The Calculation of the Magnetic Field Produced by an Arbitrary Shaped Current-Carrying Wire in its Plane

2013 ◽  
Vol 756-759 ◽  
pp. 3687-3691 ◽  
Author(s):  
Zhou Yu ◽  
Chang Han Xiao ◽  
Huan Wang ◽  
Yao Zhong Zhou
Keyword(s):  
Magnetic Field ◽  
Straight Line Segment ◽  
Computational Time ◽  
Improved Method ◽  
New Approach ◽  
Line Segments ◽  
Steady Current ◽  
Straight Line ◽  
Coordinate Rotation ◽  
The Magnetic Field

Instead of performing the integration explicitly to calculate the magnetic field from an arbitrary shaped wire, an improved method was proposed. The magnetic field generated by a straight line segment carrying steady current was calculated based on the Biot-Savart law. The new approach is to break the wire down into a number of straight line segments in its plane. According to the principle of vector superposition and coordinate rotation, the magnetic field from the complete current wire can then be calculated by summing the contribution from each of the separate straight line pieces. The simulation results show that the proposed numerical method has high accuracy and faster computational time and is efficient and convenient to the application in projects.

scholarly journals Comparison of the measured and modelled electron densities and temperatures in the ionosphere and plasmasphere during 20-30 January, 1993

2000 ◽  
Vol 18 (10) ◽  
pp. 1257-1262 ◽  
Author(s):  
A. V. Pavlov ◽  
T. Abe ◽  
K.-I. Oyama
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Electron Temperature ◽  
Field Line ◽  
Electron Density ◽  
Magnetic Field Line ◽  
New Approach ◽  
Additional Heating ◽  
Vibrational Levels ◽  
The Magnetic Field

Abstract. We present a comparison of the electron density and temperature behaviour in the ionosphere and plasmasphere measured by the Millstone Hill incoherent-scatter radar and the instruments on board of the EXOS-D satellite with numerical model calculations from a time-dependent mathematical model of the Earth's ionosphere and plasmasphere during the geomagnetically quiet and storm period on 20–30 January, 1993. We have evaluated the value of the additional heating rate that should be added to the normal photoelectron heating in the electron energy equation in the daytime plasmasphere region above 5000 km along the magnetic field line to explain the high electron temperature measured by the instruments on board of the EXOS-D satellite within the Millstone Hill magnetic field flux tube in the Northern Hemisphere. The additional heating brings the measured and modelled electron temperatures into agreement in the plasmasphere and into very large disagreement in the ionosphere if the classical electron heat flux along magnetic field line is used in the model. A new approach, based on a new effective electron thermal conductivity coefficient along the magnetic field line, is presented to model the electron temperature in the ionosphere and plasmasphere. This new approach leads to a heat flux which is less than that given by the classical Spitzer-Harm theory. The evaluated additional heating of electrons in the plasmasphere and the decrease of the thermal conductivity in the topside ionosphere and the greater part of the plasmasphere found for the first time here allow the model to accurately reproduce the electron temperatures observed by the instruments on board the EXOS-D satellite in the plasmasphere and the Millstone Hill incoherent-scatter radar in the ionosphere. The effects of the daytime additional plasmaspheric heating of electrons on the electron temperature and density are small at the F-region altitudes if the modified electron heat flux is used. The deviations from the Boltzmann distribution for the first five vibrational levels of N2(v) and O2(v) were calculated. The present study suggests that these deviations are not significant at the first vibrational levels of N2 and O2 and the second level of O2, and the calculated distributions of N2(v) and O2(v) are highly non-Boltzmann at vibrational levels v > 2. The resulting effect of N2(v > 0) and O2(v > 0) on NmF2 is the decrease of the calculated daytime NmF2 up to a factor of 1.5. The modelled electron temperature is very sensitive to the electron density, and this decrease in electron density results in the increase of the calculated daytime electron temperature up to about 580 K at the F2 peak altitude giving closer agreement between the measured and modelled electron temperatures. Both the daytime and night-time densities are not reproduced by the model without N2(v > 0) and O2(v > 0), and inclusion of vibrationally excited N2 and O2 brings the model and data into better agreement.Key words: Ionosphere (ionospheric disturbances; ionosphere-magnetosphere interactions; plasma temperature and density)  

