  Recent experiments in semiconductor nanowires with a spin-orbit coupling and
proximity-induced superconductivity exhibit signatures of Majorana bound states
predicted to exist in the topological phase. In this work we predict that these
nanowire systems exhibit unconventional magnetoelectric effects showing a sharp
crossover behavior at the topological phase transition. We find that magnetic
fields with a component parallel to the spin-orbit field can give rise to
currents in equilibrium. Surprisingly, also fields perpendicular to the
spin-orbit field may induce currents and can be employed in adiabatic charge
pumping. The perpendicular field magnetoelectric effect may be regarded as a
manifestation of the anomalous Hall effect in one dimension. We discuss how the
predicted phenomena could be observed in experiments and employed in probing
the topological phase transition.
