| Preface |
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vii | |
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1 | (12) |
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1-1 Vector and Scalar Algebra |
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1 | (1) |
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2 | (1) |
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1-3 The Product of a Vector and a Scalar; Unit Vectors |
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2 | (1) |
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1-4 Vector Representation of Plane and Elemental Surfaces |
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2 | (1) |
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1-5 The Scalar Product of Two Vectors |
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3 | (1) |
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1-6 The Vector Product of Two Vectors |
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3 | (1) |
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1-7 Triple Scalar Product |
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4 | (1) |
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1-8 Components of a Vector |
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5 | (1) |
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1-9 Triple Vector Product |
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5 | (1) |
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1-10 Orthogonal Components and Orthogonal Coordinate Systems |
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6 | (1) |
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1-11 The Unit Vectors ax, ay, ax; the Position Vector r |
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7 | (1) |
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1-12 Direction Cosines of a Vector |
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8 | (1) |
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1-13 The Sum and Products of Vectors in Terms of Their Orthogonal Components |
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9 | (2) |
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1-14 The Triple Scalar Product in Terms of Orthogonal Components |
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11 | (1) |
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1-15 True Vectors and Axial Vectors |
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11 | (2) |
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13 | (8) |
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13 | (2) |
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2-2 Definition of a Field |
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15 | (1) |
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2-3 The Position Vector and Its Functions |
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15 | (1) |
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2-4 Source Coordinates and Observer's Coordinates |
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16 | (1) |
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2-5 Point and Lumped Quantities |
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16 | (2) |
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2-6 Differentiation with Respect to Source Coordinates and Observer's Coordinates |
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18 | (1) |
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19 | (1) |
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2-8 The Electromagnetic Field |
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19 | (2) |
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Chapter 3 General Coordinates, Directional Derivatives, and Line Integrals |
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21 | (26) |
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3-1 Equations of Surfaces and Lines |
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21 | (1) |
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22 | (1) |
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3-3 Constant-value Surfaces in a Scalar Field |
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22 | (1) |
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3-4 Normal Direction of a Surface at a Point; Vector Area |
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22 | (2) |
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3-5 Gradient of a Scalar Field; Scalar Potential |
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24 | (1) |
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3-6 Partial Derivatives and Total Differentials |
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24 | (1) |
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3-7 Derivatives of a Vector Field |
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25 | (1) |
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3-8 Relation between Directional Derivative and Gradient |
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26 | (1) |
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3-9 Rectangular Components of the Gradient |
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26 | (2) |
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3-10 A Generalized System of Coordinates |
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28 | (1) |
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3-11 Orthogonal Systems of Coordinates |
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29 | (1) |
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3-12 The Coordinate Line, or the u Line |
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29 | (1) |
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3-13 Circular Cylindrical Coordinates |
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29 | (2) |
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3-14 Spherical Coordinates |
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31 | (1) |
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3-15 Metric Coefficients of General Coordinates |
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32 | (1) |
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3-16 Infinitesimal Curvilinear Volumes and Surfaces |
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32 | (1) |
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3-17 Transformation of Unit Vectors in Different Systems |
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33 | (2) |
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3-18 Components of Gradient in Orthogonal Curvilinear Coordinates |
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35 | (2) |
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3-19 Scalar Line Integral in a Vector Field; Vectormotive |
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37 | (1) |
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3-20 Line Integral in a Conservative Field |
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38 | (1) |
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3-21 Evaluation of a Scalar Field u from grad u |
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38 | (1) |
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3-22 Vector Line Integrals; Vector Moment of a Line |
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39 | (3) |
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3-23 Scalar Surface Integral in a Vector Field; Flux |
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42 | (2) |
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3-24 Flux Lines; Field Mapping |
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44 | (3) |
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Chapter 4 Volume Densities of Scalar and Vector Sources of a Vector Field: Divergence and Curl |
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47 | (30) |
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4-1 The Scalar Source of a Vector Field |