Planar Lattices

1975 ◽  
Vol 27 (3) ◽  
pp. 636-665 ◽  
Author(s):  
David Kelly ◽  
Ivan Rival
Keyword(s):  
Line Segment ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Straight Line Segment ◽  
Line Segments ◽  
Small Circle ◽  
Partially Ordered ◽  
Straight Line ◽  
Finite Partially Ordered Set ◽  
Planar Lattices

A finite partially ordered set (poset) P is customarily represented by drawing a small circle for each point, with a lower than b whenever a < b in P, and drawing a straight line segment from a to b whenever a is covered by b in P (see, for example, G. Birkhoff [2, p. 4]). A poset P is planar if such a diagram can be drawn for P in which none of the straight line segments intersect.

The magnetic field inside a long solenoid—a new approach

2010 ◽  
Vol 45 (5) ◽  
pp. 529-532
Author(s):  
David Andrews ◽  
Kevin Carlton ◽  
David Lisgarten
Keyword(s):  
Magnetic Field ◽  
New Approach ◽  
The Magnetic Field

Automatic boundary extraction from magnetic field data using triangular meshes

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. J47-J60 ◽  
Author(s):  
Nathan Leon Foks ◽  
Yaoguo Li
Keyword(s):  
Magnetic Field ◽  
Synthetic Data ◽  
Magnetic Data ◽  
Lake Area ◽  
Boundary Extraction ◽  
Data Set ◽  
Magnetic Field Data ◽  
Line Segments ◽  
Extraction Algorithm ◽  
The Magnetic Field

Boundary extraction is a collective term that we use for the process of extracting the locations of faults, lineaments, and lateral boundaries between geologic units using geophysical observations, such as measurements of the magnetic field. The process typically begins with a preprocessing stage, where the data are transformed to enhance the visual clarity of pertinent features and hence improve the interpretability of the data. The majority of the existing methods are based on raster grid enhancement techniques, and the boundaries are extracted as a series of points or line segments. In contrast, we set out a methodology for boundary extraction from magnetic data, in which we represent the transformed data as a surface in 3D using a mesh of triangular facets. After initializing the mesh, we modify the node locations, such that the mesh smoothly represents the transformed data and that facet edges are aligned with features in the data that approximate the horizontal locations of subsurface boundaries. To illustrate our boundary extraction algorithm, we first apply it to a synthetic data set. We then apply it to identify boundaries in a magnetic data set from the McFaulds Lake area in Ontario, Canada. The extracted boundaries are in agreement with known boundaries and several of the regions that are completely enclosed by extracted boundaries coincide with regions of known mineralization.

scholarly journals Valyashko – the founder of a new approach to the study of the magnetic field of the ocean

2020 ◽  
Vol 48 (1) ◽  
pp. 121-124
Author(s):  
A. M. Gorodnitskiy ◽  
N. A. Shishkina
Keyword(s):  
Magnetic Field ◽  
Personal Computers ◽  
Automated System ◽  
New Approach ◽  
Geophysical Information ◽  
Long Life ◽  
The Magnetic Field

G.M. Valyashko is one of the founders of the new methodology for processing and interpreting the results of marine magnetometric measurements. In the 70s, he created an automated system for collecting and processing geophysical information, which was called “Sailor”. G.M. Valyashko continuously improved the Sailor, who lived a long life on the ships of the Institute of Oceanology from the first on-board computers to modern personal computers.

On the method of matched asymptotic expansions

1969 ◽  
Vol 65 (1) ◽  
pp. 263-284 ◽  
Author(s):  
L. E. Fraenkel
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Formal Method ◽  
Reynolds Numbers ◽  
Linear Ordinary Differential Equation ◽  
Steady Current ◽  
Formal Procedure ◽  
Small Reynolds Numbers ◽  
The Magnetic Field

AbstractThe formal method of matched expansions is applied to two further examples. The first concerns the magnetic field induced by a steady current in a thin toroidal wire. The second, which involves a non-linear ordinary differential equation of the fourth order, has been chosen to resemble the problem of flow past a circular cylinder at small Reynolds numbers. The results of the formal procedure are proved in each case to be expansions of the exact solution.

