This paper presents a double-ion-fluid model built to simulate electron streamline distribution in the coupling area, especially the flanking area, of a Hall thruster. The computed coupling voltage, electron density and electron temperature were 55 V, 10(16) similar to 10(17)/m(3) and 3 similar to 9 eV, compared to 59 V, 3 similar to 6.6 x 10(16)/m(3) and 3.3 similar to 10.1 eV experimental results. It was noticed that the virtual cathode, the dense electron beam emitting from the cathode orifice and magnetized by the outer magnetic field, determines exterior field distribution. By changing the cathode location, vacuum backpressure and wall boundaries, the virtual cathode can relocate by rotating over 270 degrees and redistribute the entire field. In the hope of getting a transcendental expression for the coupling voltage instead of purely relying on posterior experimental output, a 1D empirical model of the coupling voltage, regarding the location/morphology of the virtual cathode was then derived, adopting the scenario of perpendicular transport near the cusp of a magnetic dipole. This model showed strong dependencies on the cathode location, backpressure and length of the ion core magnet. Based on the virtual cathode characteristics and the formulated coupling voltage, several suggestions regarding experiments, simulations and thruster designs were given.