scholarly journals Null Electromagnetic Fields from Dilatation and Rotation Transformations of the Hopfion

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1105 ◽  
Author(s):  
Manuel Arrayás ◽  
Antonio F. Rañada ◽  
Alfredo Tiemblo ◽  
José L. Trueba
Keyword(s):  
Electromagnetic Fields ◽  
Maxwell Equations ◽  
Symmetry Transformations ◽  
Field Lines

The application of topology concepts to Maxwell equations has led to the developing of the whole area of electromagnetic knots. In this paper, we apply some symmetry transformations to a particular electromagnetic knot, the hopfion field, to get a new set of knotted solutions with the properties of being null. The new fields are obtained by a homothetic transformation (dilatation) and a rotation of the hopfion, and we study the constraints that the transformations must fulfill in order to generate valid electromagnetic fields propagating in a vacuum. We make use of the Bateman construction and calculate the four-potentials and the electromagnetic helicities. It is observed that the topology of the field lines does not seem to be conserved as it is for the hopfion.

An analogy between electromagnetic and internal waves

2019 ◽  
Vol 485 (4) ◽  
pp. 428-433
Author(s):  
V. G. Baydulov ◽  
P. A. Lesovskiy
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Internal Wave ◽  
Special Relativity ◽  
Internal Waves ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Lagrange Function ◽  
Lorentz Transformations ◽  
Symmetry Transformations

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

scholarly journals ELECTROMAGNETIC FIELDS OF CHARGED AND MAGNETIZED CYLINDRICAL CONDUCTORS IN NUT SPACE

2005 ◽  
Vol 14 (03n04) ◽  
pp. 687-695 ◽  
Author(s):  
B. J. AHMEDOV ◽  
A. V. KHUGAEV ◽  
N. I. RAKHMATOV
Keyword(s):  
Magnetic Field ◽  
Gravitational Field ◽  
Electromagnetic Fields ◽  
Electric Charge ◽  
Maxwell Equations ◽  
Analytic Solutions ◽  
Vertical Magnetic Field ◽  
General Relativistic ◽  
Azimuthal Current ◽  
Cylindrical Conductors

We present analytic solutions of Maxwell equations for infinitely long cylindrical conductors with nonvanishing electric charge and currents in the external background spacetime of a line gravitomagnetic monopole. It has been shown that vertical magnetic field arising around cylindrical conducting shell carrying azimuthal current will be modified by the gravitational field of NUT source. We obtain that the purely general relativistic magnetic field which has no Newtonian analog will be produced around charged gravitomagnetic monopole.

scholarly journals Stable Knots and Links in Electromagnetic Fields

2021 ◽  
Author(s):  
Benjamin Bode
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Fields ◽  
Quantum Fluids ◽  
Closed Field ◽  
Special Role ◽  
Elastic Filaments ◽  
Legendrian Links ◽  
Field Lines ◽  
Standard Contact ◽  
The Magnetic Field

AbstractPersistent topological structures in physical systems have become increasingly important over the last years. Electromagnetic fields with knotted field lines play a special role among these, since they can be used to transfer their knottedness to other systems like plasmas and quantum fluids. In null electromagnetic fields the electric and the magnetic field lines evolve like unbreakable elastic filaments in a fluid flow. In particular, their topology is preserved for all time, so that all knotted closed field lines maintain their knot type. We use an approach due to Bateman to prove that for every link L there is such an electromagnetic field that satisfies Maxwell’s equations in free space and that has closed electric and magnetic field lines in the shape of L for all time. The knotted and linked field lines turn out to be projections of real analytic Legendrian links with respect to the standard contact structure on the 3-sphere.

Biophysical Aspects of EEG and MEG Generation

2017 ◽  
Author(s):  
Wytse J. Wadman ◽  
Fernando H. Lopes da Silva
Keyword(s):  
Electromagnetic Fields ◽  
Maxwell Equations ◽  
Brain Activity ◽  
Electrical Field ◽  
The Third ◽  
Scalp Eeg ◽  
External Electromagnetic Fields ◽  
The Common ◽  
The Brain ◽  
Physical Principles

This chapter reviews the essential physical principles involved in the generation of electroencephalographic (EEG) and magnetoencephalographic (MEG) signals. The general laws governing the electrophysiology of neuronal activity are analyzed within the formalism of the Maxwell equations that constitute the basis for understanding electromagnetic fields in general. Three main topics are discussed. The first is the forward problem: How can one calculate the electrical field that results from a known configuration of neuronal sources? The second is the inverse problem: Given an electrical field as a function of space and time mostly recorded at the scalp (EEG/MEG), how can one reconstruct the underlying generators at the brain level? The third is the reverse problem: How can brain activity be modulated by external electromagnetic fields with diagnostic and/or therapeutic objectives? The chapter emphasizes the importance of understanding the common biophysical framework concerning these three main topics of brain electrical and magnetic activities.

