The invention relates to a method and arrangement for the contactless determination of conductivity-influencing properties and their spatial distribution over the entire cross section of an electrically conductive substance moving in a primary magnetic field (B). The substance may be a liquid or a solid. A simultaneous measurement of a number of mechanical state parameters of the magnetic system is performed (three-dimensional components of the force and the torque), said parameters being variable by the effect of a secondary field on the magnetic system, the secondary field being produced on the basis of eddy currents induced in the substance by the primary field (B). To determine the spatial distribution of the property that is sought, the primary field is changed in intensity or form a number of times and a measurement of the state parameters is carried out for each change. The determination of the properties sought or their distribution takes place by solving an inverse problem using the method of least squares.