We have derived an accurate noise current density equation for homogeneous semiconductors under a constant magnetic field with three noise source terms which are the thermal noise source term and the two excess noise source terms due to either carrier number fluctuation or carrier mobility fluctuation. Based on Hooge's empirical relations for 1/f noise, the two excess noise source terms are shown to become equal to each other under zero magnetic field. Using the characteristic potential method and employing Hooge's empirical relations for 1/f noise, we have derived the formulas for the short-circuit terminal 1/f noise and thermal noise currents and the open-circuit terminal 1/f noise and thermal noise voltages of multi-terminal homogeneous semiconductor resistors with arbitrarily- shaped 2-D geometries under a constant magnetic field. We have shown that the derived formulas can explain the measured 1/f noise and thermal noise of n-GaAs rectangularly-shaped Hall devices and n-GaAs Corbino disks under magnetic field from 0 to 9 T at room temperature. It is also shown that the magnetic field dependence of 1/f noise in bulk semiconductors should be explained by the number fluctuation model rather than by the mobility fluctuation model. (C) 2003 Elsevier Ltd. All rights reserved.