Related papers: A note on the exact solution for the magnetic fiel…
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…
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…
An alternative elementary argument for the magnetic field outside a solenoid is described.
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 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…
For magnetic field calculations, cylindrical permanent magnets are often approximated as ideal, azimuthally symmetric solenoids. Despite the frequent usage of this approximation, research papers demonstrating the validity and limitations of…
In this review we give an overview about the current state-of-knowledge of the magnetic field in sunspots from an observational point of view. We start by offering a brief description of tools that are most commonly employed to infer the…
A basic family of solenoids is discussed, especially from the point of view of analysis on metric spaces.
An analytical representation of the interstellar magnetic field in the vicinity of the heliosphere is derived. The three-dimensional field structure close to the heliopause is calculated as a solution of the induction equation under 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…
In this paper we present a solution to a fractional integral of the order 3/2 with the use of a novel method. The integral arises during solving the Biot-Savart equation to find the exact analytical solution for the magnetic field…
A new method for derivation of the equation of motion from the field equation is proposed. The problem of embedding the singularities in a field satisfying the field equations is discussed.
Using superposition and numerical approximations of a published analytical expression for the magnetic field generated by a finite solenoid, we show that the magnetic field external to parallel identical solenoids can be nearly uniform and…
This chapter presents a review of observational studies to determine the magnetic field in the Milky Way, both in the disk and in the halo, focused on recent developments and on magnetic fields in the diffuse interstellar medium. I discuss…
We derive from Jefimenko's equations a multipole expansion in order to obtain the exact expressions for the electric and magnetic fields of an electric dipole with an arbitrary time dependence. A few comments are also made about the usual…
Bogomolny approach in the context of strong necessary conditions is formulated for the case of various superconducting and semiconductor structures. Certain results were obtained for a constant magnetic field, which experimentally…
We present an analytical solution for the magnetic field of a homogeneously magnetized cylinder tile and by extension solutions for full cylinders, rings, cylinder sectors and ring segments. The derivation is done by direct integration in…
In a region free of currents, magnetostatics can be described by the Laplace equation of a scalar magnetic potential, and one can apply the same methods commonly used in electrostatics. Here we show how to calculate the general vector field…
A physically consistent approach is considered for defining an external magnetic field as needed in computational fluid dynamics problems involving magnetohydrodynamics (MHD). The approach results in simple analytical formulae that can be…
A transverse multipole expansion is derived, including the longitudinal components necessarily present in regions of varying magnetic field profile. It can be used for exact numerical orbit following through the fringe field regions of…