ELECTROMAGNETIC FIELDS OF A VERTICAL MAGNETIC DIPOLE PLACED ABOVE THE EARTH’S SURFACE

Abstract

Electromagnetic fields due to a small loop antenna placed above the surface of a homogeneous and isotropic earth have been calculated. The effect of both the conduction and displacement currents are taken into account. Because of the complexity of the functions defining the fields, expressions valid separately for high and low frequencies are developed for the electric and magnetic field components. These expressions are then utilized to determine, for a step‐function current source, (a) the mutual impedance function [Formula: see text] between the primary loop and a small length of wire and (b) the voltage v(t) induced in a secondary loop. Two parameters are used to fix the locations of the primary loop and the receiving antenna with respect to the earth. A number of curves are plotted showing the mutual impedance function and the voltage function against time for different values of the parameters and the conductivity and the permittivity of the earth. With increase in either the conductivity or the permittivity, the amplitude and the rate of decay of the two functions decrease appreciably. However, the amplitudes of both [Formula: see text] and v(t) become smaller and the rate of decay higher as the receiving antenna is gradually lifted vertically from the ground. For all values of permittivity, the amplitude of the mutual impedance rises to a maximum with the horizontal separation between the two antennas before beginning to decrease, but at the same time the rate of decay of the transient becomes faster. With increase in the horizontal separation, the amplitude of the voltage function decreases inversely as the fifth power of the distance between the image of the transmitting dipole and the receiving antenna, but the rate of decay increases markedly.