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1 | (46) |
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1 | (1) |
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2 | (8) |
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1.2.1 Magnitude and Direction of Vectors: The Unit Vector and Components of a Vector |
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2 | (4) |
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1.2.2 Vector Addition and Subtraction |
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6 | (4) |
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10 | (1) |
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10 | (11) |
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10 | (3) |
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13 | (6) |
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1.3.3 Multiple Vector and Scalar Products |
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19 | (2) |
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21 | (3) |
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22 | (1) |
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22 | (2) |
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1.5 Systems of Coordinates |
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24 | (15) |
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1.5.1 The Cartesian Coordinate System |
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25 | (3) |
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1.5.2 The Cylindrical Coordinate System |
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28 | (5) |
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1.5.3 The Spherical Coordinate System |
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33 | (2) |
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1.5.4 Transformation from Cylindrical to Spherical Coordinates |
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35 | (4) |
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39 | (2) |
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41 | (6) |
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47 | (50) |
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47 | (1) |
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2.2 Integration of Scalar and Vector Functions |
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47 | (12) |
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48 | (4) |
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52 | (4) |
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56 | (3) |
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2.2.4 Symbolic Versus Numerical Integration |
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59 | (1) |
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2.3 Differentiation of Scalar and Vector Functions |
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59 | (27) |
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2.3.1 The Gradient of a Scalar Function |
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60 | (9) |
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2.3.2 The Divergence of a Vector Field |
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69 | (6) |
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2.3.3 The Divergence Theorem |
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75 | (3) |
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2.3.4 Circulation of a Vector and the Curl |
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78 | (6) |
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84 | (2) |
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2.4 Conservative and Nonconservative Fields |
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86 | (1) |
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2.5 Null Vector Identities and Classification of Vector Fields |
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87 | (4) |
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2.5.1 The Helmholtz Theorem |
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88 | (1) |
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2.5.2 Second-Order Operators |
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89 | (2) |
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2.5.3 Other Vector Identities |
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91 | (1) |
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91 | (6) |
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3 Coulomb's Law and the Electric Field |
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97 | (42) |
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97 | (1) |
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3.2 Charge and Charge Density |
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98 | (2) |
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100 | (5) |
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3.4 The Electric Field Intensity |
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105 | (19) |
