2D electrostatic fields : a complex variable approach /: a complex variable approach. (2021)

• Record Type: Book
• Other Titles: Two dimensional electrostatic fields
• Further Information: Note: Robert L. Coffie.
• Authors: Coffie, Robert L
• Contents: 1. Functions of a Complex Variable; 1.1 Complex Numbers and Variables; 1.2 Conjugate Coordinates; 1.3 Analytic Functions; 1.4 Real and Imaginary Parts of Analytic Functions; 1.5 Taylor Series; 1.6 Multi-valued Functions; 1.7 2D Vectors and Vector Operators; 1.8 Line Integrals; 1.9 Divergence Theorem in 2D; 1.10 Curl Theorem in 2D; 1.11 Divergence and Curl Theorems in Conjugate Coordinates; 1.12 Cauchy’s First Integral Theorem; 1.13 Cauchy’s Second Integral Theorem; 1.14 Laurent Series; 1.15 Classification of Singularities; 1.16 The Residue Theorem; 1.17 Green’s Identities in 2D; References 2. Electrostatics; 2.1 Coulomb’s Law; 2.2 Electric Field Intensity; 2.3 Electric Fields of Dipoles and Multipoles; 2.4 Continuous Charge Distributions; 2.5 Gauss’s Law in 2D; 2.6 Polarization; 2.7 Maxwell’s Equations; 2.8 Boundary Conditions; 2.9 Electrostatic Potential; 2.10 Complex Potential; 2.11 Complex Potential for a Dipole; 2.12 Complex Potential for a Double Layer; 2.13 Transforming Poisson’s Equation into Laplace’s Equation; 2.14 Equipotential Contours; 2.15 Lines of Force; 2.16 Field Maps; 2.17 Gauss’s Law for Inhomogeneous Mediums; 2.18 Dielectric Boundary Conditions for ф; 2.19 Uniqueness Theorem; 2.20 Conductors and Insulators; 2.21 Capacitance; 2.22 Method of Curvilinear Squares; 2.23 Energy in the Electrostatic Field; 2.24 Green’s Reciprocation Theorem; 2.25 Induced Charges on Grounded Conductors; References 3. Line Charges; 3.1 The Complex Potential Plane; 3.2 Single Line Charge; 3.3 Two Line Charges; 3.4 ф for Conductor Boundary in Parametric Form 104; 3.5 Green’s Function; 3.6 Method of Images and Green’s Functions; 3.7 Green’s Function for a Conductive Cylinder; 3.8 Green’s Function for a Conductive Plane; 3.9 Green’s Function for Two Conducting Planes; 3.10 Ray Tracing for Planar Dielectric Boundaries; 3.11 Ray Tracing for Planar Conductor Boundaries; 3.12 Ray Tracing for Planar Line of Force Boundaries; 3.13 Ray Tracing for Multiple Planar Boundaries; 3.14 1D Array of Line Charges; 3.15 2D Array of Line Charges; 3.16 Line Charge Between a Grounded Cylinder and a Floating Cylinder; 3.17 Line Charge Between Two Grounded Concentric Cylinders; References 4. Conformal Mapping I; 4.1 Defining Conformal Transformations; 4.2 Transforming Complex Potentials; 4.3 Translation; 4.4 Magnification and Rotation; 4.5 Complex Inversion and Inversion; 4.6 Inversion of a Point; 4.7 Inversion of a Triangle with Vertex at zc; 4.8 Inversion of a Line; 4.9 Inversion of a Circle; 4.10 Inversion of Orthogonal Circles; 4.11 Symmetry Preservation with Inversion; 4.12 M¨obius Transform; 4.13 Logarithm Transformation; 4.14 Riemann Sphere; 4.15 Charges at Infinity; 4.16 Dielectric Cylinder and Line Charge; 4.17 Floating Conductive Cylinder and Line Charge; 4.18 Line Charge Between Two Concentric Conductive Cylinders Revisited; 4.19 Nonconcentric Cylinders to Concentric Cylinders; References 5. Conformal Mapping II; 5.1 Riemann Mapping Theorem; 5.2 Symmetry of Conformal Maps; 5.3 van der Pauw Theorem; 5.4 Thompson-Lampard Theorem; 5.5 Schwarz-Christoffel Transformation; 5.6 S-C Transformation with bn = 1; 5.7 S-C Transformation onto a Unit Disk; 5.8 Phase of A1; 5.9 Exterior Angle for a Vertex at Infinity; 5.10 Boundary Condition for Parallel Lines that Meet at Infinity; 5.11 Polygons with Both Vertices at Infinity; 5.12 Polygons with One Finite Vertex and One Vertex at Infinity; 5.13 Polygons with One Finite Vertex and Two Vertices at Infinity; 5.14 Polygons with Two Finite Vertices and One Vertex at Infinity; 5.15 Polygons with Two Finite Vertices and Two Vertices at Infinity; 5.16 The Joukowski Transformation; 5.17 Polygons with Three Finite Vertices; 5.18 Polygons with Four Finite Vertices; References 6. Case Studies with Conformal Mapping; 6.1 Parallel Plate Capacitor; 6.2 Characteristic Impedance of Lossless Transmission Lines; 6.3 Charge Imaging on Infinite Plate; 6.4 Field Plates; 6.5 Trigate FinFETs; 6.6 Uniform Electric Field; 6.7 Circular Conducting or Dielectric Cylinder in a Uniform Electric Field; 6.8 Elliptic Dielectric Cylinder in Uniform Electric Field; 6.9 Limitations for conformal mapping; 6.10 Conclusions; References Chapter 7. Other Fields of Physics; 7.1 Translating to Other Areas of Physics; 7.2 Steady Electric Current; 7.3 Magnetostatics; 7.4 Steady Heat Power Flow; 7.5 Fluid Dynamics; References Appendix A. Differentiating an Integral; Appendix B. Dirac -Function; Appendix C. Elliptic Integrals; Appendix D. Jacobi’s Elliptic Functions; Appendix E. Gamma and Beta Functions; Appendix F. Gauss’s Hypergeometric Function; Appendix G. Dilogarithm and Trilogarithm Functions; References; Index
• Edition: 1st
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2021
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 537.2; Electrostatics; Electrostatics -- Mathematics; Functions of complex variables
• Languages: English
• ISBNs: 9781000433012; 9781000432978; 9781003169185
• Related ISBNs: 9780367769758
• Notes: Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.