This paper discusses new kinematic magnetoplasticity features established experimentally and by simulations. It examines the motion of a dislocation through randomly distributed point defects under the influence of a magnetic field which reduces the impurity pinning forces. In addition to the measurable characteristics of motion, hidden motion parameters amenable only to simulation studies are investigated for the first time. It is shown that the distribution of stoppers on a dislocation is independent of the impurity concentration C, whereas the average number of the stoppers and the critical force for the dislocation breakaway are proportional to √C. A model is proposed which for the first time explains the observed concentration dependence of the average dislocation speed in a magnetic field, ν ∝ 1/√C. The model suggests that there is hidden room for orders of magnitude increase in ν, something which was already realized in NaCl crystals additionally subjected to a weak electric field.