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3.4.1 Electric Fields of Point Charges |
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107 | (6) |
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3.4.2 Electric Fields of Charge Distributions |
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113 | (11) |
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3.5 The Electric Flux Density and Electric Flux |
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124 | (2) |
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126 | (4) |
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130 | (1) |
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130 | (9) |
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4 Gauss's Law and the Electric Potential |
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139 | (90) |
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139 | (1) |
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4.2 The Electrostatic Field: Postulates |
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139 | (4) |
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143 | (9) |
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4.3.1 Applications of Gauss's Law |
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144 | (8) |
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4.4 The Electric Potential |
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152 | (13) |
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4.4.1 Electric Potential Due to Point Charges |
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153 | (4) |
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4.4.2 Electric Potential Due to Distributed Charges |
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157 | (5) |
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4.4.3 Calculation of Electric Field Intensity from Potential |
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162 | (3) |
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4.5 Materials in the Electric Field |
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165 | (14) |
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165 | (5) |
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4.5.2 Dielectric Materials |
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170 | (1) |
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4.5.3 Polarization and the Polarization Vector |
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170 | (3) |
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4.5.4 Electric Flux Density and Permittivity |
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173 | (3) |
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4.5.5 Dielectric Strength |
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176 | (3) |
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179 | (7) |
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4.6.1 Interface Conditions Between Two Dielectrics |
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179 | (3) |
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4.6.2 Interface Conditions Between Dielectrics and Conductors |
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182 | (4) |
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186 | (11) |
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4.7.1 The Parallel Plate Capacitor |
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188 | (2) |
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4.7.2 Capacitance of Infinite Structures |
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190 | (2) |
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4.7.3 Connection of Capacitors |
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192 | (5) |
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4.8 Energy in the Electrostatic Field: Point and Distributed Charges |
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197 | (12) |
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4.8.1 Energy in the Electrostatic Field: Field Variables |
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202 | (4) |
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4.8.2 Forces in the Electrostatic Field: The Principle of Virtual Work |
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206 | (3) |
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209 | (3) |
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212 | (3) |
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215 | (14) |
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5 Boundary Value Problems: Analytic Methods of Solution |
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229 | (56) |
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229 | (1) |
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5.2 Poisson's Equation for the Electrostatic Field |
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230 | (1) |
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5.3 Laplace's Equation for the Electrostatic Field |
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231 | (1) |
