Some observations about the near zone electric field of a Hertzian dipole above a lossy earth

In some recent publications, King (1990, 1992) and King and Sandler (1994) have provided formulas for the electromagnetic field radiated by an infinitesimal vertical Hertzian dipole above a lossy homogeneous half space (earth) and above a lossy half space coated by a thin dielectric layer. Several authors have questioned the accuracy of the King-Sandler formulas, particularly for field points close to the dipole (Yokoyama (1995), Wait (1996), Mahmoud (1999)). The authors have responded to these critiques by asserting that their formulas are accurate subject only to the restriction that the magnitude of the relative permittivity of the lossy half space is greater than 9. The principal results they obtain are that the near zone fields are independent of the electrical parameters of either the coating or the homogeneous half space. In this communication we provide some results obtained from a numerical evaluation of the exact integral for the near zone axial electric field along with numerical results obtained from an evaluation of the approximate integral used by King and Sandler. The King-Sandler formulas show that there is no contribution to the near zone axial electric field from a term they called the surface wave field. Our numerical evaluations show that this is not the case, in actual fact the surface wave term makes a significant contribution to the near zone axial electric field. We also present a quasistatic analysis that provides an alternative formula for calculating the near zone field. Our analysis supports the conclusions reached by Wait and Mahmoud.