Physics
Electromagnetic Field
An electromagnetic field is a physical field produced by electrically charged particles and is characterized by the electric and magnetic forces it exerts on other charged particles. It consists of electric and magnetic field components that are interconnected and propagate through space. Electromagnetic fields play a fundamental role in the behavior of charged particles and are central to the study of electromagnetism.
Written by Perlego with AI-assistance
Related key terms
1 of 5
11 Key excerpts on "Electromagnetic Field"
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 8 Electromagnetic Field An Electromagnetic Field (also EMF or EM field ) is a physical field produced by electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The Electromagnetic Field extends indefinitely throughout space and describes the electromagnetic interaction. It is one of the four fundamental forces of nature (the others are gravitation, the weak interaction, and the strong interaction). The field can be viewed as the combination of an electric field and a magnetic field. The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field. The way in which charges and currents interact with the Electromagnetic Field is described by Maxwell's equations and the Lorentz force law. From a classical perspective, the Electromagnetic Field can be regarded as a smooth, continuous field, propagated in a wavelike manner; whereas from the perspective of quantum field theory, the field is seen as quantized, being composed of individual particles. Structure of the Electromagnetic Field The Electromagnetic Field may be viewed in two distinct ways. Continuous structure Classically, electric and magnetic fields are thought of as being produced by smooth motions of charged objects. For example, oscillating charges produce electric and magnetic fields that may be viewed in a 'smooth', continuous, wavelike fashion. In this case, energy is viewed as being transferred continuously through the Electromagnetic Field between any two locations. For instance, the metal atoms in a radio transmitter appear to transfer energy continuously. This view is useful to a certain extent (radiation of low frequency), but problems are found at high frequencies. This problem leads to another view.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Library Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 2 Electromagnetic Field An Electromagnetic Field (also EMF or EM field ) is a physical field produced by electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The Electromagnetic Field extends indefinitely throughout space and describes the electromagnetic interaction. It is one of the four fundamental forces of nature (the others are gravitation, the weak interaction, and the strong interaction). The field can be viewed as the combination of an electric field and a magnetic field. The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field. The way in which charges and currents interact with the Electromagnetic Field is described by Maxwell's equations and the Lorentz force law. From a classical perspective, the Electromagnetic Field can be regarded as a smooth, continuous field, propagated in a wavelike manner; whereas from the perspective of quantum field theory, the field is seen as quantized, being composed of individual particles. Structure of the Electromagnetic Field The Electromagnetic Field may be viewed in two distinct ways. Continuous structure Classically, electric and magnetic fields are thought of as being produced by smooth motions of charged objects. For example, oscillating charges produce electric and magne-tic fields that may be viewed in a 'smooth', continuous, wavelike fashion. In this case, energy is viewed as being transferred continuously through the Electromagnetic Field between any two locations. For instance, the metal atoms in a radio transmitter appear to transfer energy continuously. This view is useful to a certain extent (radiation of low frequency), but problems are found at high frequencies. This problem leads to another view.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 2 Electromagnetic Field An Electromagnetic Field (also EMF or EM field ) is a physical field produced by electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The Electromagnetic Field extends indefinitely throughout space and describes the electromagnetic interaction. It is one of the four fundamental forces of nature (the others are gravitation, the weak interaction, and the strong interaction). The field can be viewed as the combination of an electric field and a magnetic field. The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field. The way in which charges and currents interact with the Electromagnetic Field is described by Maxwell's equations and the Lorentz force law. From a classical perspective, the Electromagnetic Field can be regarded as a smooth, continuous field, propagated in a wavelike manner; whereas from the perspective of quantum field theory, the field is seen as quantized, being composed of individual particles. Structure of the Electromagnetic Field The Electromagnetic Field may be viewed in two distinct ways. ________________________ WORLD TECHNOLOGIES ________________________ Continuous structure Classically, electric and magnetic fields are thought of as being produced by smooth motions of charged objects. For example, oscillating charges produce electric and magnetic fields that may be viewed in a 'smooth', continuous, wavelike fashion. In this case, energy is viewed as being transferred continuously through the Electromagnetic Field between any two locations. For instance, the metal atoms in a radio transmitter appear to transfer energy continuously. This view is useful to a certain extent (radiation of low frequency), but problems are found at high frequencies.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 2 Electromagnetic Field An Electromagnetic Field (also EMF or EM field ) is a physical field produced by electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The Electromagnetic Field extends indefinitely throughout space and describes the electromagnetic interaction. It is one of the four fundamental forces of nature (the others are gravitation, the weak interaction, and the strong interaction). The field can be viewed as the combination of an electric field and a magnetic field. The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field. The way in which charges and currents interact with the Electromagnetic Field is described by Maxwell's equations and the Lorentz force law. From a classical perspective, the Electromagnetic Field can be regarded as a smooth, continuous field, propagated in a wavelike manner; whereas from the perspective of quantum field theory, the field is seen as quantized, being composed of individual particles. Structure of the Electromagnetic Field The Electromagnetic Field may be viewed in two distinct ways. Continuous structure ________________________ WORLD TECHNOLOGIES ________________________ Classically, electric and magnetic fields are thought of as being produced by smooth motions of charged objects. For example, oscillating charges produce electric and magnetic fields that may be viewed in a 'smooth', continuous, wavelike fashion. In this case, energy is viewed as being transferred continuously through the Electromagnetic Field between any two locations. For instance, the metal atoms in a radio transmitter appear to transfer energy continuously. This view is useful to a certain extent (radiation of low frequency), but problems are found at high frequencies.
