## Abstract

The steady-state fields of both electric and magnetic dipole elements in a conducting medium are discussed numerically. The dependence of the fields on the dielectric constant is noted. Considerable interest has been shown recently in the propagation of electromagnetic waves in a conducting medium. The experimental investigations are often carried out at frequencies such that the fields are observed at distances within a few effective wavelengths from the transmitting antenna. The nature of the radiated fields of a short antenna in this range is not as complicated as is commonly supposed. Also the effect of displacement currents which are usually neglected can be included. This latter point is important since dielectric constants of large values are not uncommon.It then seems desirable to present curves which show the true nature of both electric and magnetic dipole radiation in a conducting medium of infinite extent. The conductivity, dielectric constant, and the magnetic permeability are given by sigma , epsilon , and mu respectively in M.K.S. units. The fields vary with a time factor e ^{iwt} . An electric dipole or current element Ids is situated at the origin of a spherical coordinate system (r, theta , phi ) and is oriented in the polar direction as shown in a previous paper. The magnitude of the functions A and B are plotted in Figure 1 against a parameter (sigma f) ^{1} 2/r where f is the operating frequency in Megacycles per second and sigma is the conductivity in mhos per metre. Various curves are shown for typical values of the dielectric parameter Kf/sigma where K is the dielectric constant of the medium relative to free space. The value of the magnetic permeability is taken to be that of free space.It can be seen that for finite values of the dielectric parameter the attenuation is considerably less than would be obtained if displacement currents were neglected. For example, at a frequency of 0.1 Megacycles per second with a relative dielectric constant of 100 and a typical rock conductivity of 2X10 (super -3) mhos per metre the parameter Kf/sigma has a value of 5,000. It is then apparent that for distances greater than 100 metres the field strength is greater by a factor of three than the corresponding value when the relative dielectric constant is only 10.The assistance of Mr. Lorne Campbell in preparing the curves is gratefully acknowledged. FIG. 1. Relative field strength curves of a dipole in a conducting medium.