In a recent study, the classical problem of a circular loop antenna carrying a uniform current on the Earth's surface has been revisited, with a scope for deriving Closed-form formulae for the generated magnetic and electric far fields by a vertical magnetic dipole (VMD) located at certain height above the surface of a planar two-layer conducting earth, with a high degree of accuracy. The solution is obtained by reducing the field integrals to combinations of known Sommerfeld integrals (SIs), which is advantageous over the previous numerical and analytical-numerical approaches, and its usage takes negligible computation time. Numerical simulations are performed and illustrated by figures for different values of the frequency to show the accuracy of the obtained field expressions and to investigate the behavior of the above surface ground fields in a wide frequency range. Results can be used to evaluate numerical solutions of more complicated modeling algorithms, for application to mobile communication and will be useful for remote sensing especially when the transmitter is close to the surface.
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