Electromagnetic Fields

Theory and Applications

Ahmad Shahid Khan, Saurabh Kumar Mukerji

• Publisher: CRC Press
• Year: 2020
• ISBN:
  9781000168556
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

The study of electromagnetic field theory is required for proper understanding of every device wherein electricity is used for operation. The proposed textbook on electromagnetic fields covers all the generic and unconventional topics including electrostatic boundary value problems involving two- and three-dimensional Laplacian fields and one- and two- dimensional Poissonion fields, magnetostatic boundary value problems, eddy currents, and electromagnetic compatibility. The subject matter is supported by practical applications, illustrations to supplement the theory, solved numerical problems, solutions manual and Powerpoint slides including appendices and mathematical relations. Aimed at undergraduate, senior undergraduate students of electrical and electronics engineering, it:

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• Presents fundamental concepts of electromagnetic fields in a simplified manner

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• Covers one two- and three-dimensional electrostatic boundary value problems involving Laplacian fields and Poissonion fields

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• Includes exclusive chapters on eddy currents and electromagnetic compatibility

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• Discusses important aspects of magneto static boundary value problems

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• Explores all the basic vector algebra and vector calculus along with couple of two- and three-dimensional problems

1 Introduction

1.1 Introduction

A region of empty or occupied space wherein certain physical states occur is referred to as a field. A field may contain some solid, liquid, or gaseous material. A field has a manifestation of energy in some form, which may correspond to the fall of bodies, transfer of heat, flow of fluids, movement of electric charges, or attraction or repulsion of magnets. Engineers study the way a magnetic flux distributes in an air-gap, the current flows in a thick conductor, the stresses develop in a mechanical device, and vortices and eddies form in the water gushing out of a dam. Any electrical or electronic engineer must always be concerned about the characteristic structures of electrical fields, their nature and sources, the quantities involved, and the utility vis-à-vis the operations of electrical and electronic devices.

Throughout history, people have tried to solve the puzzle of life, their surroundings, and the universe. The giants of electrical sciences, particularly in the area of electromagnetics, include Coulomb, Gauss, Ampère, Hennery, Volta, Faraday, Kirchhoff, Galvani, Oersted, Fleming, Maxwell, Marconi, Bose, and many others. What they sowed we are reaping today, and what we cultivate today future generations will reap. One has to understand what these giants have done and how their successors utilized achievements for the benefit of humanity. Section 1.2 will give a brief account of the history of electromagnetic study.

1.2 Historical Perspective

The historical perspective is divided into three stages: (1) the conceptual stage, (2) the era of basic laws, and (3) the era of inventions.

1.2.1 Conceptual Stage

The concept of static electricity is not a new one. The ability of rubbed amber to attract light particles was recorded in 600 bce by the Greek thinker Thales of Miletus. For nearly 2,000 years, this concept remained almost confined to history. Then in 1296 ce, a magnetic compass was reportedly brought to Venice from the court of Kublai Khan by Marco Polo. In 1600 an English scientist, William Gilbert, demonstrated the effect on a compass of a metalized sphere (similar to earth), and published De Magnete. The word “electricity” was first used by Sir Thomas Browne in 1646 and the first electrostatic machine was reportedly built by Otto Von Guericke in 1650. In 1733 Charles Du Fay discovered two kinds of charges, which he called positive and negative. He also noted the attraction and repulsion of unlike and like charged particles. In 1735 conducting and dielectric properties were demonstrated by Stephen Grey. In 1745 the Leyden jar, the first capacitor, was invented by E. J. G. Von Kleist and P. V. Musschenbrock independently. In 1746 Benjamin Franklin classified electricity into negative (excess of electrons) and positive (deficiency of electrons). He also demonstrated the electrical nature of lightning and invented the lightning conductor in 1752. In 1787, M. Lammond invented the telegraph. In 1790 Alessandro Volta found that the chemistry acting on two dissimilar metals generates electricity, and in 1800 he invented the voltaic pile battery.

1.2.2 Era of Basic Laws

The amount of force exerted between unlike and like charges was first measured by Charles Augustine de Coulomb. The result, now known as Coulomb’s law, was first published in 1785. In 1820 Hans Christian Oersted demonstrated that electric current affects a compass needle. Biot-Savart’s law was also proposed in 1820. In 1822 André-Marie Ampère formulated the law which describes the force between current carrying conductors, known as Ampère’s (force) law. In 1826 George Simon Ohm formulated another law relating voltage, current, and resistance, known as Ohm’s law. Michael Faraday formulated his law of electromagnetic induction in 1831. He presented the idea of electric fields at the Royal Society of London. He also studied the effect of currents on magnets and magnets inducing electric currents. In 1835 Carl Friedrich Gauss formulated the mathematical theory now known as Gauss’s law.

1.2.3 Era of Inventions

Dynamo, the first practical generator, was invented by Hypolite Pixii in 1832. In 1934 André-Marie Ampère invented the galvanometer. The invention of the magnetic telegraph in 1838 is attributed to Samuel Morse and Charles Wheatstone, respectively. The first long distance telegram was exchanged by Samuel Morse and Alfred Viol in 1844. Mehlon Loomis invented radio telegraphy in 1864. The same year, James Clerk Maxwell predicted the existence of electromagnetic waves. His Treatise on Electricity and Magnetism was published in 1873. Maxwell’s equations have become the governing laws for all electromagnetic phenomena at the macro level inside material media that are described by constitutive relations. In 1873 DC Electric Motor was invented by Zénobe Gramme and in 1876 Alexander Graham Bell invented the microphone. Graham Bell also invented the telephone, which was patented that same year. The gramophone and incandescent electric lamps were invented by Thomas Alva Edison in 1878 and 1879, respectively.