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231 | (43) |
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5.4.1 Uniqueness of Solution |
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231 | (1) |
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5.4.2 Solution by Direct Integration |
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232 | (4) |
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5.4.3 The Method of Images |
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236 | (28) |
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5.4.4 Separation of Variables: Solution to Laplace's Equation |
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264 | (10) |
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274 | (2) |
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276 | (9) |
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6 Boundary Value Problems: Numerical (Approximate) Methods |
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285 | (50) |
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285 | (1) |
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6.1.1 A Note on Scripts and Computer Programs |
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286 | (1) |
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6.2 The General Idea of Numerical Solutions |
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286 | (1) |
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6.3 The Finite Difference Method: Solution to the Laplace and Poisson Equations |
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287 | (14) |
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6.3.1 The Finite Difference Approximation: First-Order Derivative |
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287 | (1) |
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6.3.2 The Finite Difference Approximation: Second-Order Derivative |
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288 | (3) |
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291 | (5) |
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6.3.4 Solution to Poisson's Equation |
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296 | (5) |
|
6.4 The Method of Moments: An Intuitive Approach |
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301 | (11) |
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6.5 The Finite Element Method: Introduction |
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|
312 | (14) |
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313 | (3) |
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6.5.2 Implementation of the Finite Element Method |
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316 | (10) |
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326 | (2) |
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328 | (7) |
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7 The Steady Electric Current |
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335 | (42) |
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335 | (1) |
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7.2 Conservation of Charge |
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336 | (1) |
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7.3 Conductors, Dielectrics, and Lossy Dielectrics |
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336 | (7) |
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7.3.1 Moving Charges in an Electric Field |
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336 | (1) |
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7.3.2 Convection Current and Convection Current Density |
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336 | (5) |
|
7.3.3 Conduction Current and Conduction Current Density |
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341 | (2) |
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343 | (4) |
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7.5 Power Dissipation and Joule's Law |
|
|
347 | (4) |
|
7.6 The Continuity Equation and Kirchhoff's Current Law |
|
|
351 | (5) |
|
7.6.1 Kirchhoff's Current Law |
|
|
352 | (4) |
|
7.7 Current Density as a Field |
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|
356 | (4) |
|
7.7.1 Sources of Steady Currents |
|
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358 | (1) |
|
7.7.2 Kirchhoff's Voltage Law |
|
|
359 | (1) |
|
7.8 Interface Conditions for Current Density |
|
|
360 | (4) |
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364 | (3) |
|
|
367 | (1) |
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|
368 | (9) |
|
8 The Static Magnetic Field |
|
|
377 | (42) |
|
|
377 | (1) |
|
8.2 The Magnetic Field, Magnetic Field Intensity, and Magnetic Flux Density |
|
|
378 | (2) |
|
|
380 | (9) |
|
8.3.1 Applications of the Biot-Savart Law to Distributed Currents |
|
|
386 | (3) |
|
|
389 | (6) |
|
8.5 Magnetic Flux Density and Magnetic Flux |
|
|
395 | (2) |
|
8.6 Postulates of the Static Magnetic Field |
|
|
397 | (2) |
|
|
399 | (9) |
|
8.7.1 The Magnetic Vector Potential |
|
|
399 | (7) |
|
