In recent years, owing to the great success of the synchrotron radiation in contemporary astrophysical research, the abusive use of synchrotron radiation has been emerged. In this paper, we show that the traditional idea, “electrons with a power-law energy distribution certainly yield a power-law radiation Spectrum”, should be changed. If the magnetic field of radiation region is not flat and straight, the synchro-curvature radiation, instead of the synchrotron radiation, should be used to get a real description. In a curved magnetic field, the resulting spectrum of electrons could obviously distinct from a power-law one. This means that the way of only adding many other mechanisms to a pure power-law spectrum to get the expected spectrum might not be reasonable.