Subsequent years saw the invention of a number of important devices as well as discoveries of phenomena, including cathode ray tubes by William Crookes (1878), the AC transformer by William Stanley (1885), the induction motor by Nikola Tesla (1888), the existence of electromagnetic waves by Heinrich Hertz (1888), the transmission of radio waves by J. C. Bose (1894), magnetic tape recorders by Valdemar Poulsen (1899), and the loudspeaker by Horace Short (1900). The radiotelegraph was invented by Guglielmo Marconi in 1900.

From the beginning of the twentieth century, the rate of discoveries and inventions multiplied enormously based on the knowledge thus far acquired. As a result, in 1900 Marconi successfully established communication between U.S. and British battleships that were thirty-eight miles apart. On December 12, 1901, Marconi received the first transatlantic radio telegraphic signals. Inventions in 1902 included the synchronous motor by Ernest Danielson, the photo-electric-cell by Arthur Korn, and the radio telephone by Valdemar Poulsen and Reginald Fessenden. The subsequent years saw the discoveries of the electrocardiograph (ECG or EKG) by Willem Einthoven (1903), the electrostatic precipitator by Frederick Gardner Cottrell (1905), the vacuum tube triode by Lee De Forest (1906), the radio receiver by Ernst Alexanderson and Reginald Fessenden (1913), and the electrical method for recording sound by L. Guest and H. O. Merriman (1920).

One of the most fascinating and useful devices, radar, was invented by A. H. Taylor and L. C. Young (1922). Another useful device, television, was developed over time by Philo Farnsworth (1923), C. Francis Jenkins (1925), John Baird (1926), and P. T. Farnsworth (1927). Subsequent years witnessed the development of many other useful tools such as the electroencephalograph (EEG) by Hans Berger (1929) and the radio telescope by Karl Jansky and Grote Reber (1931). In 1943 Zoltán Bay sent ultra-short radio waves to the moon. Robert Dicke and Robert Beringer used the word microwave in an astronomical context in 1946. Further developments included mobile telephone service by AT & T and Southwestern Bell (1946), the first-generation computer with vacuum tube technology by John Mauchly and John Eckert (1946), the transistor by W. Shockley, J. Bardeen, and W. Brattain (1947), optical fiber by N. S. Kapany (1952), the integrated circuit by Jack Kilby and Robert Noyce (1948), the communications satellite by Kenneth Masterman Smith (1958), the microprocessor by Robert Noyce and Gordon Moore, the computerized tomography scanner (CAT-SCAN) by Sir Godfrey Newbold Hounsfield, magnetic resonance imaging (MRI) by Raymond V. Damadian (1971), and the mobile phone by Bell Labs in 1977. The idea of maglev, a contraction of magnetic levitation was put forward in 1988, along with the Global Positioning System (GPS) by the U.S. Department of Defense in 1993.

1.3 Sphere of Electromagnetics

The word “field” is used in various contexts. It is used for land under cultivation, for playgrounds, and for areas of studies, such as “field of medicine”, “field of engineering”, and so on. Thus, the word “field” covers a variety of areas and actions which need not be confined to living creatures; these actions may also belong to non-living entities such as tiny particles.

1.3.1 Tiny Charged Particles

As all matter in the universe is composed of tiny particles called atoms which in itself is composed of a number of subatomic particles viz. electrons, protons, and neutrons. Electrons and protons are called charge particles since these are assumed to possess an electrical property called charge. The charge content of an electron [(1.60210 ± 0.00007) × 10⁻¹⁹ C] is assumed to be negative whereas that of a proton is of opposite polarity (thus positive) but of the same order. The (rest) mass of an electron (m) is estimated to be [(9.1091 ± 0.0004) × 10⁻³¹ kg], whereas its radius (at rest) is said to be 3.8 × 10⁻¹⁵ meters. The study of activities of these tiny particles has not only revolutionized the world, it influenced almost every sphere of human life.

1.3.2 Behaviour of Tiny Charged Particles

The tiny charged particles referred to above may behave in a variety of ways. When these charges are stationary, their field of influence is called an electrostatic field. The moving charges (with constant speed) constitute steady electric current, which results in a magnetostatic field. The static charges give an effect termed “static electricity,” which does not have any magnetic effect. A steady (dc) current flowing in a conductor produces a magnetic field without any electric field. However, if time-varying or alternating current (ac) flows in a conductor both electric and magnetic fields are produced, such a field is referred to as an electromagnetic or time-varying field. The charged particles act differently in free space or vacuum and in the presence of matter in the media. It is the behavior of these particles that leads to the general categorization of materials as conductors, semiconductors, and insulators (or dielectrics). Thus the fields resulting due to different modes of behavior of charges in different materials need to be thoroughly and systematically studied.

1.3.3 Role of Maxwell Equations

Electromagnetics relates space, time, spatial and temporal frequencies, spatial vectors, complex vectors (or phasors), power, and distributions in three-dimensional ...