## The Theory Of Electromagnetic Field – Polivanov

In this post, we will see the book The Theory Of Electromagnetic Field by K. Polivanov. The theory of an electromagnetic field is a concluding subject in the curriculum of the theoretical training of electrical engineers. The field theory course usually follows the course in the basic theory of electric circuits.
The author covers the basic aspects of the theory of an electromagnetic field within the restricted space so that the text can fit the interest of students and answer the practical engineering needs. The emphasis therefore is on the behavior of fer­romagnetic bodies in an electromagnetic field and on the processes in real imperfect dielectrics and poor conductors. The text also gives strict definitions of the basic vec­tors and shows the differences between them.
Many of the aspects discussed in the book focus on the problems one has to deal with in electrical engineering practice. This is one of the factors that influenced the organization of the book and the manner of presentation of the material. A similar treatment of the field theory was also given in the book by A. Netushil and K. Polivanov The Theory o f Electromagnetic Field. Theoretical Principles o f Elec­trical Engineering. Part 3 (Gosenergoizdat, in Russian). No effort has been made to cite a great number of contributors in this area. In the author’s opinion, of many valuable texts, the following books will be very helpful to students in the study of the theory of electrical engineering: Analysis and Synthesis o f Electric Circuits (Mir Publishers) by G. Zeveke, P. Ionkin, A. Netushil, and S. Strakhov, The Feynman Lectures on Physics (Addison-Wesley) by R. Feynman, R. Leighton, and M. Sands, Electricity and Magnetism (McGraw-Hill) by E. Purcell that treats the effects of moving bodies in an electromagnetic Field, and Fundamentals of the Theory of Elec­tricity (Mir Publishers) by I. Tamm. Special mention should be made of Maxwell’s Treatise on Electricity and Magnetism which forms the basis of the course in the field theory.
In preparing the book for its publication in English, the author revised the text and added some useful information.

The book was translated from Russian by P. Ivanov was published in 1983 by Mir Publishers.

PS: This book was in my collection for a very long time, digitised recently.

You can get the book here.

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# Contents

## Chapter 1. Maxwell’s Equations 9

1.1. Classical Electrodynamics 9
1.2. Maxwell’s Equations in Integral Form 10
1.3. Principal Electric Field Vector 12
1.4, Principal Magnetic Field Vector 14
1.5. Principle of Superposition 16
1.6. Field Calculation by Equations in Integral Form 17

## Chapter 2. Differential Field Equations 21

2.1. Differential Operators 21
2.2. Examples of Operations on Various Fields 24
2.3. Displacement Current in Vacuum 26
2.4. Corollaries to Maxwell’s Equations 29
2.5. Scalar and Vector Potentials 33
2.6. Electric Field Expressed in Terms of Two Potentials 39

## Chapter 3. Electromagnetic Field in Polarizable Bodies and Conductors. Static and Quasistatic Conditions 45

3.1. Stationary (Quasistatic) Field in the Presence of Polarized 45
3.2. A Dielectric in a Time-Varying Field 55
3.3. Stationary Magnetic Fields in Magnetized Media 64
3.4. Ferromagnet in a Time-Varying Field 76
3.5. Notes on Sections 3.1 t0 3.4 80
3.6. Electric Field in a Conducting Medium. Quasistatic Conditions 80

## Chapter 4. Simple Solutions of Field Equations and Their Applications in Circuit Theory 81

4.1. Electric Field and Electric Parameters of Parallel Wires 81
4.2. Self-Inductance and Mutual Inductance 89
4.3. Equations of Field Lines 97
4.4. Approximate Methods of Calculation of Potential Fields 98
4.5. Simple Approximate Calculations of Capacitance and Inductance 103
4.6. Potential Field Modeling. Electrolytic Tanks 105
4.7. The Reciprocity Principle for a DC Circuit 109
4.8. Theorems of a Magnetic Flux and Induced Electric Charge 110

## Chapter 5 Potential Electric Fields 119

5.1. General Features of Calculation Methods 119
5.2. Solution to Partial Differential Equations by the Fourier-Euler Method 122
5.3. Simple Problems Solvable in the Cylindrical and Spherical Coordinate Systems 123
5.4. Polarized Ellipsoid. Coefficients of Depolarization 131
5.5. Polarizable Bodies in an AC Field 133
5.6. Transients in Quasistatic Fields. Relaxation 133
5.7. Method of Images 135
5.8. Method of Complex Functions. Conformal Mapping 139
5.9. Van-der-Pauw’s Theorem 143

## Chapter 6. Magnetic Fields. Quasistatic and Quasistationary Conditions 146

6.1. Solution of Magnetostatic Field Equations 146
6.2. Demagnetization Factors 146
6.3. Method of Images for a Magnetic Field 153
6.4. Magnetic Field in Electrical Machines 155
6.5. Vector Potential for the Magnetic Field in an Electrical Machine 158

## Chapter 7. Energy and Force 162

7.1. General 162
7.2. Field Energy and its Flow 172
7.3. Energy Transfer in Electrical Machines 180
7.4. Energy Converters 183
7.5. Lifting Force of a Magnet 183
7.6. Determining Forces from Reluctance 185

## Chapter 8. Varying Electromagnetic Field in a Conducting Medium. Skin Effect 186

8.1 General 186
8.2. Varying Magnetic Field in a Thin Plate 198
8.3. The Skin Effect in a Coaxial Cable 206
8.4. Electromagnetic Field in Conductors of a Two-Wire Line 212
8.5. Conductors in the Slot of an Electrical Machine 213
8.6. Study of the Skin Effect on Models 217

## Chapter 9. Propagation and Reflection of Electromagnetic Waves 221

9.1. Plane Wave Propagation 221
9.2. Cavity Resonators and Waveguides 233
9.3. Waves in a Nonlinear Medium 244

## Chapter 10. Electromagnetic Wave Radiation

10.1. Introductory Remarks 246
10.2. Delayed Potentials 248
10.4. Half-Wave Antenna 256 