Low Frequency Fields Excited by a Horizontal Magnetic Dipole Near Boundary of lossy Half-Space

摘要

In this paper, based on the model of a horizontal magnetic dipole located near the boundary of a lossy half-space, a set of expressions of the electromagnetic field consist of integrals of the Sommerfeld type has been derived firstly. Under the conditions of k₀ρ ? 1, z/ρ ? 1, h/ρ ? 1, the terms of higher order k₀/k₁ could be neglected. Thus the integral expressions are simplified into a set of analytical formulas. When the horizontal distance ρ between the observer and the source dipole is less than 0.1 times of the skin depthδ of the lossy media, the magnetic field of the observer may be considered as quasi-static field. Our analytical formulas coincide with the formulas proposed by National Bureau of Standards (NBS). When ρ δ > 10, the surface of lossy media may be considered as an ideal reflecting plane, so the horizontal magnetic field near the surface consists of the direct wave and the reflected wave. The field is two times the amplitude of that calculated with NBS's formula. When 0.1<; ρ δ <; 10 , the field of the observer both depends on the frequency and the conductivity of the lossy media. The amplitudes of the magnetic field calculated by our analytical formulas coincide with the numerical results from Sommerfeld integral.