8.7.2 The Magnetic Scalar Potential |
|
|
406 | (2) |
|
|
408 | (1) |
|
|
409 | (1) |
|
|
410 | (9) |
|
9 Magnetic Materials and Properties |
|
|
419 | (86) |
|
|
419 | (2) |
|
9.2 Magnetic Properties of Materials |
|
|
421 | (19) |
|
9.2.1 The Magnetic Dipole |
|
|
421 | (5) |
|
9.2.2 Magnetization: A Model of Magnetic Properties of Materials |
|
|
426 | (8) |
|
9.2.3 Behavior of Magnetic Materials |
|
|
434 | (6) |
|
9.3 Magnetic Interface Conditions |
|
|
440 | (5) |
|
9.3.1 Interface Conditions for the Tangential and Normal Components of the Magnetic Field Intensity H |
|
|
440 | (5) |
|
9.4 Inductance and Inductors |
|
|
445 | (11) |
|
9.4.1 Inductance per Unit Length |
|
|
452 | (1) |
|
9.4.2 External and Internal Inductance |
|
|
453 | (3) |
|
9.5 Energy Stored in the Magnetic Field |
|
|
456 | (10) |
|
9.5.1 Magnetostatic Energy in Terms of Fields |
|
|
461 | (5) |
|
|
466 | (5) |
|
9.7 Forces in the Magnetic Field |
|
|
471 | (10) |
|
9.7.1 Principle of Virtual Work: Energy in a Gap |
|
|
478 | (3) |
|
|
481 | (3) |
|
|
484 | (3) |
|
|
487 | (2) |
|
|
489 | (16) |
|
10 Faraday's Law and Induction |
|
|
505 | (46) |
|
|
505 | (1) |
|
|
506 | (2) |
|
|
508 | (1) |
|
10.4 Motional Electromotive Force: The DC Generator |
|
|
509 | (5) |
|
10.5 Induced emf Due to Transformer Action |
|
|
514 | (2) |
|
10.6 Combined Motional and Transformer Action Electromotive Force |
|
|
516 | (8) |
|
10.6.1 The Alternating Current Generator |
|
|
516 | (8) |
|
|
524 | (7) |
|
10.7.1 The Ideal Transformer |
|
|
524 | (1) |
|
10.7.2 The Real Transformer: Finite Permeability |
|
|
525 | (2) |
|
10.7.3 The Real Transformer: Finite Permeability and Flux Leakage |
|
|
527 | (4) |
|
|
531 | (3) |
|
|
534 | (7) |
|
|
541 | (1) |
|
|
542 | (9) |
|
|
551 | (32) |
|
11.1 Introduction: The Electromagnetic Field |
|
|
551 | (1) |
|
|
552 | (7) |
|
11.2.1 Maxwell's Equations in Differential Form |
|
|
553 | (3) |
|
11.2.2 Maxwell's Equations in Integral Form |
|
|
556 | (3) |
|
11.3 Time-Dependent Potential Functions |
|
|
559 | (4) |
|
|
559 | (1) |
|
11.3.2 The Magnetic Vector Potential |
|
|
560 | (1) |
|
11.3.3 Other Potential Functions |
|
|
561 | (2) |
|
11.4 Interface Conditions for the Electromagnetic Field |
|
|
563 | (6) |
|
11.4.1 Interface Conditions for the Electric Field |
|
|
564 | (1) |
|
11.4.2 Interface Conditions for the Magnetic Field |
|
|
565 | (4) |
|
11.5 Particular Forms of Maxwell's Equations |
|
|
569 | (5) |
|
11.5.1 Time-Harmonic Representation |
|
|
569 | (3) |
|
11.5.2 Maxwell's Equations: The Time-Harmonic Form |
|
|
572 | (1) |
|
11.5.3 Source-Free Equations |
|
|
573 | (1) |
|
|
574 | (1) |
|
|
575 | (8) |
|
12 Electromagnetic Waves and Propagation |
|
|
583 | (68) |
|
|
583 | (1) |
|
|
583 | (5) |
|
12.3 The Electromagnetic Wave Equation and Its Solution |
|
|
588 | (13) |
|
12.3.1 The Time-Dependent Wave Equation |
|
|
588 | (2) |
|
12.3.2 Time-Harmonic Wave Equations |
|
|
590 | (2) |
|
12.3.3 Solution of the Wave Equation |
|
|
592 | (1) |
|
12.3.4 Solution for Uniform Plane Waves |
|
|
592 | (1) |
|
12.3.5 The One-Dimensional Wave Equation in Free-Space and Perfect Dielectrics |
|
|
593 | (8) |
|
12.4 The Electromagnetic Spectrum |
|
|
601 | (2) |
|
12.5 The Poynting Theorem and Electromagnetic Power |
|
|
603 | (8) |
|
12.6 The Complex Poynting Vector |
|
|
611 | (3) |
|
12.7 Propagation of Plane Waves in Materials |
|
|
614 | (17) |
|
12.7.1 Propagation of Plane Waves in Lossy Dielectrics |
|
|
614 | (5) |
|
12.7.2 Propagation of Plane Waves in Low-Loss Dielectrics |
|
|
619 | (3) |
|
12.7.3 Propagation of Plane Waves in Conductors |
|
|
622 | (5) |
|
12.7.4 The Speed of Propagation of Waves and Dispersion |
|
|
627 | (4) |
|
12.8 Polarization of Plane Waves |
|
|
631 | (5) |
|
12.8.1 Linear Polarization |
|
|
632 | (1) |
|
12.8.2 Elliptical and Circular Polarization |
|
|
632 | (4) |
|
|
636 | (2) |
|
|
638 | (3) |
|
|
641 | (10) |
|
13 Reflection and Transmission of Plane Waves |
|
|
651 | (58) |
|
|
651 | (1) |
|
13.2 Reflection and Transmission at a General Dielectric Interface: Normal Incidence |
|
|
652 | (19) |
|
13.2.1 Reflection and Transmission at an Air-Lossy Dielectric Interface: Normal Incidence |
|
|
658 | (3) |
|
13.2.2 Reflection and Transmission at an Air-Lossless Dielectric Interface: Normal Incidence |
|
|
661 | (1) |
|
13.2.3 Reflection and Transmission at an Air-Conductor Interface: Normal Incidence |
|
|
662 | (9) |
|
13.3 Reflection and Transmission at an Interface: Oblique Incidence on a Perfect Conductor |
|
|
671 | (6) |
|
13.3.1 Oblique Incidence on a Perfectly Conducting Interface: Perpendicular Polarization |
|
|
671 | (4) |
|
13.3.2 Oblique Incidence on a Perfectly Conducting Interface: Parallel Polarization |
|
|
675 | (2) |
|
13.4 Oblique Incidence on Dielectric Interfaces |
|
|
677 | (13) |
|
13.4.1 Oblique Incidence on a Dielectric Interface: Perpendicular Polarization |
|
|
677 | (3) |
|
13.4.2 Oblique Incidence on a Dielectric Interface: Parallel Polarization |
|
|
680 | (5) |
|
|
685 | (2) |
|
|
687 | (3) |
|