eBook - PDF- Cynthia Furse, Douglas A. Christensen, Carl H. Durney(Authors)
- 2009(Publication Date)
- CRC Press(Publisher)
The purpose of this book is to help you understand Electromagnetic Fields and how they interact with the body, how they are created, how they can be measured and evaluated, and how they can be controlled. This book begins with the field of classical electromagnetics, which stems from the phenomenon that electric charges exert forces on each other. The concepts of electric and magnetic fields are used to describe the multitude of complex bioeffects that result from this basic phenomenon. Although classical electromagnetic (EM) field theory is typically couched in vector calculus and partial differential equations, many of the basic concepts and characteristic behaviors can be understood without a strong mathematical background. The purpose of this book is to describe and explain these basic concepts and characteris-tic behaviors with a minimum of mathematics, and to show how they are used in a wide variety of bioelectromagnetic applications. In this chapter we explain the basic concepts of electric and magnetic fields as a basis for what follows in the remainder of the book. 1.2 Electric Field Concepts A fundamental law, Coulomb’s law, states that electric charges exert forces on each other in a direction along the line between the charges. Charges with the same sign repel, and charges with opposite signs attract. The magnitude of the force exerted on one charge by 2 Basic Introduction to Bioelectromagnetics, Second Edition another charge is inversely proportional to the square of the distance between the two charges. Because keeping track of the forces exerted on individual charges in a complex system of charges is almost impossible in practice, the concept of electric field is used to account for the forces. The concept of electric field is illustrated by this thought experiment: Place a small test charge Q test at a point in space P, as shown in Figure 1.1(a). Whatever other charges exist will exert a force on this test charge.
eBook - PDF- Roger G. Newton(Author)
- 2021(Publication Date)
- Princeton University Press(Publisher)
Furthermore, electro-magnetic waves transport both energy and momentum over long distances—light exerts pressure—and the transport takes time to travel at the speed of light. Only the total energy and the total momentum of the charged particles and the field together are con-served. There is, therefore, good reason to ascribe reality to the field as a condition of space. It has to be considered just as real as the charges themselves—perhaps even more so. DIFFERENTIAL EQUATIONS FOR THE FIELDS If Faraday's principal aim in introducing electric and magnetic fields was to rid physics of action at a distance, the field con-cept alone achieved this purpose only partially. After all, there is little conceptual difference between stating Coulomb's law di-rectly for the force between two distant charges—the force is inversely proportional to the square of the distance between the charges—and formulating the same law for the field at a dis-tant point P B , where the field strength is inversely proportional to the square of the distance of P B to the charge at P A . Maxwell's achievement was carrying the aim of abolishing action at a dis-tance to its logical conclusion by formulating the laws governing the Electromagnetic Field in terms of partial differential equa-tions. While it is true that Coulomb's law is nothing but the FIELDS AND PARTICLES solution of Poisson's equation (with appropriate boundary con-ditions), there is a profound conceptual difference between the two. The former expresses the field at point P B directly in terms of the charges at points P Ai , i = 1,2, ... , and their distances from P B , as would be proper for a force in an action-at-a-distance theory, whereas Poisson's partial differential equation relates the value of the electric field at each point to its values at infinitesimally neighboring points.
