The floating-zone-process with needle-eye inductor is a complex process with many coupled parameters that have nonlinear influence on the process stability and resistivity distribution in the silicon single crystal. To fulfill the requirements of semiconductor industry for tighter specification of resistivity distribution, additional means like magnetic fields can be used to reach a more homogeneous resistivity distribution without disturbing process stability. The current paper analyses the influence of static and alternating fields on the fluid motion and macroscopic and microscopic resistivity profile by means of numerical calculations. It is found that with a lower frequency of the HF-inductor current and with an additional AC-field the radial resistivity profile can be made more homogeneous. Rotating magnetic fields give only a slightly more homogeneous resistivity profile. DC-fields do not change the radial resistivity distribution qualitatively, but suppress all flow oscillations and therefore axial microscopic resistivity variations.