Magnetic vector potential and magnetic field intensity due to a finite current carrying cylinder considering a variable current density along its axial dimension

2012 ◽  
Vol 40 (2) ◽  
pp. 133-147 ◽  
Author(s):  
Guillermo A. Díaz ◽  
Enrique E. Mombello ◽  
Voss Stephan
Keyword(s):  
Magnetic Field ◽  
Field Intensity ◽  
Current Density ◽  
Vector Potential ◽  
Magnetic Field Intensity ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Axial Dimension

Transient magnetic field formulation for solid source conductors

2020 ◽  
Vol 64 (1-4) ◽  
pp. 1539-1545
Author(s):  
Georg Wimmer ◽  
Sebastian Lange
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Vector Potential ◽  
Numerical Scheme ◽  
Eddy Currents ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Time Step ◽  
Azimuthal Component ◽  
Transient Magnetic Fields

The formulation for the azimuthal component of the magnetic vector potential for axisymmetric magnetostatic applications is well known. However for transient magnetic fields with solid source conductors and eddy currents the formulation has to be revised. A variable transformation is introduced to remove the singularity from the numerical scheme. The numerical error cannot accumulate and is put instead to the postprocessing at every time step.

scholarly journals Vector Potential, Magnetic Field, Mutual Inductance, Magnetic Force, Torque and Stiffness Calculation between Current-Carrying Arc Segments with Inclined Axes in Air

2021 ◽  
Author(s):  
Slobodan Babic
Keyword(s):  
Magnetic Field ◽  
Numerical Integration ◽  
Vector Potential ◽  
Magnetic Force ◽  
Analytical Form ◽  
Mutual Inductance ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Special Cases ◽  
Incomplete Elliptic Integrals

In this paper we give the improved and new analytical and semi-analytical expression for calcu-lating the magnetic vector potential, magnetic field, magnetic force, mutual inductance, torque, and stiffness between two inclined current-carrying arc segments in air. The expressions are ob-tained either in the analytical form over the incomplete elliptic integrals of the first and the sec-ond time or by the single numerical integration of some elliptical integrals of the first and the second kind. The validity of the presented formulas is proved from the special cases when the inclined circular loops are treated. We mention that all formulas are obtain by the integral ap-proach except the stiffness which is found by the derivative of the magnetic force.

The Analysis of Pressure Capability of Different Teeth Structures in Ferrofluid Seal

2010 ◽  
Vol 146-147 ◽  
pp. 1278-1284 ◽  
Author(s):  
Fei Fei Xing ◽  
De Cai Li ◽  
Wen Ming Yang
Keyword(s):  
Magnetic Field ◽  
Finite Element Method ◽  
Finite Element ◽  
Theoretical Model ◽  
Vector Potential ◽  
Potential Method ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Two Sides ◽  
Sealing Gap

Theoretical model of calculating magnetic field of typical ferrofluid sealing structures with magnetic vector potential method is built. Based on the theoretical model, magnetic field distribution of rectangular teeth, two-sides dilated shape and one-side dilated shape teeth structures with common other conditions were calculated using finite element method when the sealing gap was 0.1mm and 0.12mm. The comparison of their results with the same sealing gap showed that one-side dilated shape teeth structure had higher pressure capability than other shape teeth under reasonable design.

Surface Morphology and Texture of Nickel Crystal Micro-Casting by Electroforming under Magnetic Field

2012 ◽  
Vol 535-537 ◽  
pp. 450-454 ◽  
Author(s):  
Wei Ping Jia ◽  
Meng Hua Wu ◽  
Fan Yang
Keyword(s):  
Magnetic Field ◽  
Surface Morphology ◽  
Field Intensity ◽  
Current Density ◽  
Magnetic Field Intensity ◽  
Diffraction Peak ◽  
Texture Orientation ◽  
Crystal Grains ◽  
The Magnetic Field ◽  
Nickel Crystal

Micro-components were electroplated using composite electroforming technology under magnetic field. The surface morphology of the micro components was examined using scanning electron microscope (SEM) and X-ray spectrometer was used to detect texture. The results show that: the texture and surface morphology of the micro components are influenced by the current density and the magnetic field intensity. With the increase of current density, the size of crystal grains decrease firstly but increase later .And as the increase of the magnetic field intensity, the size of crystal grains become smaller and more uniform. Besides, the current density and the magnetic field intensity have a great impact on the texture of castings. As the increase of the current density, the texture orientation changes from (111) to (200). At the same time, along with the increase of the magnetic field intensity, the diffraction peak (200) is suppressed while the diffraction peak (111) is enhanced obviously.

