Measurements of current have been performed on a very long wave infrared quantum cascade detector under strong magnetic field applied parallel to the growth axis, both under dark and light conditions. The analysis of dark current as a function of temperature highlights three regimes of transport involving the different energy levels of the structure. For photocurrent analysis, we developed a model based on a rate equation approach taking into account all the electronic levels of the structure. This model is in agreement with the oscillatory component of the experimental magnetophotocurrent. It allows to identify the key points controlling the electronic transport such as extraction from the upper level of the optically active quantum well, location of ionized impurities, and scattering mechanisms involved in the structure. This work is valuable for the future conception of high-performance quantum cascade detectors in infrared and far infrared range.