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47 | (2) |
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4-2 The Scalar Source Density, or Divergence, of a Vector Field |
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49 | (1) |
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4-3 Evaluation of Divergence in a System of Rectangular Coordinates |
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50 | (2) |
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4-4 Evaluation of Divergence in Orthogonal Curvilinear Coordinates |
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52 | (1) |
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4-5 Gauss' Divergence Theorem |
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53 | (2) |
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4-6 Point Sources; Spatial Delta Functions |
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55 | (1) |
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4-7 Conservation of Charge; the Continuity Equation |
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56 | (1) |
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57 | (1) |
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4-9 Twist of a Vector Field over a Surface |
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57 | (2) |
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4-10 The Vector Source Density, or Curl, of a Vector Field |
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59 | (3) |
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62 | (1) |
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4-12 An Alternative Definition of Curl |
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63 | (1) |
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64 | (2) |
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4-14 Components of Curl in General Orthogonal Coordinates |
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66 | (2) |
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4-15 A Gradient Lemma to Stokes' Theorem |
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68 | (1) |
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68 | (1) |
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4-17 Divergence of the Curl of a Vector Field |
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69 | (1) |
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4-18 Push of a Scalar Field over a Surface |
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70 | (1) |
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4-19 An Alternative Definition of Gradient |
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71 | (1) |
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72 | (1) |
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4-21 The Vector Differential Operator and Its Components |
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73 | (2) |
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4-22 Summary of Vector Identities |
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75 | (2) |
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Chapter 5 The Evaluation of Fields from Their Sources; Poisson's Equation and the Wave Equation |
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77 | (24) |
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5-1 The Concentration of a Scalar Field; the Laplacian |
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77 | (1) |
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5-2 The Gradient and Laplacian of 1/|r - r'| |
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78 | (3) |
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5-3 Evaluation of a Scalar Field from Its Concentration; Solution of Poisson's Equation in an Unbounded Medium |
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81 | (1) |
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5-4 Green's Identities; Solution of Poisson's Equation in a Bounded Medium |
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82 | (2) |
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5-5 Uniqueness Theorem for the Solution of Poisson's Equation |
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84 | (2) |
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86 | (2) |
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5-7 Techniques for the Solution of Potential Problems |
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88 | (3) |
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5-8 The Laplacian of a Vector Field |
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91 | (1) |
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5-9 Evaluation of a Vector Field from Its Sources |
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91 | (2) |
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5-10 The Helmholtz Theorem; Scalar and Vector Potentials |
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93 | (2) |
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5-11 Common Partial Differential Equations of Physics |
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95 | (1) |
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5-12 The Fourier Heat-flow Equation |
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96 | (2) |
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5-13 The Wave Equation for the Acoustic Field |
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98 | (1) |
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5-14 Solution of the Inhomogeneous Wave Equation |
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99 | (2) |
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Chapter 6 The Laws of Electromagnetic Theory |
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101 | (38) |
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6-1 Microscopic and Macroscopic Fields |
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102 | (1) |
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6-2 Classification and Motion of Charges |
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103 | (2) |
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6-3 Conservation of Charge; Current Density |
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105 | (1) |
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6-4 Polarization Charge and Current |
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106 | (4) |
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6-5 Amperian Current Density; Magnetization |
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110 | (2) |
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112 | (3) |
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6-7 The D and H Fields; Permittivity, Permeability, and Conductivity |
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115 | (3) |
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6-8 Conditions in the Interior of a Conducting Medium |
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118 | (1) |
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6-9 Conditions in the Interior of a Homogeneous Medium |
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119 | (2) |
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6-10 Discussion of the Form of Maxwell's Equations |
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121 | (1) |
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6-11 The Relativistic Nature of the Electromagnetic Field |
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121 | (2) |
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6-12 Energy in the Electromagnetic Field |
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123 | (1) |
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6-13 Conservation of Energy; Poynting's Theorem |
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124 | (5) |
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6-14 The Momentum Theorem; Electromagnetic Momentum |
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129 | (4) |
