Magnetic fields can increase the intensity of terahertz (THz) waves due to changing the dipole moment direction using the Lorentz force. This study reports the increase in the THz-wave intensity generated by differential frequency mixing using commercial permanent magnets under exciton-excitation. While a weak magnetic field applied to a multiple quantum well increases the THz-wave intensity due to excitons, a strong field causes its decrease. According to the calculations, the increase is caused by the electron-hole separation due to the Lorentz force. Furthermore, the calculations suggest the importance of carrier acceleration to enhance the intensity. Importantly, the increase in the THz-wave intensity due to differential frequency mixing does not require a strong magnetic field and can be achieved with inexpensive commercially available magnets.