Abstract: The Sq (solar quiet) geomagnetic field is generated by the electric currents in the E-region of the ionosphere, driven by the atmospheric tides. It is a critical part of high-precision geomagnetic field modeling. Based on the classic thermal tide theory and atmospheric electrodynamics, this research, for the first time, developed an Sq geomagnetic field model that is directly built on the physical mechanism of the ionospheric dynamo, which is responsible for daily variations of the geomagnetic field. The performance in Sq geomagnetic field modeling was investigated using the Macau Science Satellite-1 (MSS-1) data. Our model can enhance the physics-based framework of comprehensive geomagnetic field modeling for the MSS-1 and ensuing missions.