Vector potential and magnetic field of current-carrying circular finite arc segment in analytical form. V. Polygon cross section

1990 ◽  
Vol 26 (3) ◽  
pp. 1171-1180 ◽  
Author(s):  
L. Urankar
Keyword(s):  
Magnetic Field ◽  
Cross Section ◽  
Vector Potential ◽  
Analytical Form

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.

scholarly journals Laser Assisted Dirac Electron in a Magnetized Annulus

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 642
Author(s):  
Emilio Fiordilino
Keyword(s):  
Magnetic Field ◽  
Analytical Form ◽  
Relative Energy ◽  
Radial Force ◽  
Rate Of Change ◽  
Orthogonal Direction ◽  
Linearly Polarized ◽  
Dirac Electron ◽  
A Charge ◽  
Stretching Effect

We study the behaviour of a charge bound on a graphene annulus under the assumption that the particle can be treated as a massless Dirac electron. The eigenstates and relative energy are found in closed analytical form. Subsequently, we consider a large annulus with radius ρ∈[5000,10,000]a0 in the presence of a static magnetic field orthogonal to its plane and again the eigenstates and eigenenergies of the Dirac electron are found in both analytical and numerical form. The possibility of designing filiform currents by controlling the orbital angular momentum and the magnetic field is shown. The currents can be of interest in optoelectronic devices that are controlled by electromagnetic radiation. Moreover, a small radial force acts upon the annulus with a stretching effect. A linearly polarized electromagnetic field propagating in the orthogonal direction is added; the time evolution of the operators show that the acceleration of the electron is proportional to the rate of change of the spin of the particle.

scholarly journals The on-axis magnetic well and Mercier's criterion for arbitrary stellarator geometries

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
P. Kim ◽  
R. Jorge ◽  
W. Dorland
Keyword(s):  
Magnetic Field ◽  
Original Work ◽  
Three Dimensional ◽  
Radial Distance ◽  
Analytical Form ◽  
One Dimensional ◽  
Modern Notation ◽  
Magnetic Well ◽  
First Time ◽  
Dimensional Integral

A simplified analytical form of the on-axis magnetic well and Mercier's criterion for interchange instabilities for arbitrary three-dimensional magnetic field geometries is derived. For this purpose, a near-axis expansion based on a direct coordinate approach is used by expressing the toroidal magnetic flux in terms of powers of the radial distance to the magnetic axis. For the first time, the magnetic well and Mercier's criterion are then written as a one-dimensional integral with respect to the axis arclength. When compared with the original work of Mercier, the derivation here is presented using modern notation and in a more streamlined manner that highlights essential steps. Finally, these expressions are verified numerically using several quasisymmetric and non-quasisymmetric stellarator configurations including Wendelstein 7-X.

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