We investigate the zero-temperature superradiant phase transition of an ultracold uniform noninteracting spin-1/2 Fermi gas coupled to a single-mode optical cavity. Starting from a generalized Dicke-model Hamiltonian and incorporating cavity photon loss through the Lindblad master equation, within the mean-field approximation, we derive the equations of motion for the superradiant order parameter and the average atomic spin vector at zero-temperature, and show that the superradiant order parameter is self-consistently coupled to a Bloch-type equation describing the spin precession of the fermionic atoms. This coupled dynamics reveals a transparent physical picture: Through the light-atom coupling, the superradiant order parameter serves as an effective external magnetic field that drives the precession of the average atomic spin vector, while the precession of the average atomic spin vector, in turn, feeds back on the dynamics of the photon superradiance. Based on the steady-state solutions of equations of motion together with a linear stability analysis of the normal state, and by expressing the thermodynamic quantities in terms of the density of states of a d-dimensional uniform noninteracting Fermi gas, we obtain the analytical expressions for the critical light-atom coupling strength of the superradiant transition in different spatial dimensions, and systematically analyze how the critical light-atom coupling strength depends on the cavity frequency, cavity dissipation, and Zeeman field. Our results show that both the cavity frequency and cavity dissipation increase the critical light-atom coupling strength and therefore suppress the emergence of the superradiant phase. In contrast, the role of Zeeman field is strongly dimension dependent. In one- and two-dimensional systems, the critical light-atom coupling strength is found to be completely independent of the Zeeman field. In the three-dimensional case, the critical light-atom coupling strength increases monotonically with the Zeeman field. These results provide a theoretical basis for experimentally controlling the superradiant phase transition by tuning the spatial dimensionality, Zeeman field, cavity frequency, and cavity dissipation.