NEW REPRESENTATION FOR GAUGE-INVARIANT WIGNER OPERATOR OF AN ELECTRON IN A UNIFORM MAGNETIC FIELD

1998 ◽  
Vol 13 (33) ◽  
pp. 2679-2687 ◽  
Author(s):  
HONG-YI FAN ◽  
ZHEN-SHAN YANG
Keyword(s):  
Magnetic Field ◽  
Vector Potential ◽  
Uniform Magnetic Field ◽  
Magnetic Vector Potential ◽  
Wigner Functions ◽  
Magnetic Vector ◽  
Ladder Operators ◽  
Gauge Invariant ◽  
Wigner Operator ◽  
Normal Product

By using the technique of integration within an ordered product (IWOP) of operators, we derive the normal-product form of the gauge-invariant Wigner operator of an electron in a uniform magnetic field and its expression in the newly constructed |λ> representation. The virtue of working in the |λ> representation lies in the fact that it is expressed in terms of the ladder operators Π±, K±(see Eq. (10)), thus the magnetic vector potential can naturally be included. On these bases we can easily obtain Wigner functions of some important electron states.

Modeling of an inductively coupled system

2018 ◽  
Vol 37 (4) ◽  
pp. 1500-1514 ◽  
Author(s):  
Rafael Psiuk ◽  
Alisa Artizada ◽  
Daniel Cichon ◽  
Hartmut Brauer ◽  
Hannes Toepfer ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Vector Potential ◽  
Coupled Systems ◽  
Magnetic Flux Density ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Content Type ◽  
Primary Loop ◽  
Inductively Coupled

Purpose This paper aims to provide a flexible model for a system of inductively coupled loops in a quasi-static magnetic field. The outlined model is used for theoretical analyses on the magnetic field-based football goal detection system called as GoalRef, where a primary loop generates a magnetic field around the goal. The passive loops are integrated in the football, and a goal is deduced from induced voltages in loop antennas mounted on the goal frame. Design/methodology/approach Based on the law of Biot–Savart, the magnetic vector potential of a primary current loop is calculated. The induced voltages in secondary loops are derived by Faraday’s Law. Expressions to calculate induced voltages in elliptically shaped loops and their magnetic field are also presented. Findings The induced voltages in secondary loops close to the primary loop are derived by either numerically integrating the primary magnetic flux density over the area of the secondary loop or by integrating the primary magnetic vector potential over the boundary of that loop. Both approaches are examined and compared with respect to accuracy and calculation time. It is shown that using the magnetic vector potential instead of the magnetic flux density can decrease the processing time by a factor of around 100. Research limitations/implications Environmental influences like conductive or permeable obstacles are not considered in the model. Practical implications The model can be used to investigate the theoretical behavior of inductively coupled systems. Originality/value The proposed model provides a flexible, fast and accurate tool for calculations of inductively coupled systems, where the loops can have arbitrary shape, position and orientation.

Harmonic Computation and Analysis of Nonlinear Magnetic Field in the Ferromagnetic Core of the Transformer

2014 ◽  
Vol 1003 ◽  
pp. 165-168
Author(s):  
Xiao Jun Zhao ◽  
Xiao Li Chen ◽  
Can Cui ◽  
Yu Ting Zhong
Keyword(s):  
Magnetic Field ◽  
Finite Element Method ◽  
Finite Element ◽  
Harmonic Analysis ◽  
Vector Potential ◽  
Single Phase ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Harmonic Solution ◽  
Ferromagnetic Core

The single-phase three-limb transformer is used to carry out experiments under sinusoidal and dc-biased excitations. The exciting currents and magnetic vector potential are computed simultaneously by the harmonic-balanced finite-element method. Harmonic analysis of the nonlinear magnetic field is presented based on the harmonic solution of the magnetic vector potential. The calculated exciting current agrees well with the measured result, which verifies the effectiveness of the proposed method.

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