The Magnetic Field Study of a Finite Solenoid

Abstract

This paper presents the axial and radial magnetic fields strength equations at any point inside or outside a finite solenoid with infinitely thin walls. Solution of the equation has been obtained in terms of tabulated complete elliptic integrals. For the axial field, an accurate approximation is given in terms of elementary function. Internal and external magnetic fields to the solenoid are presented in graphical form with normalized values for a wide variety of solenoid dimensions. A comparison with previous studies has been done, a good correlation between the two results is achieved and the ratio of error is calculated

The Magnetic Field from Cylindrical Arc Coils and Magnets: A Compendium with New Analytic Solutions for Radial Magnetization and Azimuthal Current

“…The analytic solution for the axisymmetric shell was given in terms of Legendre elliptic integrals [ [ 72 ] , eq.39] () (and later in ref. [85] using the Heuman lambda function, as in ref. [53]).…”

Spatial Manipulation of Particles and Cells at Micro- and Nanoscale via Magnetic Forces

“…In the case of axially magnetized cylinder (Figure 1a), a convenient method of field calculation is based on representing the cylinder as a set of current loops with the total magnetization 𝑛𝐼 (𝐼 is the loop current and 𝑛 is the number of turns per unit length). In cylindrical coordinates (𝑟, 𝜑, 𝑧), the magnetic field can be calculated in terms of generalized complete elliptic integrals [45][46][47]:…”