The electromagnetic field generated by a vertical electric dipole on or near the surface of the Earth is studied for continuous-wave excitation. The analytical foundation established by Sommerfeld and developed by many others is reviewed, and simple explicit new formulas are derived for the three components of the electromagnetic field and represented graphically. Their range of validity is defined. They show that the surface waves constitute the entire far field along the air-earth boundary.

Electromagnetic field of a vertical dipole over an imperfectly conducting half‐space

In this paper, approximate formulas are derived for the electromagnetic pulse due to a delta-function current in a horizontal electric dipole on the planar boundary between a homogeneous isotropic medium and one-dimensionally anisotropic medium. The components of the electric field consist of two delta-function lateral pulses which decrease with the amplitude factor /spl rho//sup -2/ and travel along the boundary with different velocities and different amplitudes. Also, it is noted that the formulas for the time-dependent magnetic field components obtained by Fourier transforms from the approximate formulas in the frequency domain are not adequate.

Approximate formulas for lateral electromagnetic pulses from a horizontal electric dipole on the surface of one-dimensionally anisotropic medium

The exact lateral electromagnetic pulse generated by a vertical dipole excited by a Gaussian pulse is derived. A comparison with the previously derived approximate formula shows that the latter gives the correct field at all radial distances except for the nonappearance of the relatively small second pulse. Corresponding approximate formulas are derived for the electric field of a horizontal dipole. These should give the correct field except for the nonappearance of the small second pulse in some components.

Lateral electromagnetic pulses generated on a plane boundary between dielectrics by vertical and horizontal dipole sources with Gaussian pulse excitation

The propagation of a single Gaussian pulse in sea water and of a Gaussian pulse as an envelope for a low-frequency burst are analyzed and their anomalous behavior determined. The use of such a pulse to locate a metal cylinder submerged in the sea is studied quantitatively for two pulse widths. It is concluded that detection of the cylinder by means of its backscattered field should be possible. >

The propagation of a Gaussian pulse in sea water and its applicaiton to remote sensing

The propagation of lateral electromagnetic waves and pulses on microstrip is investigated. Interference patterns generated by the superposition of the lateral and direct waves along the air-substrate surface are shown. The field generated by the pulse excitation of a horizontal dipole on the air-substrate boundary is shown to consist of a lateral-wave pulse and a slower direct-wave pulse. Their differences in shape and decay rate are clarified. It is shown that the shape of a Gaussian pulse propagating along an open microstrip transmission line is closely related to the shape of the lateral electric-field pulse generated by a Gaussian current pulse in a dipole on the air-substrate boundary. >

Lateral electromagnetic waves and pulses on open microstrip

Approximate, quite simple formulas are derived for the transient field generated by a vertical electric dipole on the boundary between two dielectric half-spaces when the permittivity of one of these is much greater than that of the other. The three components of the field are determined for both delta-function and Gaussian-pulse excitation. The field of the former is compared with the corresponding exact expressions with generally good agreement and some interesting, readily explained differences.

Lateral Electromagnetic Pulses Generated by a Vertical Dipole on a Plane Boundary Between Dielectrics

After a review of work leading to the determination of the electric field induced in the human body when exposed to the electromagnetic field near an extremely-low-frequency high-voltage transmission line, attention is directed to a spherical cell exposed to the electric field in the body. Following a brief discussion of the potential biological significance of the study, the electric field acting on the surface of the cell and the electric field induced by it in the region between the outer cell membrane and the nuclear envelope are determined analytically, as is the field induced in the nucleus. It is shown, as an example, that when the body is exposed to a 60-Hz axial electric field of 2100 V/m, the field induced in the nucleus of a cell in the body is 0.27 nV/m when the radius of the nucleus is half that of the cell. The biologically interesting electric field along the outer surface of the nuclear envelope is in this case 2.7 sV/m. The simple analytical formulas can be applied to other values of the ...

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R.W.P. King

Papers

Lateral electromagnetic pulses generated on a plane boundary between dielectrics by vertical and horizontal dipole sources with Gaussian pulse excitation

Lateral Electromagnetic Pulses Generated by a Vertical Dipole on a Plane Boundary Between Dielectrics

The Low-Frequency Electric Fields Induced in a Spherical Cell Including Its Nucleus