a continuation of previous investigations, the formalism used there is extended to the case when an external electric field is present and the covariant formulation is performed again. The equation system obtained allows no restriction…

We introduce a Dirac equation which reproduces the usual radial sextic oscillator potential in the non-relativistic limit. We determine its energy spectrum in the presence of the magnetic field. It is shown that the equation is solved in…

We investigate properties of the image and kernel of the Biot-Savart operator in the context of stellarator designs for plasma fusion. We first show that for any given coil winding surface (CWS) the image of the Biot-Savart operator is…

In this paper we examine the Casimir effect for charged fields in presence of external magnetic field. We consider scalar field (connected with spinless particles) and the Dirac field (connected with 1/2-spin particles). In both cases we…

The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is an example of the so-called quasi-exactly solvable models. The solvable parts of its spectrum was previously solved from the…

A procedure for solving the Maxwell equations in vacuum, under the additional requirement that both scalar invariants are equal to zero, is presented. Such a field is usually called a null electromagnetic field. Based on the complex Euler…

It is first shown that the scalar product on any orthogonal space (V, g) allows one to define linear isomorphisms of the vector spaces of bivectors and 2-forms on V with the underlying vector spaces of the Lie algebra so(p, q) and its dual,…

A simple model of eddy currents in which current is computed solely from magnetic forces acting on electrons proves accessible to introductory students and gives a good qualitative account of eddy current forces. However, this model cannot…

Generation of electromagnetic fields by moving charges is a fascinating topic where the tight connection between classical electrodynamics and special relativity becomes particularly apparent. One can gain direct insight into the…