Introduction to Electromagnetic Waves with Maxwell's Equations

Discover an innovative and fresh approach to teaching classical electromagnetics at a foundational level

Introduction to Electromagnetic Waves with Maxwell's Equations delivers an accessible and practical approach to teaching the well-known topics all electromagnetics instructors must include in their syllabus. Based on the author's decades of experience teaching the subject, the book is carefully tuned to be relevant to an audience of engineering students who have already been exposed to the basic curricula of linear algebra and multivariate calculus.

Forming the backbone of the book, Maxwell's equations are developed step-by-step in consecutive chapters, while related electromagnetic phenomena are discussed simultaneously. The author presents accompanying mathematical tools alongside the material provided in the book to assist students with retention and comprehension. The book contains over 100 solved problems and examples with stepwise solutions offered alongside them. An accompanying website provides readers with additional problems and solutions.

Readers will also benefit from the inclusion of:

• A thorough introduction to preliminary concepts in the field, including scalar and vector fields, cartesian coordinate systems, basic
• vector operations, orthogonal coordinate systems, and electrostatics, magnetostatics, and electromagnetics
• An exploration of Gauss' Law, including integral forms, differential forms, and boundary conditions
• A discussion of Ampere's Law, including integral and differential forms and Stoke's Theorem

• An examination of Faraday's Law, including integral and differential forms and the Lorentz Force Law
  Perfect for third-and fourth-year undergraduate students in electrical engineering, mechanical engineering, applied maths, physics, and computer science, Introduction to Electromagnetic Waves with Maxwell's Equations will also earn a place in the libraries of graduate and postgraduate students in any STEM program with applications in electromagnetics.

Auteur

Ozgur Ergul, PhD, is Professor at the Middle East Technical University in Ankara, Turkey. His research focus is on the development of fast and accurate algorithms for the solution of electromagnetics problems involving large and complicated structures, integral equations, iterative methods, parallel programming, and high-performance computing.

Contenu

Preface 15

Mathematical Notation 23

List of Symbols 27

Special Functions 31

Frequently Used Identities 33

Tools to Understand Maxwell's Equations 37

0 Preliminary 39

0.1 Scalar and Vector Fields 40

0.2 Cartesian Coordinate Systems 42

0.3 Basic Vector Operations 42

0.4 Orthogonal Coordinate Systems 43

0.4.1 Properties of a Cartesian Coordinate System 43

0.4.2 Cylindrical Coordinate System 44

0.4.3 Spherical Coordinate System 45

0.5 Electrostatics, Magnetostatics, and Electromagnetics 47

0.6 Time in Electromagnetics 49

0.7 Final Remarks 51

1 Gauss' Law 53

1.1 Integral Form of Gauss' Law 54

1.1.1 Differential Surface With Direction 55

1.1.2 Dot Product 56

1.1.3 Flux of Vector Fields 62

1.1.4 Meaning of Gauss' Law and Its Application 66

1.1.5 Examples 67

1.2 Using the Integral Form of Gauss' Law 69

1.2.1 Examples 71

1.3 Differential Form of Gauss' Law 73

1.3.1 Electric Charge Density 73

1.3.2 Divergence of Vector Fields 75

1.3.3 Divergence Theorem and the Differential Form of Gauss' Law 81

1.3.4 Examples 83

1.4 Using the Differential Form of Gauss' Law 85

1.4.1 Examples 88

1.5 Boundary Conditions for Normal Electric Fields 89

1.6 Static Cases and Coulomb's Law 92

1.6.1 Superposition Principle 93

1.6.2 Coulomb's Law and Electric Force 99

1.6.3 Examples 101

1.7 Gauss' Law and Dielectrics 106

1.7.1 Electric Dipole 112

1.7.2 Polarization 113

1.7.3 Equivalent Polarization Charges 115

1.7.4 Examples 120

1.8 Final Remarks 123

1.9 Exercises 124

1.10 Questions 127

2 Ampere's Law 133

2.1 Integral Form of Ampere's Law 134

2.1.1 Differential Length With Direction 135

2.1.2 Circulation of Vector Fields 137

2.1.3 Meaning of Ampere's Law and Its Application 140

2.1.4 Examples 143

2.2 Using the Integral Form of Ampere's Law 145

2.2.1 Examples 147

2.3 Differential Form of Ampere's Law 151

2.3.1 Electric Current Density 152

2.3.2 Cross Product 154

2.3.3 Curl of Vector Fields 157

2.3.4 Stoke's Theorem and the Differential Form of Ampere's Law 164

2.3.5 Examples 165

2.4 Using the Differential Form of Ampere's Law 169

2.4.1 Examples 172

2.5 Boundary Conditions for Tangential Magnetic Fields 173

2.6 Gauss' Law and Ampere's Law 176

2.7 Static Cases, Biot-Savart Law, and Ampere's Force Law 179

2.7.1 Superposition Principle 180

2.7.2 Ampere's Force Law and Magnetic Force 190

2.7.3 Examples 194

2.8 Ampere's Law and Magnetic Materials 200

2.8.1 Magnetic Dipole 206

2.8.2 Magnetization 208

2.8.3 Equivalent Magnetization Currents 210

2.8.4 Examples 217

2.9 Final Remarks 218

2.10 Exercises 219

2.11 Questions 221

3 Faraday's Law 225

3.1 Integral Form of Faraday's Law 226

3.1.1 Meaning of Faraday's Law and Its Application 227

3.1.2 Lorentz Force Law 229

3.2 Using the Integral Form of Faraday's Law 231

3.2.1 Examples 236

3.3 Differential Form of Faraday's Law 240

3.4 Boundary Conditions for Tangential Electric Fields 242

3.5 Combining Faraday's Law with Gauss' and Ampere's Laws 244

3.6 Static Cases and Electric Scalar Potential 246

3.6.1 Gradient of Scalar Fields 248

3.6.2 Examples 252

3.6.3 Gradient Theorem 253

3.6.4 Gradient in Gauss' Law, Ampere's Law, and Faraday's Law 254

3.6.5 Electric Potential Energy 257 3.6.5.1 Electric Potential Energy of Discrete Charg...