Abstract
The analytical solution is carried our for the electromagnetic field in the air of a dipole over the spherical surface of the multi-layered Earth. The region of interest consists of a spherical dielectric Earth, coated with the dielectric layer composed of a succession of n spherically bounded layer under air. The surface impedance for the electric-type field is presented and the formulas are obtained for the electromagnetic field in the air radiated by a vertical electric dipole. Similarly, the surface admittance for the magnetic-type field is presented and the formulas are obtained for the electromagnetic field radiated by a vertical magnetic dipole. Based on the above results, the formulas are derived readily for the six components of the electromagnetic field of a horizontal electric dipole by using a reciprocity theorem.
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