13.5 Reflection and Transmission for Layered Materials at Normal Incidence |
|
|
690 | (5) |
|
|
695 | (3) |
|
|
698 | (2) |
|
|
700 | (9) |
|
14 Theory of Transmission Lines |
|
|
709 | (66) |
|
|
709 | (2) |
|
14.2 The Transmission Line |
|
|
711 | (1) |
|
14.3 Transmission Line Parameters |
|
|
712 | (7) |
|
14.3.1 Calculation of Line Parameters |
|
|
713 | (6) |
|
14.4 The Transmission Line Equations |
|
|
719 | (4) |
|
14.5 Types of Transmission Lines |
|
|
723 | (8) |
|
14.5.1 The Lossless Transmission Line |
|
|
723 | (2) |
|
14.5.2 The Long Transmission Line |
|
|
725 | (2) |
|
14.5.3 The Distortionless Transmission Line |
|
|
727 | (2) |
|
14.5.4 The Low-Resistance Transmission Line |
|
|
729 | (2) |
|
14.6 The Field Approach to Transmission Lines |
|
|
731 | (3) |
|
14.7 Finite Transmission Lines |
|
|
734 | (17) |
|
14.7.1 The Load Reflection Coefficient |
|
|
736 | (2) |
|
14.7.2 Line Impedance and the Generalized Reflection Coefficient |
|
|
738 | (3) |
|
14.7.3 The Lossless, Terminated Transmission Line |
|
|
741 | (4) |
|
14.7.4 The Lossless, Matched Transmission Line |
|
|
745 | (1) |
|
14.7.5 The Lossless, Shorted Transmission Line |
|
|
746 | (1) |
|
14.7.6 The Lossless, Open Transmission Line |
|
|
747 | (1) |
|
14.7.7 The Lossless, Resistively Loaded Transmission Line |
|
|
748 | (3) |
|
14.8 Power Relations on a General Transmission Line |
|
|
751 | (3) |
|
14.9 Resonant Transmission Line Circuits |
|
|
754 | (3) |
|
|
757 | (2) |
|
|
759 | (4) |
|
|
763 | (12) |
|
15 The Smith Chart, Impedance Matching, and Transmission Line Circuits |
|
|
775 | (38) |
|
|
775 | (1) |
|
|
776 | (8) |
|
15.3 The Smith Chart as an Admittance Chart |
|
|
784 | (3) |
|
15.4 Impedance Matching and the Smith Chart |
|
|
787 | (15) |
|
15.4.1 Impedance Matching |
|
|
787 | (1) |
|
|
788 | (14) |
|
15.5 Quarter-Wavelength Transformer Matching |
|
|
802 | (4) |
|
|
806 | (2) |
|
|
808 | (5) |
|
16 Transients on Transmission Lines |
|
|
813 | (36) |
|
|
813 | (1) |
|
16.2 Propagation of Narrow Pulses on Finite, Lossless Transmission Lines |
|
|
814 | (3) |
|
16.3 Propagation of Narrow Pulses on Finite, Distortionless Transmission Lines |
|
|
817 | (4) |
|
16.4 Transients on Transmission Lines: Long Pulses |
|
|
821 | (6) |
|
16.5 Transients on Transmission Lines: Finite-Length Pulses |
|
|
827 | (3) |
|
16.6 Reflections from Discontinuities |
|
|
830 | (3) |
|
16.7 Transients on Lines with Reactive Loading |
|
|
833 | (5) |
|
16.7.1 Capacitive Loading |
|
|
834 | (2) |
|
|
836 | (2) |
|
16.8 Initial Conditions on Transmission Lines |
|
|
838 | (3) |
|
|
841 | (3) |
|
|
844 | (5) |
|
17 Waveguides and Resonators |
|
|
849 | (66) |
|
|
849 | (1) |
|
17.2 The Concept of a Waveguide |
|
|
850 | (1) |
|
17.3 Transverse Electromagnetic, Transverse Electric, and Transverse Magnetic Waves |
|
|
850 | (9) |
|
17.3.1 Transverse Electromagnetic Waves |
|
|
852 | (1) |
|
17.3.2 Transverse Electric (TE) Waves |
|
|
853 | (4) |
|
17.3.3 Transverse Magnetic (TM) Waves |
|
|
857 | (2) |
|
17.4 TE Propagation in Parallel Plate Waveguides |
|
|
859 | (9) |
|
17.5 TM Propagation in Parallel Plate Waveguides |
|
|
868 | (5) |
|
17.6 TEM Waves in Parallel Plate Waveguides |
|
|
873 | (1) |
|
17.7 Rectangular Waveguides |
|
|
874 | (20) |
|
17.7.1 TM Modes in Rectangular Waveguides |
|
|
875 | (7) |
|
17.7.2 TE Modes in Rectangular Waveguides |
|
|
882 | (7) |
|
17.7.3 Attenuation and Losses in Rectangular Waveguides |
|
|
889 | (5) |
|
|
894 | (1) |
|
|
895 | (6) |
|
17.9.1 TM Modes in Cavity Resonators |
|
|
896 | (2) |
|
17.9.2 TE Modes in Cavity Resonators |
|
|
898 | (3) |
|
17.10 Energy Relations in a Cavity Resonator |
|
|
901 | (1) |
|
17.11 Quality Factor of a Cavity Resonator |
|
|
901 | (1) |
|
|
902 | (3) |
|
|
905 | (3) |
|
|
908 | (7) |
|
18 Antennas and Electromagnetic Radiation |
|
|
915 | (78) |
|
|
915 | (1) |
|
18.2 Electromagnetic Radiation and Radiation Safety |
|
|
915 | (2) |
|
|
917 | (1) |
|
|
917 | (9) |
|
|
921 | (1) |
|
|
922 | (4) |
|
18.5 Properties of Antennas |
|
|
926 | (9) |
|
|
926 | (1) |
|
18.5.2 Radiation Resistance |
|
|
927 | (1) |
|
18.5.3 Antenna Radiation Patterns |
|
|
928 | (4) |
|
18.5.4 Radiation Intensity and Average Radiation Intensity |
|
|
932 | (1) |
|
18.5.5 Antenna Directivity |
|
|
933 | (1) |
|
18.5.6 Antenna Gain and Radiation Efficiency |
|
|
934 | (1) |
|
|
935 | (6) |
|
18.6.1 Near Fields for the Magnetic Dipole |
|
|
938 | (1) |
|
18.6.2 Far Fields for the Magnetic Dipole |
|
|
938 | (1) |
|
18.6.3 Properties of the Magnetic Dipole |
|
|
939 | (2) |
|
|
941 | (12) |
|
18.7.1 Linear Antennas of Arbitrary Length |
|
|
942 | (9) |
|
18.7.2 The Monopole Antenna |
|
|
951 | (2) |
|
|
953 | (13) |
|
18.8.1 The Two-Element Array |
|
|
955 | (7) |
|
18.8.2 The n-Element Linear Array |
|
|
962 | (4) |
|
18.9 Reciprocity and Receiving Antennas |
|
|
966 | (1) |
|
|
967 | (6) |
|
|
973 | (4) |
|
|
975 | (2) |
|
|
977 | (1) |
|
|
977 | (1) |
|
|
978 | (4) |
|
|
982 | (11) |
Answers |
|
993 | (20) |
Appendix: Summary of Vector Relations and Physical Constants |
|
1013 | (2) |
Index |
|
1015 | |