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Cấu trúc
Visualising Magnetic Fields
Copyright Page
Contents
Chapter 1. Introduction
Magnetic lines of force
What is visualisation?
The purpose of this book
The software
Communications to the author
Reviewing the physics
Chapter 2. Physics of the magnetic field
Fields and field lines
Gauss’s Law
The Biot–Savart law
Ampere’s Law
Magnetic force on a conductor
Magnetic materials and permanent magnets
The magnetisation curve
Hysteresis
Maxwell’s equations
The magnetic circuit
The first step in visualisation
Chapter 3. The basic technique
Overview
Characteristics of the technique
Generating the equations
The matrix form
Making use of the technique
Chapter 4. Numerical algorithm theory
Gaussian elimination
The conjugate gradient method
Double versus single precision arithmetic
Theory of the conjugate gradient method
The equations being solved
The quadratic form
The method of steepest descent
The method of conjugate gradients
Comparing the two algorithms
Preconditioning
Timing and storage results
Indirect addressing for arrays
Choice of analysis method and mesh size
16 and 32 bit operating systems
Progress indicator
Error level setting
Understanding the matrix solving algorithms
Chapter 5. Visualising the algorithms
Conjugate gradient visualisation
Use of the options panel
Example of use of the options
Sample files included with SHOWALG
Error level versus number of iterations
Gaussian elimination visualisation
Completing the theory
Chapter 6. The boundary region, smoothing and external fields
Why a boundary region is needed
Mesh impedance characteristics
Distortion performance
Smoothing
Using the boundary for external field simulation
Magnetic field lines and magnetic flux density
Chapter 7. The magnetic flux density function
Magnetic flux density filter and log scale
Putting the theory to work
Chapter 8. Model creation
Model functions provided
Data structure
Structure of object storage
Model generation
Equation generation
Event driven code
Editing
Running the program
Chapter 9. Program installation and use
Installation
Using VIZIMAG
On-line help
The source code
Hints and tips on using VIZIMAG
Chapter 10. Sample results
Magnetic samples
References
Appendix: The source code
Running the source code
Programming style
Architecture
Global variables
Resizing arrays
Code flow descriptions: overview
Application start up
Application close down
Form.Update
Form.Refresh
Program procedures initiated by a menu item or speedbutton
General program procedures in unit VIZGlobal
General program procedures in unit VIZ1
General program procedures in VIZ2
General program procedures in VIZ3
Other mouse and keyboard event initiated procedures
Index to source code procedures
Index
Gray Plate Section
Color Plate Section
Nội dung
[...]... poles attract, and therefore magnetic lines of force are directed away from the north pole of a magnet and towards the south pole In fact, although scientists have searched for, and are still searching for, isolated magnetic poles (i.e magnetic monopoles), they have never been discovered The magnitude and direction of a magnetic field is B, the magnetic flux 8 Physics of the magnetic field Figure 2-1:... equations showed that electric and magnetic fields were inextricably entwined, and it is not surprising that (for linear materials) there are close analogies between electric and magnetic quantities A system comprising one or more flux sources and magnetic materials is called a magnetic circuit and, just like an electric circuit, with voltages, resistance, currents, etc., magnetic circuits can be analysed... in visualisation The analogies between electric and magnetic circuits are so close that it is a reasonable assumption that an electric circuit analysis method might be extended to solve magnetic circuits In creating a complete methodology for visualising magnetic fields, the first step is to find a technique that can provide a representation of the magnetic field line patterns and a method to do this,... magnets, coils and magnetic materials, and sketch how they think the lines of magnetic force will link everything together They try to gain an intuitive feeling for the behaviour of the system, as a precursor to moving to a full quantitative analysis on a suitable computational platform Thus magnetic lines of force are as useful a concept to us today, in the visualisation of magnetic fields, as they were... density When we draw magnetic field lines to represent a magnetic field, the direction of the line at any point is tangential to the direction of the magnetic flux density, and the magnitude of the field is proportional to the number of field lines per unit area There are two important rules to remember about magnetic field lines: first that field lines can never cross, and second that magnetic field lines... We can see that magnetic field lines near the centre of the coil have nearly uniform spacing, showing that the magnetic flux density (B) is nearly constant in magnitude and direction At the ends of the coil the magnetic field lines are more widely and less uniformly spaced, and for a long solenoid the magnetic flux density on axis at the ends is half that at the centre Physics of the magnetic field... the magnetic field of a material is linearly dependant on the external field However, it is still possible to use a linear model to assess the performance of magnetic systems, because many systems are designed to operate in the linear region, and points of high magnetic flux density, where saturation would first occur, are easily seen A linear model is nearly always the first step in visualising a magnetic. .. the modelling method and the algorithms, the next chapter gives a brief review of the physics of magnetic fields, and illustrates the principles with magnetic field plots made using the VIZIMAG application This Page Intentionally Left Blank 2 Physics of the magnetic field The properties of magnetite, the magnetic ore of iron, have been known since ancient times, and this has made the study of magnetism... with the path of the flux shown by the magnetic field lines The permeability of the coil, magnetic domain material in the core, and the air gap form the reluctance elements of the magnetic circuit and (together with leakage flux into the surrounding air) determine the total amount of flux produced Figure 2-10: Magnetic circuit with air gap 18 Physics of the magnetic field The first step in visualisation... textbooks available Fields and field lines A bar magnet, or a wire carrying a current, produces a magnetic field permeating the space all around it The direction of the field at any point is defined to be the direction in which a north magnetic pole would move due to the field at that point, and the path through which this pole would freely move is the magnetic line of force or magnetic field line .