Related papers: Simple analysis of off-axis solenoid fields using …
The purpose of this paper is to derive the on and off-axes magnetic field of a solenoid with the use of a novel method. We have found a solution for the Biot-Savart law by considering the solenoid with a stationary electric current. The…
Finite-element simulations of magnetostatic fields are performed in terms of magnetic vector and total scalar potentials and compared for purpose of modeling the accelerator magnets. The potentials represent the unknown variables associated…
A general method for deriving exact expressions for vector potentials produced by arbitrarily knotted solenoids is presented. It consists of using simple physics ideas from magnetostatics to evaluate the magnetic field in a surrogate…
In this paper we present the analytical calculations to derive the magnetic field of a solenoid by solving exactly a fractional integral with the use of a novel method. Starting from the Biot-Savart law, we consider a coil of negligible…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
To determine the magnetic field distribution in the KATRIN main-spectrometer with magnetic field sensors that are placed outside the main-spectrometer vessel one can utilize the absence of magnetic rotation in main-spectrometer volume.…
We comment on a recent paper regarding the derivation of the magnetic field components of a solenoid in analytical form by proposing a different and simpler method
A scalar field method to obtain transverse solutions of the vector Laplace and Helmholtz equations in spherical coordinates for boundary-value problems with azimuthal symmetry is described. Neither scalar nor vector potentials are used.…
A solution is proposed for finding the vector potential and magnetic field of any distribution of currents with axial symmetry. In this approach, the magnetic field and the vector potential are looked for not by solving a differential…
Both wire-wound solenoids and cylindrical magnets can be approximately modeled as ideal, azimuthally symmetric solenoids. We present here an exact solution for the magnetic field of an ideal solenoid in an especially easy to use form. The…
The evaluation of the magnetic field inside and outside a uniform current density infinite solenoid of uniform cross-section is an elementary problem in classical electrodynamics that all undergraduate Physics students study. Symmetry…
The Maxwell equations for the spherical components of the electromagnetic fields outside sources do not separate into equations for each component alone. We show, however, that general solutions can be obtained by separation of variables in…
This work introduces a systematic method for identifying analytical and semi-analytical solutions of force-free magnetic fields with plane-parallel and axial symmetry. The method of separation of variables is used, allowing the…
In this paper we present eight-component values "octons", generating associative noncommutative algebra. It is shown that the electromagnetic field in a vacuum can be described by a generalized octonic equation, which leads both to the wave…
The numerical solution of problems in nonlinear magnetostatics is typically based on a variational formulation in terms of magnetic potentials, the discretization by finite elements, and iterative solvers like the Newton method. The vector…
The vector potential for the Ohmic heating coil system of a tokamak is obtained in semi-analytical form. Comparison is made to the potential of a simple, finite solenoid. In the quasi-static limit, the time rate of change of the potential…
The series solution to Laplace's equation in a helical coordinate system is derived and refined using symmetry and chirality arguments. These functions and their more commonplace counterparts are used to model solenoidal magnetic fields via…
We analytically solve Poisson's equation for the magnetic scalar potential generated by a uniformly magnetized rectangular prism and determine a closed-form solution for the magnetic scalar potential given only in terms of arctan and…
We introduce a simple approach to evaluate the magnetic field distribution around superconducting samples, based on the London equations; the elementary variable is the vector potential. This procedure has no adjustable parameters, only the…
The measurement of solar magnetic fields using the Zeeman effect diagnostics has a fundamental 180 degree ambiguity in the determination of the azimuth angle of the transverse field component. There are several methods that are used in the…