Maxwell Equations for Slow-Moving Media

2015 ◽  
Vol 70 (12) ◽  
pp. 1019-1024 ◽  
Author(s):  
Andrey Rozov
Keyword(s):  
Experimental Data ◽  
Electromagnetic Fields ◽  
Maxwell Equations ◽  
Classical Mechanics ◽  
Theory Of Relativity ◽  
Maxwell Theory ◽  
Electromagnetic Processes ◽  
Maxwell Models ◽  
Slow Moving ◽  
Moving Media

AbstractIn the present work, the Minkowski equations obtained on the basis of theory of relativity are used to describe electromagnetic fields in moving media. But important electromagnetic processes run under non-relativistic conditions of slow-moving media. Therefore, one should carry out its description in terms of classical mechanics. Hertz derived electrodynamic equations for moving media within the frame of classical mechanics on the basis of the Maxwell theory. His equations disagree with the experimental data concerned with the moving dielectrics. In the paper, a way of description of electromagnetic fields in slow-moving media on the basis of the Maxwell theory within the frame of classical mechanics is offered by combining the Hertz approach and the experimental data concerned with the movement of dielectrics in electromagnetic fields. Received Maxwell equations lack asymmetry in the description of the reciprocal electrodynamic action of a magnet and a conductor and conform to known experimental data. Comparative analysis of the Minkowski and Maxwell models is carried out.

GEOMETRICAL PROPERTIES OF ELECTROMAGNETIC TIDAL FORCES

2010 ◽  
Vol 25 (29) ◽  
pp. 5383-5398
Author(s):  
ÉRICO GOULART ◽  
FELIPE TOVAR FALCIANO
Keyword(s):  
General Relativity ◽  
Electromagnetic Fields ◽  
Local Field ◽  
Degrees Of Freedom ◽  
Charged Particles ◽  
Tidal Effects ◽  
Geometrical Properties ◽  
Tidal Forces ◽  
Field Lines ◽  
Internal Degrees Of Freedom

In general, elementary particles as well as extensive bodies have internal degrees of freedom that naturally turn their trajectories into accelerated curves. Hence, we propose to describe the kinematical properties of nongeodesic congruences and study how tidal forces are modified. Once the general scenario is well established, we analyze in details tidal effects due to electromagnetic fields, i.e. the relative acceleration between test charged particles. An algebraic analysis of these fields is developed together with a geometrical interpretation in terms of local field lines. In this framework, we compare general relativity and electrodynamics in terms of operationally equivalent objects.

Analysis on Lightning Electromagnetic Fields

2013 ◽  
Vol 401-403 ◽  
pp. 350-353 ◽  
Author(s):  
Pi Cui Zhang ◽  
Wei He ◽  
Liu Ling Wang ◽  
Li Feng Ma
Keyword(s):  
Electromagnetic Field ◽  
Spatial Distribution ◽  
Electromagnetic Fields ◽  
Maxwell Equations ◽  
Practical Significance ◽  
Lightning Protection ◽  
Perfect Conductor ◽  
Fundamental Theory ◽  
Lightning Current ◽  
The Earth

t is generally needed to know precisely spatial distribution of lightning electromagnetic fields in the lightning protection measurements. Therefore, the research on the lightning electromagnetic field is of practical significance. In this paper, the Maxwell equations were used to calculate and analyze the spatial distribution of lightning electromagnetic fields surrounding lightning current. And the expressions of lightning current electromagnetic fields were deduced under the assumption that the earth was under the condition of perfect conductor. The spatial distributions of the components of lightning electromagnetic fields have been plotted by Matlab. The results would provide fundamental theory for the research of lightning electromagnetic field and lightning protection measurements.

scholarly journals Mathematical model of penetration of cylindrical electromagnetic fields with axial symmetry through the plane screen from permalloy

Informatics ◽  
2020 ◽  
Vol 17 (2) ◽  
pp. 103-119
Author(s):  
V. Т. Erofeenko
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Electromagnetic Fields ◽  
Axial Symmetry ◽  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Boundary Value ◽  
Algebraic Equations ◽  
The Face ◽  
Classical Boundary

The method for solving the boundary-value problem of penetration of monochromatic electromagnetic fields with axial symmetry through the plane screen made from the permalloy is developed. The boundary-value problem is based on the use of differential Maxwell equations and complementary nonlinear differential equation for the field of magnetization, characterizing the permalloy. Classical boundary conditions of continuity of the tangential components of the fields and complementary boundary conditions for the field of magnetization on the face surfaces of the shield are used. For solution simplification of the boundary-value problem as a result of exclusion value the entering in nonlinear equation second-order infinitesimal, nonlinear task is transformed into linear task. Roots (wave numbers) of a dispersion algebraic equations of four order, which characterizing electromagnetic fields with axial symmetry in layer made from the permalloy, is constructed. The sequences of four forward and four backward counter-propagating electromagnetic waves with axial symmetry in the layer of permalloy is formed. Two-sided boundary conditions connecting electromagnetic fields with axial symmetry on both sides of the screen is constructed. The amplitudes of reflected and transient through the shield electromagnetic fields are calculated.

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