n 7.31 it can be seen that the part in square brackets has the dimensions of resistance. This is known as the radiation resistance of the current element. Radiation from an Oscillating Current in a Small Loop The magnetic equivalent of the infinitesimal linear element is the small loop of radius a. Consider such a current loop at the center of a spherical coordinate system. The electric and magnetic field components generated by such a loop can be derived, as for the infinitesimal linear current element, and are given by equations 7.32 to 7.34, where X is given by equation 7.35. Eo=nx(1-a) (7.32) He=x(1-a+a2) (7.33) H,=2xcot0a(1-a) (7.34) (7.35) Integration of the Poynting vector over the surface of a surrounding sphere gives the total radiated power as in equation 7.36. (7.36) Chapter 7 Electromagnetic Waves Again the part in square brackets is the radiation resistance, which can be increased by constructing the loop from N turns, wound SO that the magnetic field passes through all the turns. The radiation resistance is then given by equation 7.37. (7.37) Radiation from a Short Dipole The derivation of the radiation characteristics of practical antennas, from the equations for the infinitesimal current element, requires a knowledge of the current distribution in the practical antenna. In the case of the center-fed short dipole (Figure 7.9), the current distribu- tion can be regarded as linearly tapering from a maximum value at the center to zero at the tips, provided that the electrical length is small (i.e., less than 0.1 wavelength). In this figure the current distribution is given by equation 7.38. Current distribution I = Im(1-2) (7.38) The mean value of the current along the dipole is half the current at the center. Thus, the magnitudes of the far-field terms are half what would be given by equations 7.26 to 7.30 for a current element of the same length. Therefore, the total power radiated and the radia- tion resistance, expressed in terms of the r.m.s. current, Io, at the center of the dipole, are a quarte