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6-15 The Electromagnetic Wave Equation |
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133 | (2) |
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6-16 Potential Functions of the Electromagnetic Field |
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135 | (4) |
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Chapter 7 Fields of Static Charge and Current Distributions |
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139 | (24) |
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7-1 Potentials for Static Fields |
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140 | (1) |
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7-2 Potentials of Point Charges at Rest |
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141 | (1) |
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7-3 The Electric Dipole Moment of a Charge Distribution |
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142 | (1) |
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7-4 The Dipole Moment and Field of an Electric Point Dipole |
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143 | (3) |
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7-5 Multipole Expansion of the Potential of an Arbitrary Charge Distribution |
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146 | (5) |
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7-6 The Magnetic Dipole Moment of a Current Distribution |
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151 | (1) |
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7-7 The Dipole Moment and Field of a Magnetic Point Dipole |
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151 | (3) |
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7-8 Static Magnetic Field of Filamentary Currents; Ampere's Law |
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154 | (4) |
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7-9 The Scalar Potential of the Magnetic Field |
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158 | (5) |
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Chapter 8 Singular Source Densities and Discontinuous Fields; Capacitance and Inductance |
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163 | (36) |
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8-1 Charge and Current Singularities |
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163 | (4) |
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8-2 Infinities and Discontinuities in Fields Due to Source Singularities |
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167 | (9) |
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8-3 Conducting Medium in an Electrostatic Field |
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176 | (1) |
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177 | (1) |
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8-5 Some Boundary-value Problems of Static Fields |
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178 | (3) |
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8-6 Coefficients of Potential and Capacitance |
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181 | (4) |
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8-7 The Electric Energy Stored in a System of Charged Conductors |
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185 | (2) |
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8-8 Coefficients of Inductance |
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187 | (2) |
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8-9 Energy Stored in the Field of Current-carrying Conductors; Inductance Formulas |
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189 | (2) |
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8-10 Application of Green's Method to Electrostatics |
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191 | (1) |
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8-11 Calculation of Capacitance Coefficients from the Green's Function |
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192 | (2) |
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8-12 The Method of Images for Obtaining the Green's Function |
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194 | (5) |
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Chapter 9 Fields in Source-free Regions; Separation of Variables |
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199 | (52) |
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9-1 The Wave Equation in Rectangular Coordinates; Separation of Variables |
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202 | (4) |
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9-2 Solution of the Two-dimensional Laplace Equation in Rectangular Coordinates |
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206 | (3) |
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9-3 Examples of Boundary-value Problems for a Rectangular Enclosure; Field Mapping of Flow Lines |
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209 | (11) |
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9-4 The Solution of Laplace's Equation in a Three-dimensional Rectangular Enclosure |
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220 | (4) |
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9-5 The Uniform Plane Wave |
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224 | (1) |
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9-6 Wavefront, Wavelength, and Wave Number of a Plane Wave |
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225 | (1) |
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9-7 Solution of the Three-dimensional Wave Equation in Rectangular Coordinates |
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226 | (2) |
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9-8 Separation of Variables in Cylindrical Coordinates |
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228 | (2) |
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9-9 Two-dimensional Cylindrical Zonal Harmonics |
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230 | (4) |
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9-10 Separation of Variables in Spherical Coordinates |
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234 | (1) |
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9-11 Two-dimensional Spherical Zonal Harmonics |
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235 | (6) |
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9-12 Numerical Solution of Laplace's Equation |
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241 | (4) |
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9-13 Difference Equations |
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245 | (1) |
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9-14 Trial Method for Sketching Equipotentials and Flow Lines; Graphical Estimation of Capacitance and Inductance |
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245 | (6) |
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Chapter 10 Some Properties of Matter |
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251 | (28) |
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10-1 Electric Polarization |
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251 | (2) |
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10-2 Ferroelectricity; Permanent Electrets |
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253 | (3) |
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10-3 Hysteresis in Electrets; Ferroelectric Memories |
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256 | (2) |
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258 | (2) |
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10-5 Magnetic Effects in Matter; Permanent Magnets |
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260 | (2) |
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262 | (3) |
