Physics
Relativistic Electrodynamics
Relativistic electrodynamics is a branch of physics that combines the principles of special relativity with classical electrodynamics. It describes the behavior of electric and magnetic fields in the presence of high speeds and strong gravitational fields. This theory has been crucial in understanding phenomena such as electromagnetic radiation, particle accelerators, and the behavior of charged particles in magnetic fields.
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4 Key excerpts on "Relativistic Electrodynamics"
eBook - PDF- Frederic V. Hartemann(Author)
- 2001(Publication Date)
- CRC Press(Publisher)
3 1 Overview 1.1 Introduction Electrodynamics is the branch of physics concerned with the interaction of charged particles and electromagnetic fields. Most macroscopic phenomena fall under this area of scientific knowledge, including optics, from lasers to astronomy; chemistry, from biomolecular physics to inorganic compounds; and solid-state physics, from semiconductors to superconductivity. The other three known interactions, namely gravitation and the weak and strong inter-actions, are somewhat more limited in scope. They apply either to very large-scale systems, such as galaxies, star clusters, and the topology of the universe, or to processes involving subatomic particles, including quarks, neutrinos, and charged leptons. The latter is exemplified by nuclear fusion reactions of elements lighter than iron in stars, for the strong force, and β -decay and the recently observed neutrino oscillations, for the weak interaction. Recently, with the experimental discovery of the W + , W − , and Z 0 bosons, elec-trodynamics and the weak interaction have been unified into the electro-weak interaction, which governs the interaction of leptons, such as the electron, muon, and tau, and their antiparticles; vector bosons such as the photon, and the intermediate gauge bosons mentioned above; and the three generations of neutrinos associated with these leptons. Within this context, Maxwell’s equations play a major role, as they describe the behavior of the electromagnetic field both in vacuum and in the presence of sources. Historically, these equations were first discovered through the work of Ampère, Coulomb, Faraday, Gauss, and Laplace, to name a few, and were written in integral form. Maxwell unified these equa-tions in a single set, gave their expression in differential form, and modified Ampère’s theorem by introducing the concept of displacement current, as required for reasons of symmetry.
eBook - PDF- Robert J. Gould(Author)
- 2020(Publication Date)
- Princeton University Press(Publisher)
Chapter Two Classical Electrodynamics Classical electrodynamics is contained within quantum electrodynamics as a limit-ing case. It has a domain of validity and applicability to certain problems for which the classical treatment is clearly preferable to the more general quantum-mechanical approach. There is also a close relationship between a number of results in classical radiation theory and corresponding expressions derived in quantum electrodynam-ics. In fact, sometimes classical formulas have a range of validity greater than that expected on the basis of elementary considerations. The relationship between classical and quantum electrodynamics will be discussed briefly in Chapter 3. The quantum-mechanical formulation relies heavily on the classical theory as a guide, starting with the classical field Hamiltonian. This chapter will give a purely classical treatment of radiation. It will not attempt to be a complete description of classical electrodynamics, since that general subject is treated well in several textbooks. However, starting from basic principles, a num-ber of useful and general results will be derived. Applications to specific radiative processes will be given in later chapters. 2.1 RETARDED POTENTIALS 2.1.1 Fields, Potentials, and Gauges In non-covariant form, the four Maxwell equations are An 1 dE VxB = —./ + - — , c c dt VE = Anp, (2.1) V-.B = 0, VxE-| = 0 . c dt These are the microscopic Maxwell equations in terms of the electric and magnetic fields E and B. The sources of the fields are the charge and current densities and would include contributions from the polarization and magnetization of the medium. In the macroscopic form of Maxwell's equations, only the conduction charge densities and currents appear in the equations, which are now equations for D and H and also involve the dialectric constant and magnetic permeability. The forms (2.1) are more convenient for our purposes.
eBook - PDF- David J. Griffiths(Author)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
C H A P T E R 12 Electrodynamics and Relativity 12.1 THE SPECIAL THEORY OF RELATIVITY 12.1.1 Einstein’s Postulates Classical mechanics obeys the principle of relativity: the same laws apply in any inertial reference frame. By “inertial” I mean that the system is at rest or moving with constant velocity. 1 Imagine, for example, that you have loaded a billiard table onto a railroad car, and the train is going at constant speed down a smooth straight track. The game will proceed exactly the same as it would if the train were parked in the station; you don’t have to “correct” your shots for the fact that the train is moving—indeed, if you pulled all the curtains, you would have no way of knowing whether the train was moving or not. Notice by contrast that you know immediately if the train speeds up, or slows down, or rounds a corner, or goes over a bump—the billiard balls roll in weird curved trajectories, and you yourself feel a lurch and spill coffee on your shirt. The laws of mechanics, then, are certainly not the same in accelerating reference frames. In its application to classical mechanics, the principle of relativity is hardly new; it was stated clearly by Galileo. Question: does it also apply to the laws of electrodynamics? At first glance, the answer would seem to be no. After all, a charge in motion produces a magnetic field, whereas a charge at rest does not. A charge carried along by the train would generate a magnetic field, but someone on the train, applying the laws of electrodynamics in that system, would predict no magnetic field. In fact, many of the equations of electrodynamics, starting with the Lorentz force law, make explicit reference to “the” velocity of the charge. It certainly appears, therefore, that electromagnetic theory presupposes the exis- tence of a unique stationary reference frame, with respect to which all velocities are to be measured. And yet there is an extraordinary coincidence that gives us pause.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Orange Apple(Publisher)
In 1905 Albert Einstein published what is now called Special Relativity (SR) – he radically reinterpreted Lorentzian Electrodynamics by changing the concepts of space and time and abolishing the aether. This paved the way to General Relativity. Subsequent work of Hermann Minkowski laid the foundations of Relativistic Field Theories. ________________________ WORLD TECHNOLOGIES ________________________ Aether and Electrodynamics of Moving Bodies Aether models and Maxwell's equations Following the work of Thomas Young (1804) and Augustin-Jean Fresnel (1816), it was believed that light propagates as a transverse wave within an elastic medium called lum-iniferous aether. However, a distinction was made between optical and electrodynamical phenomena so it was necessary to create specific aether models for all phenomena. Attempts to unify those models or to create a complete mechanical description of them did not succeed, but after considerable work by many scientists, including Michael Faraday and Lord Kelvin, James Clerk Maxwell (1864) developed an accurate theory of electromagnetism by deriving a set of equations in electricity, magnetism and inductance, named Maxwell's equations. He first proposed that light was in fact undulations (Electromagnetic radiation) in the same aetherial medium that is the cause of electric and magnetic phenomena. However, Maxwell's theory was unsatisfactory regarding the optics of moving bodies, and while he was able to present a complete mathematical model, he was not able to provide a coherent mechanical description of the aether. After Heinrich Hertz in 1887 demonstrated the existence of electromagnetic waves, Maxwell's theory was widely accepted. In addition, Oliver Heaviside and Hertz further developed the theory and introduced modernized versions of Maxwell's equations.
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