Recently, we formulated an effective scalar electrodynamics model of relativistic type-II superconductivity. We discussed possible electromagnetic behaviors of superconductivity along the lines of the nonrelativistic Ginzburg-Landau theory. This brief work considers a 2D condensate subjected not only to a homogeneous magnetic field but also to a static radial electric field (polar coordinates). The electric field is regarded to have two components: a central constant field and a Coulomb-like field with "charge"g, where g can take only evenly spaced real numbers. We provide the single-vortex supercurrent density together with its associated magnetic flux density for the ground state of the system. Feasible extensions of this example in 3D curvilinear geometries could explain some superconductivity phenomena which do not occur in planar 2D geometries.