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

Physics ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 1054-1087
Author(s):  
Slobodan Babic
Keyword(s):  
Magnetic Field ◽  
Vector Potential ◽  
Magnetic Force ◽  
Analytical Form ◽  
Mutual Inductance ◽  
Integral Approach ◽  
Magnetic Vector Potential ◽  
Incomplete Elliptic Integrals ◽  
Electromagnetic Quantities ◽  
Analytical Expressions

In this paper, the improved and the new analytical and semi-analytical expressions for calculating the magnetic vector potential, magnetic field, magnetic force, mutual inductance, torque, and stiffness between two inclined current-carrying arc segments in air are given. The expressions are obtained either in the analytical form over the incomplete elliptic integrals of the first and the second kind 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 particular cases when the inclined circular loops are addressed. We mention that all formulas are obtained by the integral approach, except the stiffness, which is found by the derivative of the magnetic force. The novelty of this paper is the treatment of the inclined circular carting-current arc segments for which the calculations of the previously mentioned electromagnetic quantities are given.

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.

Vector Potential and Magnetic Field of Current-carrying Finite Elliptic Arc Segment in Analytical Form

1985 ◽  
Vol 40 (11) ◽  
pp. 1069-1074 ◽  
Author(s):  
L. Urankar
Keyword(s):  
Magnetic Field ◽  
Vector Potential ◽  
Elliptic Functions ◽  
Analytical Form ◽  
Efficient Computation ◽  
Jacobian Elliptic Functions ◽  
Arbitrary Length ◽  
Computation Algorithm ◽  
Incomplete Elliptic Integrals ◽  
Analytical Expressions

Analytical expressions for the components of the vector potential and magnetic field of a current-carrying elliptic arc filament of arbitrary length are derived. All the expressions developed consist of only known functions such as Jacobian elliptic functions, complete and incomplete elliptic integrals of the first, second and third kind, and thus permit a compact timesaving efficient computation algorithm.

Static magnetic fields in vacuum

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Magnetic Field ◽  
Problem Solving ◽  
Magnetic Fields ◽  
Vector Potential ◽  
Scalar Potential ◽  
Multipole Expansion ◽  
Magnetic Vector Potential ◽  
Magnetic Dipoles ◽  
Static Magnetic Fields ◽  
The Magnetic Field

Wherever possible, an attempt has been made to structure this chapter along similar lines to Chapter 2 (its electrostatic counterpart). Maxwell’s magnetostatic equations are derived from Ampere’s experimental law of force. These results, along with the Biot–Savart law, are then used to determine the magnetic field B arising from various stationary current distributions. The magnetic vector potential A emerges naturally during our discussion, and it features prominently in questions throughout the remainder of this book. Also mentioned is the magnetic scalar potential. Although of lesser theoretical significance than the vector potential, the magnetic scalar potential can sometimes be an effective problem-solving device. Some examples of this are provided. This chapter concludes by making a multipole expansion of A and introducing the magnetic multipole moments of a bounded distribution of stationary currents. Several applications involving magnetic dipoles and magnetic quadrupoles are given.

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.

The field of current in a thin wire ring

1964 ◽  
Vol 60 (3) ◽  
pp. 613-619
Author(s):  
G. W. Carter ◽  
S. C. Loh ◽  
C. Y. K. Po
Keyword(s):  
Digital Computer ◽  
Vector Potential ◽  
Mutual Inductance ◽  
Simple Expression ◽  
Zero Order ◽  
Magnetic Vector Potential ◽  
Thin Wire ◽  
Magnetic Vector ◽  
First Derivative ◽  
Thin Ring

AbstractA simple expression is derived for the magnetic vector potential of current in a thin ring, in terms of the first derivative of toroidal functions of zero order. The axial and radial field components and the mutual inductance between two wire rings are obtained. These expressions are evaluated on a digital computer and the results are summarized in a series of graphs.

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.

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