The transient behaviour of the magnetic field strength at any distance above the duct

摘要

A simple and explicit derivation is given for the source of the electromagnetic field. This source is taken to be a vertical magnetic dipole, in the upper surface layer, with an arbitrary time-varying moment. The method used for solution is essentially based on the application of two functional transforms. Starting with the wave equation of the magnetic field strength and applying a Laplace transform in time, one then finds a two-dimensional Fourier transform in the horizontal coordinates in space leading to an integral representation of the solution of the wave equation in transform space, considering initial, boundary, and transition conditions. Having chosen a horizontal polarization of the primary source, one can determine the transient behaviour of the magnetic field strength at any distance above the duct.