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Dipole antennas over the boundary between two different media have been widely used in the fields of geophysics exploration, oceanography, and submerged communication. In this paper, an analytical method is proposed to analyse the near-zone field at the extremely low frequency (ELF)/super low frequency (SLF) range due to a vertical magnetic dipole (VMD). For the lack of feasible analytical techniques to derive the components exactly, two reasonable assumptions are introduced depending on the quasi-static definition and the equivalent infinitesimal theory. Final expressions of the electromagnetic field components are in terms of exponential functions. By comparisons with direct numerical solutions and exact results in a special case, the correctness and effectiveness of the proposed quasi-static approximation are demonstrated. Simulations show that the smallest validity limit always occurs for component,  and the value ofshould be no greater than 0.6 in order to keep a good consistency.

Quasi-Static Solution for ELF/SLF near-Zone Field of a Vertical Magnetic Dipole near the Surface of a Lossy Half-Space