There have been several studies that have considered an anisotropic Coulomb interaction potential of a specific form to model anisotropic quantum Hall states of two-dimensional systems of electrons in a perpendicular constant magnetic field. The motivation and justification behind such a choice is tacitly implied without providing too many details. This work explains the physical reasons that lead to an anisotropic Coulomb interaction potential of such a form for the case of a two-dimensional system of charged particles with anisotropic effective band mass.