Equations of electrodynamics: Final essence of EM phenomena

In this article we will discus the usage feature of the ground penetrating radar (GPR) for the solution underground geotechnologies problems. One of the main problems by the usage GPR method is that the surface of the workings is shielded by metal elements of support (frames, fittings, tightening and other). In this article we suggest to use one- dimensional GPR-scanning method instead of traditional GPR-profiling method. We assume that the scanning will be performed on the development contour in areas free from shielding. For justification one- dimensional GPR method we propose a mathematical model for the propagation of an electromagnetic signal in an inhomogeneous medium based on classical equations of electrodynamics. We also present a numerical implementation of it, which confirms the validity of the accepted problem statement.

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The Governing Equations of Electrodynamics

Introduction to Magnetohydrodynamics ◽

10.1017/9781316672853.005 ◽

2017 ◽

pp. 27-56

Keyword(s):

Governing Equations ◽

Equations Of Electrodynamics

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Integrals of the equations of electrodynamics with to the electric constants of a transparent medium

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1926.0151 ◽

1926 ◽

Vol 113 (764) ◽

pp. 237-253 ◽

Cited By ~ 2

Keyword(s):

Electric Current ◽

Current Distribution ◽

Magnetic Force ◽

Small Radius ◽

Transparent Medium ◽

Electric Force ◽

Present Communication ◽

Magnetic Current ◽

Magnetic Forces ◽

Equations Of Electrodynamics

Integrals of the equations of propagation of electrical disturbances have been given by the present writer which express the electric and magnetic forces at any point outside a surface enclosing all the sources in terms of an electric current distribution and a magnetic current distribution over the surface. The result for a source at a point can be obtained by taking as the surface a sphere of very small radius with its centre at the point. This suggests that the equations representing Faraday’s laws can be written 1/V 2 ∂X/∂ t +4π i x = ∂ϒ/∂ y – ∂β/∂ z , 1/V 2 ∂X/∂ t + 4π i v =∂∝/∂ z – ∂ϒ/∂ x , 1/V 2 ∂z/∂ t – 4π i z = ∂β/∂ x – ∂∝/∂ y (1) – ∂∝/∂ t + 4π m x = ∂z/∂ y – ∂Y/∂y, – ∂β/∂t + 4π my = ∂X/∂ z – ∂Z/∂ x , – ∂ϒ/∂ t + 4π mz ∂Y/∂ x – ∂X/∂ y , (2) where X, Y, Z are the components of the electric force, α, β, γ are the components of the magnetic force, i x , i y , i z are the components of an electric current distribution, and m x , m y , m z are the components of a magnetic current distribution throughout the space. The object of the present communication is to express X, Y, Z, α, β, γ in terms of the electric current and magnetic current distributions and to apply the result to the discussion of the electric constants of a transparent medium. It is convenient to take instead of equations (1) and (2) the following equations, which include (1) and (2) as a particular case

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