الفهرس 
MAXWELL’S EQUATION.Only 14 pages are availabe for public view
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Abstract
INTRODUCTICN
The purpose of the present work is to discuss in detail systematic and unified treatment of the
electromagnetic field in the two half - space problem, which is bounded by a horizontal
plane interface separating the upper-half dielectric space (air} from the homogeneous and isotropic
lower half - space (ground, salt water, fresh water, etc. , ) , where the field is due to
source dipoles in air.
The main features of the study depend upon making use of a suitable Hankel transformation.
Thus, the two - media boundary value problem is reduced to the evaluation of
two fundamental integrals. These integrals help in computing the electromagnetic field
components for all pertinent cases of the dipole radiation, where both the dipole and the
point of observation lie in the air.
The underlying basis of the study is the numerical treatment of Sommerfeld integrals,
where the evaluation accuracy of the integrals will be carried out subject to the
condition that the wave number of the lower half - space would be much greater in
magnitude than that of the upper half - space (in which the tenna is located) , i.e., the
grou._Tld conductivity is sufficiently large. Thus we present, for points of observation
everywhere asy:::ptotic expansions which are valid quite generally.
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Various asymptotic solutions have been developed for different ranges of observation. Recent
development concerning far-field evaluation was carried out by Wait (1985), who used the saddle -
point technique which assumes large refractive index. As an extension of the problem we
have already used another approximation to increase the range of the applicability of this
technique. This is one of the main goals of the present study.
Historically, the boundary between two electrically different media such as air and earth greatly
alters the nature of the electromagnetic waves travelling outward from an electric dipole
near the surface. The original work on this subject started analytically by Sommerfeld [1,2) and
appeared in a series of papers and articles that have served as the foundation for related
investigations by others up to the present time. Thus, the integrals expressing tbe
interaction of electromagnetic sources with the ground are known as Sommerfeld integrals. The
solution obtained by sommerfeld was for the Hertz potential of the two half
- space model (earth and air) with an oscillating vertical electric dipole on the boundary as the
source. The effects of the earth’s curvature and reflection from the ionosphere, which
further complicate the actual propagation over the surface of earth, are not included. The
components of the electric and magnetic fields are determined by differentiation.
2