The apparent permeability and the amplification factor of magnetic wires and wire arrays

Abstract We have calculated and plotted the apparent permeability and the demagnetization factor of single magnetic wires. We have also confirmed the accuracy of the analytical formula for the conversion between the apparent permeability and the demagnetization factor. We also show that, as regards wire geometry, the effective permeability calculated from the inductance does not provide a good estimate of the apparent permeability, but that it is close to the amplification factor for induction sensors. We extend the concept of apparent permeability to a wire array. This will allow us to design multiwire magnetic sensors, mainly induction sensors and fluxgates. FEM calculations have been verified on physical models with up to 91 wires. Finally, we show a simplified 2D model for studies of larger wire arrays, and we verify the accuracy of the model.