scholarly journals Two basic systems of maxwell’s equations in a rotating frame: application in theory of ring laser gyro

2020 ◽  
pp. 64-73
Author(s):  
Evgen Bondarenko
Keyword(s):  
Ring Laser ◽  
Electromagnetic Waves ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Plane Waves ◽  
Rotating Frame ◽  
Cylindrical Coordinates ◽  
Laser Gyro ◽  
Component Form ◽  
Velocity Approximation

In the paper, using a linear in angular velocity approximation, two basic well-known systems of Maxwell’s equations in a uniformly rotating frame of reference are considered. The first system of equations was first obtained in the work [L. I. Schiff, Proc. Natl. Acad. Sci. USA 25, 391 (1939)] on the base of use of the formalism of the theory of general relativity, and the second one – in the work [W. M. Irvine, Physica 30, 1160 (1964)] on the base of use of the method of orthonormal tetrad in this theory. In the paper, in the approximation of plane waves, these two vectorial systems of Maxwell’s equations are simplified and rewritten in cylindrical coordinates in scalar component form in order to find the lows of propagation of transversal components of electromagnetic waves in a circular resonator of ring laser gyro in the case of its rotation about sensitivity axis. On the base of these two simplified systems of Maxwell’s equations, the well-known wave equation and its analytical solutions for the named transversal components are obtained. As a result of substitution of these solutions into the first and second simplified systems of Maxwell’s equations, it is revealed that they satisfy only the second one.  On this basis, the conclusion is made that the second system of Maxwell’s equations is more suitable for application in the theory of ring laser gyro than the first one.

XXVI.—On a Polarised Light Quantum

1927 ◽  
Vol 46 ◽  
pp. 306-313
Author(s):  
J. M. Whittaker
Keyword(s):  
Electromagnetic Waves ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Point Of View ◽  
Light Quantum ◽  
Electric Force ◽  
Polarised Light

In the theory of radiation recently advanced by Sir J. J. Thomson it is supposed that electromagnetic waves and quanta are both present in a beam of light. The quanta, which are responsible for the photoelectric effects, are closed rings of electric force propagated in the direction normal to the plane of the ring. Professor Whittaker has discussed this conception from the point of view of Maxwell's equations, and has shown that it is consistent with them ; or rather with an extension of them in which a magnetic density μ analogous to the electric density ρ is introduced.

ELECTROMAGNETIC WAVES AND MAXWELL'S EQUATIONS

1984 ◽  
pp. 730-750
Author(s):  
George B. Arfken ◽  
David F. Griffing ◽  
Donald C. Kelly ◽  
Joseph Priest
Keyword(s):  
Electromagnetic Waves ◽  
Maxwell’S Equations ◽  
Maxwell's Equations

Static and propagating exponential solutions of Maxwell’s equations for crystals

1992 ◽  
Vol 438 (1904) ◽  
pp. 485-510
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Plane Waves ◽  
Electric Permittivity ◽  
Complex Vector ◽  
Time Harmonic ◽  
Inhomogeneous Plane ◽  
Isotropic Media ◽  
Special Case ◽  
Inhomogeneous Plane Waves

Solutions of Maxwell’s equations are considered for anisotropic media for which the electric permittivity κ and magnetic permeability µ are assumed to be arbitrary real positive definite symmetric second order tensors. The propagation of time-harmonic electromagnetic inhomogeneous plane waves or ‘propagating exponential solutions’ in such media has been presented previously. These solutions were systematically obtained by prescribing an ellipse - the directional ellipse associated with a bivector (complex vector) C - and finding the corresponding slowness bivectors. Here, it is shown that for some prescribed directional ellipses, not only propagating exponential solutions (PES), but also static exponential solutions (SES), may be obtained. There are a variety of possibilities. For example, for one choice of directional ellipse it is found that two SES and one PES are possible, whereas, for some other choices, only one SES or only one PES is possible. By a systematic use of bivectors and their associated ellipses, all the possible SES and PES are classified. To complete the classification it is necessary to examine special elliptical sections of the ellipsoids associated with the tensors κ , µ , κ -1 , µ -1 . In particular, sections by planes orthogonal to special directions called ‘generalized optic axes’ and ‘generalized ray axes’ play a major role. These axes reduce to the standard optic axes and ray axes in the special case of magnetically isotropic media.

Solar Radiation through the Atmosphere

2018 ◽  
Author(s):  
E. L. Wolf
Keyword(s):  
Water Vapor ◽  
Thermal Equilibrium ◽  
Electromagnetic Waves ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Black Body ◽  
Black Body Radiation ◽  
The Sun ◽  
Radiated Power ◽  
The Earth

Maxwell’s equations describe radiated power from the Sun through space and the atmosphere to the Earth. Black-body radiation arises from matter in thermal equilibrium, as is derived in this chapter. The Stefan–Boltzmann power law is derived, and its consequences are discussed. Basics of the atmosphere are discussed, including kinetic energy arising from the condensation of water vapor to liquid water. The temperatures in the atmosphere are discussed in a layered model. The Sun’s light arrives at Earth through vacuum and the Earth’s atmosphere as electromagnetic waves described by Maxwell’s equations. In contemporary electrical engineering jargon, this is “wireless”, that connects cellphones.

scholarly journals The quantum theory of dispersion in metallic conductors

1929 ◽  
Vol 124 (794) ◽  
pp. 409-422 ◽  
Keyword(s):  
Electrical Conductivity ◽  
Dielectric Constant ◽  
Electromagnetic Field ◽  
Quantum Theory ◽  
Isotropic Medium ◽  
Electromagnetic Waves ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Classical Electrodynamics ◽  
Metallic Conductivity

1. Formulation of the problem. - The propagation of electromagnetic waves in a homogeneous isotropic medium showing metallic conductivity has been treated phenomenologically on the basis of classical electrodynamics. If in Maxwell's equations for the electromagnetic field curl E = - 1/ c ∂B/∂ t , curl H = 1/ c (∂D/∂ t + 4πI), div D = 4πρ, div B = 0, we assume that D = εE, B = μH, I = σE, (1) where e is the dielectric constant, u the permeability and q the electrical conductivity, we get curl E = - μ/c ∂H/∂ t , curl H = 1/ c (ε ∂E/∂ t 4πσE), div E = 4πρ/ε. div H =0.

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