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10-7 Energy Dissipation Due to Hysteresis |
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265 | (2) |
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10-8 Use of Magnetic Cores for Memory |
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267 | (1) |
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10-9 Free Electric Currents in Matter; Ohm's Law |
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267 | (3) |
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10-10 Frequency Dependence of Dielectric and Conductive Properties |
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270 | (4) |
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10-11 Isotropy in Linear Media |
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274 | (2) |
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10-12 Linear Anisotropic Media |
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276 | (3) |
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Chapter 11 Radiating and Quasi-static Fields |
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279 | (38) |
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11-1 Phasor Notation for Fields with Sinusoidal Time Variations; Definition of Impedance |
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279 | (3) |
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11-2 Current Distribution in Thin Linear Antennas |
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282 | (2) |
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11-3 Vector Potential of a Straight Thin-wire Antenna |
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284 | (2) |
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11-4 The Field of an Electric Dipole Antenna |
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286 | (2) |
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11-5 The Near Fields of an Electric Dipole Antenna |
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288 | (1) |
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11-6 Radiation and the Poynting Flux of an Electric Dipole Antenna |
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289 | (1) |
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11-7 Driving-point Impedance of an Electric Dipole Antenna; Radiation Resistance |
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290 | (1) |
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11-8 The Far or Radiation Field |
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291 | (1) |
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11-9 Radiation Patterns; Antenna Gain |
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291 | (2) |
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11-10 Transverse Electromagnetic (TEM) Waves |
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293 | (1) |
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11-11 Polarization of Vector Fields |
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293 | (3) |
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11-12 Series Expansion of Retarded Potentials; Approximation for Near Fields |
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296 | (5) |
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11-13 Quasi-static Fields; Series Solution for Dynamic Fields |
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301 | (6) |
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11-14 The Field Basis of Circuit Theory |
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307 | (10) |
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Chapter 12 Propagation of Guided Plane Waves; Transmission Lines and Rectangular Waveguides |
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317 | (57) |
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12-1 Wave Equation in Simple Media |
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318 | (1) |
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12-2 An Example of Propagation in a Lossy Medium |
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319 | (1) |
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12-3 An Example of Space-Time Harmonics in a Lossless Medium |
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320 | (2) |
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12-4 Interdependence of the Orthogonal Components of Dynamic Fields and Their Values at a Boundary |
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322 | (2) |
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12-5 Formulas Relating the Tangential and Normal Components of the E and H Fields at a Boundary |
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324 | (4) |
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12-6 General Cylindrical Coordinates and Cylindrical Components |
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328 | (1) |
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12-7 Relationships between Transverse and Longitudinal Components of Sinusoidal Plane Waves |
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329 | (3) |
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12-8 Boundary Conditions on the Transverse Components of the Fields |
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332 | (1) |
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12-9 Some Properties of TEM Waves |
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333 | (2) |
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12-10 The Scalar Potential of a Plane TEM Wave |
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335 | (2) |
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12-11 Plane TEM Waves on Lossless Straight Transmission Lines of Arbitrary but Uniform Cross Section |
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337 | (3) |
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12-12 Transmission of TEM Waves in a Straight Coaxial Line |
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340 | (1) |
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12-13 Power Transmission on a Coaxial Line |
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341 | (1) |
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12-14 Advantages and Disadvantages of Coaxial Lines |
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341 | (1) |
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12-15 The Open-wire Transmission Line |
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342 | (1) |
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12-16 Voltage-Current Relationships on a Transmission Line |
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343 | (2) |
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12-17 Transmission-line Equations |
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345 | (1) |
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12-18 Modification of the Transmission-line Equations for a Lossy Dielectric |
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346 | (2) |
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12-19 Application of Scale-change Technique to the Problem of Transmission Lines; Approximate Circuit Representation of Transmission Lines |
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348 | (5) |
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12-20 Some Properties of TM and TE Waves |
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353 | (3) |
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12-21 TEM and TM Waves between Parallel Conducting Plates |
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356 | (3) |
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12-22 TE Waves between Parallel Plates |
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359 | (1) |
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12-23 TM Waves in Rectangular Waveguides |
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359 | (4) |
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12-24 TE Waves in Rectangular Waveguides |
