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A comparative study of the electromagnetic field excited by a vertical electric dipole on the Earth is presented. Four sets of formulas for both the planar Earth model and the spherical Earth model (of large radius) are compared to find out their valid ranges. Numerical computations are also carried out specifically for a three-layered Earth model. For the planar Earth model, when both the source and observation points are on the surface, and the planar Earth covered with a thick-enough dielectric layer, the method by Zhang is more accurate; while for the fields above the surface and the thin-enough dielectric layer, the method by King and Sandler is more accurate. However, the hybrid of the trapped surface wave and the lateral wave were exhibited in the curves in, but they were not shown in the curves. Numerical calculation also shows that the amplitude of the trapped surface wave attenuates as rho-1/2 in the rho direction as expected. However, the lateral wave given by does not exhibit rho-2 decay in the rho direction. For the layered spherical Earth model, the exact series summation, which serves as an exact solution to the classic problem, is computed and compared with the residue series. Numerical results show that the residue series gives a good approximation to the field, but the smooth curve illustrates that the hybrid effect due to the trapped surface wave and the lateral wave was ignored in literature. The field strength of the trapped surface wave decreases with the dielectric layer thickness and is affected by the curvature of the Earth. The exact series shows the oscillation of the field caused by the hybrid effects, which can be considered as the dielectric resonance between the upper and lower dielectric interfaces when it is guided to propagate, but none of the other three approximations can depict the effects.