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On the Alternative Vector Potential Formulation of the Sommerfeld Half-Space Problem

We address the non-uniqueness of the vector potential for the Sommerfeld half-space problem with a horizontal Hertzian dipole. In contrast to the classical solution, which utilizes horizontal and vertical components of the vector potential, the formulation presented here employs two horizontal components. In this approach, unlike in the traditional one, the scalar potentials of single-point charges associated with the vertical and horizontal Hertzian dipoles are identical.