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363 | (2) |
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12-25 Transmitted Power and Energy Density Associated with Guided Plane Waves |
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365 | (4) |
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12-26 Lossless Rectangular Cavity Resonators |
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369 | (3) |
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12-27 The Energy Stored in a Cavity Resonator |
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372 | (2) |
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Chapter 13 Plane Waves in Lossy Media; Signal Propagation and Dispersion |
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374 | (25) |
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13-1 Propagation of Plane Sinusoidal Waves in a Conducting Medium |
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374 | (3) |
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13-2 Good Dielectrics and Good Conductors |
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377 | (2) |
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379 | (2) |
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13-4 Power Loss in Good Conductors |
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381 | (1) |
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13-5 Attenuation in Waveguides |
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382 | (2) |
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13-6 Q of Rectangular Cavity Resonators |
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384 | (1) |
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13-7 Dispersion; Velocities Significant in the Description of Wave Propagation |
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385 | (2) |
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13-8 The Group Velocity of a Signal |
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387 | (2) |
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13-9 Geometric Dispersion of Plane Waves |
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389 | (2) |
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13-10 Conductive Dispersion of Plane TEM Waves |
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391 | (3) |
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13-11 Parametric Dispersion |
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394 | (5) |
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Chapter 14 Reflection of Plane Waves at Plane Boundaries; Stress and Momentum |
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399 | (48) |
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14-1 Reflection of Plane TEM Waves at a Plane Boundary; Normal Incidence |
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399 | (5) |
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14-2 Reflection at Normal Incidence from a Perfect Conductor |
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404 | (2) |
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14-3 TEM Waves on Terminated Transmission Lines |
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406 | (3) |
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14-4 Resolution of TEM Fields into Orthogonal Components |
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409 | (1) |
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14-5 Reflection at Oblique Incidence; The Incident Field |
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410 | (3) |
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14-6 The Laws of Reflection and Refraction |
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413 | (3) |
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14-7 Electric Field Normal to the Plane of Incidence |
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416 | (2) |
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14-8 Electric Field in the Plane of Incidence |
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418 | (1) |
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14-9 Total Reflection at a Boundary between Two Perfect Dielectrics |
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419 | (5) |
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14-10 Total Transmission; The Polarizing Angle |
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424 | (1) |
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14-11 Oblique Incidence on a Perfect Conductor from a Perfect Dielectric |
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425 | (2) |
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14-12 Reflection and Transmission at Oblique Incidence with a Lossy Second Medium |
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427 | (2) |
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14-13 Resolution of TM and TE Waves into TEM Waves; Interpretation of Guided Waves in Terms of Reflections |
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429 | (4) |
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14-14 The Dielectric Waveguide |
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433 | (2) |
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14-15 The Force Applied to a Volume; Electromagnetic Stress |
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435 | (3) |
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14-16 Forces Exerted on Material Bodies by Electromagnetic Waves |
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438 | (9) |
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447 | (26) |
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15-1 The Fields of a Long Straight-wire Antenna |
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447 | (4) |
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15-2 The Effect of Ground on the Radiation Pattern of a Vertical Antenna |
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451 | (2) |
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15-3 Schelkunoff's Radiation Formula |
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453 | (2) |
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15-4 Radiation from a Circular-loop Antenna |
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455 | (1) |
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15-5 The Horizontal Pattern of Two Vertical Antennas |
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456 | (5) |
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15-6 Linear Antenna Arrays |
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461 | (5) |
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15-7 Receiving Antennas; Reciprocity |
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466 | (7) |
| Appendix I Rotation of Orthogonal Base Vectors |
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473 | (4) |
| Appendix II An Expression for the V Operator in Curvilinear Coordinates |
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477 | (3) |
| Appendix III Green's Function: The Superposition Principle and Green's Reciprocity Theorem |
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480 | (3) |
| Appendix IV The Gradient and Laplacian of a Vector Field |
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483 | (2) |
| Appendix V The Wave Equation for the Acoustic Field |
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485 | (2) |
| Appendix VI Solution of the Inhomogeneous Wave Equation in an Unbounded Region |
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487 | (2) |
| Appendix VII The Polarization and Magnetization Theorems |
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489 | (3) |
| Appendix VIII Transmission-line Techniques |
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492 | (5) |
| Problems |
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497 | (22) |
| Index |
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519 | |