- Henry Kressel(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
Chapter 4 Relevant Concepts in Electromagnetic Field Theory 4.1 Introduction This chapter deals with some of the more fundamental aspects of classical electromagnetic theory, with the emphasis placed on those results applicable to wave phenomena in the optical frequency spectrum. Since wave phenome-na can be derived from Maxwell's equations it is appropriate to consider some of the more fundamental aspects of these equations. For the most general case, the electric and magnetic fields are generally written as a function of both spatial variables, x, y, z and time t as follows Because mathematical tools such as Fourier analysis can be applied to an arbitrary time varying signal, we can assume without loss of generality the harmonic time varying signals where Re means the real part of the term in brackets. In these expressions, the quantities E and H are complex functions. To simplify the field expressions, the Re designation is dropped, and the resulting field expressions become e = e (x,y,z;t) h = h (x,y,z;t) (4.1.1) (4.1.2) e = Re[E(x, y, z)e i(0t ] h = Re [H (x, y, z)e i0 ><] (4.1.3) (4.1.4) e = E(JC, y, z)e icot h = H(x, y, z)e icot (4.1.5) (4.1.6) 117 118 4. RELEVANT CONCEPTS IN Electromagnetic Field THEORY The complex notation illustrated here is very useful in analysis; however, certain basic precautions should be taken with some algebraic manipulations such as multiplication of two complex quantities. This situation arises when energy and power are derived from products of the electric and magnetic fields. To discuss the complex number manipulations, consider the electric / i d ) I v(t) Z L . _y FIG. 4.1.1 Power considerations in an electric circuit. The instantaneous voltage and current are shown in the circuit. circuit shown in Fig. 4.1.1. The time average power flowing to the load Z L is given by [1] = ±fi(t)v(t)dt (4.1.7) where the brackets enclosing p(t) indicate the time average.
eBook - PDF- Ole Keller(Author)
- 2016(Publication Date)
- CRC Press(Publisher)
2 Fundamentals of free Electromagnetic Fields 2.1 Maxwell equations and wave equations Classical electromagnetics is summed up in the Maxwell–Lorentz equations [56, 57, 133], and in the absence of charges the electric and magnetic fields, E ( r ,t ) and B ( r ,t ), satisfy the equations ∇ × E ( r ,t ) = − ∂ ∂t B ( r ,t ) , (2.1) ∇ × B ( r ,t ) = c − 2 ∂ ∂t E ( r ,t ) , (2.2) ∇ · E ( r ,t ) = 0 , (2.3) ∇ · B ( r ,t ) = 0 , (2.4) in space ( r )-time ( t ). Eqs. (2.3) and (2.4) specify that both E and B are divergence-free (solenoidal) fields in matter-free regions of space. The magnetic field remains divergence-free in matter-filled domains, and this is so because our present theory is based on the fact that there is no experimental evidence for the existence of magnetic charges or monopoles. Since electric charges do exist, the electric field will not be divergence-free in matter-filled regions, and Eq. (2.3) thus must be modified in such regions. Whether a region can be characterized as matter-filled in the context of classical electromagnetics requires some remarks. In the macroscopic Maxwell theory matter is conceived as a continuum and the characterization complies with this. In the microscopic Maxwell–Lorentz theory all relevant charged particles (electrons, protons, ions) are treated as point-like entities. In consequence matter is present only in discrete points, and in these the charge density is infinite. In the covering theory of classical electrodynamics, named semiclassical electrodynamics [206], the dynamics of the charged elementary particles (electrons, etc.) is treated on the basis of quantum mechanics. Although we think of these particles as point-like entities, quantum theory does not allow one to determine (at a given time) a particle’s position precisely. The probabilistic nature of quantum mechanics in a way leads us back to a continuum view of matter, yet in a quantum statistical sense to be described later on.
