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MATLAB-Based Electromagnetics, 1st edition

Published by Pearson (May 9, 2013) © 2014

  • Branislav Notaros
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Can be used to either complement available electromagnetics text, or as an independent resource. Designed primarily for undergraduate electromagnetics, but can also be used in follow-up courses on antennas, propagation, microwaves, advanced electromagnetic theory, computational electromagnetics, electrical machines, signal integrity, etc.


MATLAB-Based Electromagentics provides engineering and physics students and other users with an operational knowledge and firm grasp of electromagnetic fundamentals aimed toward practical engineering applications, by teaching them “hands on” electromagnetics through a unique and comprehensive collection of MATLAB computer exercises and projects. Essentially, the book unifies two themes: it presents and explains electromagnetics using MATLAB on one side, and develops and discusses MATLAB for electromagnetics on the other.

MATLAB codes described (and listed) in TUTORIALS or proposed in other exercises provide prolonged benefits of learning. By running codes; generating results, figures, and diagrams; playing movies and animations; and solving a large variety of problems in MATLAB, in class, with peers in study groups, or individually, students gain a deep understanding of electromagnetics.

1 Electrostatic Field in Free Space 1
1.1 Coulomb’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Electric Field Intensity Vector Due to Given Charge Distributions . . . . . . . . . 9
1.3 Electric Scalar Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.4 Differential Relationship Between the Field and Potential in Electrostatics, Gradient 26
1.5 Electric Dipole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.6 Gauss’ Law in Integral Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.7 Differential Form of Gauss’ Law, Divergence . . . . . . . . . . . . . . . . . . . . . . 31
1.8 Method of Moments for Numerical Analysis of Charged Metallic Bodies . . . . . . 33
2 Electrostatic Field in Dielectrics 41
2.1 Characterization of Dielectric Materials . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2 Dielectric—Dielectric Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . 46
2.3 Poisson’s and Laplace’s Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.4 Finite-Difference Method for Numerical Solution of Laplace’s Equation . . . . . . . 51
2.5 Evaluation of Capacitances of Capacitors and Transmission Lines . . . . . . . . . . 59
2.6 Capacitors with Inhomogeneous Dielectrics . . . . . . . . . . . . . . . . . . . . . . 69
2.7 Dielectric Breakdown in Electrostatic Systems . . . . . . . . . . . . . . . . . . . . . 70
3 Steady Electric Currents 73
3.1 Continuity Equation, Conductivity, and Ohm’s Law in Local Form . . . . . . . . . 73
3.2 Boundary Conditions for Steady Currents . . . . . . . . . . . . . . . . . . . . . . . 79
3.3 Relaxation Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.4 Resistance and Ohm’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4 Magnetostatic Field in Free Space 86
4.1 Magnetic Force and Magnetic Flux Density Vector . . . . . . . . . . . . . . . . . . 86
4.2 Magnetic Field Computation Using Biot—Savart Law . . . . . . . . . . . . . . . . . 92
4.3 Ampere’s Law in Integral Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.4 Differential Form of Ampere’s Law, Curl . . . . . . . . . . . . . . . . . . . . . . . . 102
4.5 Magnetic Vector Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.6 Magnetic Dipole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5 Magnetostatic Field in Material Media 106
5.1 Permeability of Magnetic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.2 Boundary Conditions for the Magnetic Field . . . . . . . . . . . . . . . . . . . . . . 108
5.3 Magnetic Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
vi Contents, Preface, and m Files on Instructor Resources
6 Time-Varying Electromagnetic Field 118
6.1 Faraday’s Law of Electromagnetic Induction . . . . . . . . . . . . . . . . . . . . . . 118
6.2 Self-Inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.3 Mutual Inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.4 Displacement Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.5 Maxwell’s Equations for the Time-Varying Electromagnetic Field . . . . . . . . . . 130
6.6 Boundary Conditions for the Time-Varying Electromagnetic Field . . . . . . . . . . 132
6.7 Time-Harmonic Electromagnetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.8 Complex Representatives of Time-Harmonic Field and Circuit Quantities . . . . . 137
6.9 Instantaneous and Complex Poynting Vector . . . . . .

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