Related papers: On sector magnets or transverse electromagnetic fi…
It is shown that Maxwell equations for electromagnetic fields generated by the uniformly accelerated charge could be reduced to the Laplace equation (in {\L}obaczewski geometry) for a single scalar potential. The full solution of this…
A complex potential is a holomorphic function $\Omega:\mathbb{C} \to \mathbb{C}$ whose real and imaginary parts generate a pair of orthogonal foliations, representing the equipotential lines and the streamlines of $\dot{z} =…
The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz's…
The derivation of the Maxwell equations is reproduced whereby magnetic charges are included. This ansatz yields the results: 1) Longitudinal Ampere forces in a differential magnetostatic force law are improbable. Otherwise an electric…
The Laplace equation in three dimensional Euclidean space is $R$-separable in bi-cyclide coordinates leading to harmonic functions expressed in terms of Lam\'e-Wangerin functions called internal and external bi-cyclide harmonics. An…
We develop self-adjoint extensions of the l=1 radial part of the Laplace operator in a special scalar product. The product arises as the transfer of the plain product from R^3 into the set of functions parametrizing one of the two…
In this paper, we define a scalar complex potential $\mathcal{S}$ for an arbitrary electromagnetic field. This potential is a modification of the two scalar potential functions introduced by E. T. Whittaker. By use of a complexified…
The paper focuses on applying the algebra of octonions to study some coordinate transformations in the octonion spaces, exploring the contribution of partial field potential on the speed of light. J. C. Maxwell was the first to introduce…
We construct combined electric and magnetic field variables which independently represent energy flows in the forward and backward directions respectively, and use these to re-formulate Maxwell's equations. These variables enable us to not…
Relations have been derived which establish connection between a scalar or a vector functions and the integral of Laplace operator of these functions (the integral property of Laplace operator). The integral property of Laplace operator was…
The development of the theory of three-dimensional harmonic mappings is considered. The new classes of mappings that generate three-dimensional harmonic functions are introduced. The physical interpretation of these mappings is applied to…
We discuss some elementary examples of interactions (at low velocity) between point charges and magnetic dipoles using potentials, along the lines indicated by Konopinsky, and show that the physical interpretation might look quite different…
In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of (m+1)-dimensional Euclidean space was recently constructed, including a higher dimensional analogue of the logarithmic function in the…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider orbital motion in transverse plane for a single…
We show that a non-relativistic particle in a combined field of a magnetic monopole and 1/r^2 potential reveals a hidden, partially free dynamics when the strength of the central potential and the charge-monopole coupling constant are…
The problems considered refer to the material equations of electric- and magnetoelectric induction. Some contradictions found in fundamental studies on classical electrodynamics have been explained. The notion magnetoelectric induction has…
We investigate the electromagnetic dynamics of spin-nondegenerate classical particle models arising from Lorentz-violating sectors of the Standard-Model Extension, focusing on the $b_\mu$ background. Starting from the type-2 relativistic…
Magnetic Reconnection is an efficient and fast acceleration mechanism by means of direct electric field acceleration parallel to the magnetic field. Thus, acceleration of particles in reconnection regions is a very important topic in plasma…
In the previous paper we proved that the Evans-Vigier definitions of B^{(0)} and {\bf B}^{(3)} may be related {\it not} with magnetic fields but with a 4-vector field. In the present {\it Addendum} it is shown that the terms used in the…
The Maxwell field equations relative to a uniformly accelerated frame, and the variational principle from which they are obtained, are formulated in terms of the technique of geometrical gauge invariant potentials. They refer to the…