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We investigate the magnetic field effects on the terahertz (THz) response of grain boundary Josephson junctions. First, we show some experimental results of the THz response enhanced by a dc magnetic field. The experimental results and device configuration indicate that the THz RF magnetic field plays a role in enhancing the response. Second, we numerically simulate the current-voltage characteristics and obtain the power dependence of Shapiro steps. Since the junctions are wide compared to the inferred Josephson penetration depth, multiple current paths within a junction are possible and superconducting quantum interference device (SQUID) models should be used. Two kinds of SQUID models are used: an RF-current drive model and an RF-field activation model. Shapiro step enhancement by a dc magnetic field can be reproduced with the use of the RF-field activation model. Finally, we discuss step-height dependence on SQUID parameters as well as give a qualitative explanation for the different predictions of two SQUID models.