Calculation of electric and magnetic field strengths of any oscillating straight conductors

Abstract
There are two methods for the calculation of the electric and magnetic field strengths in any straight oscillators such as antennas and antenna systems. One method depends on the fact that the fields produced by the individual elements in the arrangement, are superposed according to their amplitudes and phases. The fields of the elements thus are produced by Hertzian dipoles. The other method depends on the formation of Hertzian vectors for the given arrangement, and the derivation of the components of the electric and magnetic fields in the usual manner. The electric field of a Hertzian dipole can be divided into three parts, designated as the near-by field, the transition field, and the remote field. The magnetic field of a Hertzian dipole is divided in two parts, a near-by field, and a remote field. On using the first method, the component fields, corresponding to the magnetic and electric field, can be represented as the sum of integrals that are determined by the arrangement of the elements on the given conductors, that is, by the current distribution along the conductor. In general, this integration cannot be completed. Using the second method, as shown in the following, we start out in a general way to give complete expressions for the electric and magnetic fields of any oscillating straight conductors. We shall now form the Hertzian vectors for such arrangements. For this also we obtain a complete representation. The expressions that have been derived here make possible simple calculation of the radiation conditions near the conductor. This is of practical importance in the calculation of radiation characteristics and radiation resistances of any linear antenna arrangements.

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