Physics
Local Field
In physics, a local field refers to a physical quantity, such as an electric or magnetic field, that exists at a specific point in space and time. It is characterized by its strength and direction at that particular location. Local fields play a crucial role in describing the interactions and behavior of particles and objects within a given region.
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9 Key excerpts on "Local Field"
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 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)
- 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- 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.
eBook - PDFGravitation
Foundations and Frontiers
- T. Padmanabhan(Author)
- 2010(Publication Date)
- Cambridge University Press(Publisher)
2 Scalar and electromagnetic fields in special relativity 2.1 Introduction This chapter develops the ideas of classical field theory in the context of spe-cial relativity. We use a scalar field and the electromagnetic field as examples of classical fields. The discussion of scalar field theory will allow us to under-stand concepts that are unique to field theory in a somewhat simpler context than electromagnetism; it will also be useful later on in the study of topics such as infla-tion, quantum field theory in curved spacetime, etc. As regards electromagnetism, we concentrate on those topics that will have direct relevance in the development of similar ideas in gravity (gauge invariance, Hamilton–Jacobi theory for particle motion, radiation and radiation reaction, etc.). The ideas developed here will be used in the next chapter to understand why a field theory of gravity – developed along similar lines – runs into difficulties. The concept of an action principle for a field will be extensively used in Chapter 6 in the context of gravity. Other topics will prove to be valuable in studying the effect of gravity on different physical systems. 1 2.2 External fields of force In non-relativistic mechanics, the effect of an external force field on a particle can be incorporated by adding to the Lagrangian the term − V ( t, x ) , thereby adding to the action the integral of − V dt . Such a modification is, however, not Lorentz invariant and hence cannot be used in a relativistic theory. Our first task is to determine the form of interactions which are permitted by the Lorentz invariance. The action for the free particle was the integral of dτ (see Eq. (1.72) ), which is Lorentz invariant. We can modify this expression to the form A = − L ( x a , u a ) dτ, (2.1) 54 2.3 Classical scalar field 55 where L ( x a , u a ) is a Lorentz invariant scalar dependent on the position and veloc-ity of the particle, and still maintain Lorentz invariance.
eBook - PDF- Mackillo Kira, Stephan W. Koch(Authors)
- 2011(Publication Date)
- Cambridge University Press(Publisher)
2 Central concepts in classical electromagnetism The mass of a classical particle defines its inertia against force-induced motion changes. The resulting dynamics can be completely described on the basis of Newton’s three laws, see Chapter 1. As an additional feature, some particles are electrically charged. These charges do not only lead to forces between the particles but they also determine how strongly they interact with an electromagnetic force field. Furthermore, charged particles act as sources of electromagnetic fields themselves. If we want to model these effects, we have to describe the interplay between the charges and the electromagnetic fields. This analysis involves a simultaneous treatment of particles, their charges, and the fields induced by them. As a first step, we present in this chapter the fundamental axioms leading to the theory of classical electromagnetism. 2.1 Classical description of electromagnetic fields The classical electromagnetism follows axiomatically from Maxwell’s equations: ∇ · E(r) = 1 ε 0 ρ Q (r), ∇ · B(r) = 0, ∇ × E(r) = − ∂ ∂ t B(r), ∇ × B(r) = 1 c 2 ∂ ∂ t E(r) + μ 0 j(r). (2.1) Here, E(r) is the electric field, B(r) denotes the magnetic field, ρ Q (r) is the charge density, and j(r) the current density. The constants appearing in Eq. (2.1) define the speed of light c = 1/ √ 0 μ 0 via the dielectric constant 0 and the vacuum permeability μ 0 : c = 299 792 458 m s −1 , 0 = 8.854 187 817 × 10 −12 F m −1 , μ 0 = 4π 10 −7 NA −2 , (2.2) expressed in SI units. 26 2.1 Classical description of electromagnetic fields 27 If the particles are described classically, the definition of the charge and current distribution follows from ρ Q (r) ≡ d 3 p Q ρ(r, p ; t ) = Qρ p (r ; t ), j(r) ≡ d 3 p Qv ρ(r, p ; t ), (2.3) respectively. Here, Q is the charge, v is the velocity, and ρ(r, p ; t ) is the phase-space distribution representing the state of the particle.
eBook - PDF- D. S. Jones, I. N. Sneddon, S. Ulam, M. Stark(Authors)
- 2013(Publication Date)
- Pergamon(Publisher)
It is hoped that the discussion of the advanced methods will also be useful to those who have no special interest in electromagnetism. This first chapter will be devoted to deriving general formulae without any rela-tion to specific physical problems ; the application to special problems will be under-taken in later chapters. M A X W E L L ' S E Q U A T I O N S 1.1 The field equations The electromagnetic field is produced by a distribution of electric current and charge. It is now generally accepted that matter is not continuously divisible but is composed of small discrete particles. The motion of such a charged particle is equivalent to a current. However, we are not concerned with the individual microscopic particles — the theory of their motion belongs more properly to quantum theory —but only the average behaviour such as would be determined experimentally. Of course, no T.o.B.j. 2 1 2 THEORY OF ELECTROMAGNETISM strict dividing line can be drawn between the macroscopic theory and quantum theory, but where the processes about to be described are valid should be the domain of macroscopic theory. The final justification can only be provided by obtaining results which are in agreement with experiment. The straightforward definition of the charge density as the limit of the charge per unit volume when the enclosing volume shrinks to zero leads to difficulty when we deal with discrete particles. For, as the volume shrinks, the point is eventually reached when the volume either contains one or no particle and the limit is then either infinite or zero. The same kind of difficulty arises in the kinetic theory of gases and we may overcome it in the same way as in that theory. Let ôv be the volume of a small volume element, which is large enough to contain a large number of particles although its dimensions are small compared with the scale of variation of such macroscopic quantities as the electric and magnetic forces.
- B N Basu(Author)
- 1996(Publication Date)
- World Scientific(Publisher)
PART ONE PRELIMINARY CONCEPTS OF ELECTROMAGNETIC THEORY CHAPTER 2 STA TIC ELECTRIC FIELDS 2.0 Introduction Electrostatics is that branch of electromagnetic theory that deals with static electric fields; it deals with the effects of static or stationary charges. In numerous problems one may be interested to know the static electric field intensity due to these charges distributed in a known manner in a medium or on the surface of a conductor. Also, in some static electric field problems one may have to consider effectively stationary charges which are actually in a state of motion. One such example is an electron beam which may be considered to be smeared out as a continuous fluid of electronic charges. The concepts of electrostatics may, therefore, be applied to electron beam problems, for instance, to the study of the formation of an electron beam by an electron gun — a problem that has been dealt with in details in Chapter 6. In one school of thought the laws of static field problems are derived as the special cases of those of more general, time-varying electromagnetic problems by putting equal to zero all the quantities representing a time-rate of variation. This results into the electric field decoupled from the magnetic field as well as the electric charge decoupled from the electric current. In another school of thought, and that is what we have chosen to adopt in this chapter for electrostatics, we traditionally start from the most fundamental Coulomb's law for the force between two point charges separated by a distance in a homogeneous medium. This law is taken as granted on the basis of experimental observations. It is from this law that all other concepts related to static electric field problems such as Gauss's law, Poisson's and Laplace's equations, etc., would follow m sequence.
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