New scheme for computing the magnetic field resulting from a uniformly magnetized arbitrary polyhedron

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 70-74 ◽  
Author(s):  
D. Guptasarma ◽  
B. Singh
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Arbitrary Shape ◽  
Numerical Evaluation ◽  
Solid Angle ◽  
New Approach ◽  
Polygonal Surface ◽  
Magnetic Poles ◽  
The Magnetic Field

The magnetic field at any point outside a uniformly magnetized polyhedron of arbitrary shape is obtained by adding the fields resulting from the effective free magnetic poles on each of the polygonal surfaces of the polyhedron. For each polygonal surface, the components of the field at the point of observation are expressed in terms of new line integrals around the edges of the polygon and the solid angle subtended by the polygon at the point of observation. The line integrals are standard elementary forms. This new approach makes the numerical evaluation of the magnetic fields for such models much simpler and faster than previously published methods.

scholarly journals Mathematical Considerations for Unmanned Aerial Vehicle Navigation in the Magnetic Field of Two Parallel Transmission Lines

2021 ◽  
Vol 11 (8) ◽  
pp. 3323
Author(s):  
Dean Martinović ◽  
Stjepan Bogdan ◽  
Zdenko Kovačić
Keyword(s):  
Magnetic Field ◽  
Transmission Lines ◽  
Characteristic Property ◽  
Computational Time ◽  
Field Equations ◽  
Specific Detection ◽  
Parallel Transmission ◽  
Aerial Vehicle ◽  
The Magnetic Field ◽  
Sensor Positions

This publication deals with the navigation of unmanned aerial vehicles (UAVs) moving in the magnetic field of two long, straight, parallel conductors, which is of high interest for several new technical applications. How the position and orientation of the UAV can be calculated using a minimal number of only three three-axis magnetometers are discussed. It is shown that the angles can be determined without the knowledge of the conductor currents and the magnetic field equations, but only by combining the sensor measurements with the rotation matrix and exploiting a characteristic property of the magnetic field. Furthermore, different strategies were investigated to determine the respective sensor positions. An analytical solution was derived from the nonlinear magnetic field equations, which promises a low computational time. It is shown that for a given sensor, several solutions exist, from which the correct one has to be selected. Therefore, a specific detection method is introduced. Once the solution is known, the UAV location can be determined. Finally, the overall algorithm was tested by simulations far from and near the conductors with superimposed typical magnetic noise.

scholarly journals Analysis of Magnetic Forces in Axial-Flux Permanent-Magnet Motors with Rotor Eccentricity

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Xiaoting Zhang ◽  
Bingyi Zhang
Keyword(s):  
Magnetic Field ◽  
Permanent Magnet ◽  
Air Gap ◽  
Computational Time ◽  
End Effect ◽  
Permanent Magnet Motors ◽  
Axial Flux ◽  
Magnetic Forces ◽  
Rotor Eccentricity ◽  
The Magnetic Field

In this study, an analytical model is established to efficiently compute the magnetic field and unbalanced magnetic pull (UMP) in axial-flux permanent-magnet motors (AFPMMs). The effects of stator slotting, end effect, and rotor eccentricity on the magnetic field and forces were investigated. Static and dynamic eccentricities are analyzed and considered in the model. An effective function of the air gap permeance was introduced for effect of the stator slots to compute the flux density. A specific coefficient function is defined to calculate the end effect. A Fourier transform is used to compute the variations of the permanent-magnet remanence and the air gap permeance due to the slotted stator opposite to a slotless stator. The unbalanced magnetic forces were evaluated as a function of the air gap magnetic field using analytical equations. The proposed analytical method dramatically reduces the model size and computational time. It can be applied to the analysis of AFPMMs and is much faster than the three-dimensional finite element method (FEM). By comparing with the obtained using the FEM, the model results are validated.

Sign in / Sign up

Export Citation Format

Share Document