The excitation-fluence and magnetic-field dependence of terahertz (THz) radiation power from InAs is investigated. For magnetic-field dependence, two completely different behaviors were observed depending on the excitation fluence. At low excitation fluence, the enhanced THz-radiation mainly originates from the carrier acceleration by the surface electric field. The Lorentz force changes the direction of carrier acceleration toward surface parallel, and the THz-radiation power is enhanced regardless of magnetic field direction. In contrast, at high excitation fluence, the surface electric field is almost screened out and the diffusion process becomes significant. By applying a magnetic field, the dipole is rotated to the direction in which the THz-radiation is efficiently or inefficiently extracted from the surface, and the radiation power is either enhanced or reduced depending on the magnetic-field direction. Additionally, from the magnetic-field dependence up to 27 T, it is found that THz-radiation power saturates at approximately 3 T and also at 13 T, and that the THz-radiation power at 3 T is much higher than that at 13 T. For the generation of broadband THz-radiation, focus is made on n-type InAs irradiated by ultrafast optical pulses. From the magnetic-field dependence of THz-radiation power, using n-type InAs under magnetic field is found to be the practical method to generate broadband THz-radiation, and the origin of higher-frequency component is identified to the hybrid modes.