- Robert C. Scully, Mark A. Steffka, Clayton R. Paul(Authors)
- 2022(Publication Date)
- Wiley(Publisher)
APPENDIX B The Electromagnetic Field Equations and Waves Electromagnetic Field theory and Maxwell’s equations underlie all electrical phenomena. This appendix summarizes the essential Electromagnetic Field concepts necessary for understanding and solving EMC problems, as well as designing modern electronic systems that are electromagnetically compatible with their environment. Standard electrical engineering curricula require at least one semester covering this material. Hence, this appendix will serve as a brief review of that important topic. The reader is referred to [1, 2] or other standard undergraduate electromagnetics texts for a more thorough discussion. Recall that the frequency range of the regulations is rather large: from 150 kHz to 30 MHz for conducted emissions and from 30 MHz to above 1 GHz for radiated emissions. Thus, the electri- cal dimensions of an electronic product and its associated connection cables (as well as the ac power cord) may not be electrically small (much less than a wavelength), in which case the usual lumped-circuit notions and analysis principles such as Kirchhoff’s laws do not apply. Attempting to analyze electrically large structures using these lumped-circuit analysis principles will lead to erro- neous conclusions and faulty designs. The laws governing the behavior of electrically large structures (Maxwell’s equations) are not as simple to use as are the lumped-circuit analysis principles. However, for electrically large structures, we have no other recourse. Some problems are sufficiently small, electrically, so that the simpler lumped-circuit analysis techniques will be applicable (in a reason- ably approximate sense). An example is the modeling of small, electronic components. Where it is possible, we will utilize the simpler analysis method. All macroscopic electromagnetic phenomena are governed by Maxwell’s equations.
- Wenquan Sui(Author)
- 2018(Publication Date)
- CRC Press(Publisher)
19 CHAPTER 2 Electromagnetic Field THEORY 2.1 I ntroduction The discovery and understanding of electromagnetic phenomena in general can be traced back thousands of years ago when ancient philosophers were interested in the physical world around them. When amber was rubbed by fur, it could attract small objects; in today’s theory, it had been electrically charged. Lightning in the sky of course was the subject of heavenly worship, but complex electromagnetic processes were involved in the natural phenomenon, which is still being studied by scientists armed with the latest equipment. Those natural phenomena led to the recognition of the existence of electric power, yet a truly scientific explanation and quantization was completed a little more than a century ago. Generation and utilization of such power for human life have fully blossomed only in the last few decades. With the proliferation of modern electronic devices, high-power electricity became a daily necessity, and a pocket-sized gameboy, to a seven-year-old, is something that naturally exists, like stars in the night sky. It took generations of scientists in hundreds of years to complete the theory of electromagnetics. Although not a focus of this book, a brief introduction of electromagnetics would be helpful to start our journey, which will eventually bring us to the state of art of computational electromagnetics. Predicting the future is always dangerous, but there is an old Chinese saying “knowing the past will help understanding the new.” Keeping that in mind, some historical review is probably not too far out of the scope of this chapter. In fact, when those names of the pioneers and their contributions are mentioned in this chapter, the theory they developed, in the forms of theorem that many of them are familiar to high-school seniors, will be introduced.
eBook - PDFEngineering Electromagnetics
Pergamon Unified Engineering Series
- David T. Thomas, Thomas F. Irvine, James P. Hartnett, William F. Hughes(Authors)
- 2013(Publication Date)
- Pergamon(Publisher)
By traditional usage these four vectors are called E, the electric field intensity, D, the electric displacement vector, H, the magnetic field intensity, B, the magnetic induction or flux density. Precise definition of each field vector will be withheld until the appropriate experiments or problems are discussed which describe the properties of each. In the real world these vectors are finite at every point in space, and for all time; furthermore, they must be continuous functions of space and time and have continuous derivatives whenever the material in the region is continuous (in the macroscopic sense). However, in the models of the real world which we must use in order to work problems we allow the field vectors to become infinite at a point charge, and to be discontinuous at any boundary separating two materials or media. Excluding these possibilities, all field vectors must be continuous functions of space and time, and have continuous derivatives. In terms of these four vectors, Maxwell's Equations are, (2.1) (2.2) (2.3) (2.4) Sources of Electromagnetic Fields 41 These equations are valid at all points in space, and for all time. They are in differential form (as opposed to integral form, which will be seen later). Macroscopic Fields This text will deal with macroscopic fields only. While Maxwell's Equations are valid at microscopic or atomic levels, the material properties to be dis-cussed strongly depend on quantum mechanics at microscopic levels. Since our purpose in this text is electromagnetics, not atomic physics or quantum me-chanics, all fields are assumed of macroscopic size. But just what is macro-scopic? Macroscopic is when spatial variations are orders of magnitude longer than atomic sizes. This could include variations of size one millimeter or even less! RMKS Units The system of units used here and throughout this text are the Rationalized Meters-Kilograms-Seconds units (RMKS).
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
