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Abstract. Due to rapid development of the scientific and applied research in magnetic control and magnetophoresis of ferro-and ferromagnetic disperse fraction of various technological, natural and industry-specific media, the Faraday method is again in high demand as it is mainly aimed at defining magnetic susceptibility of solid and heterogeneous samples of small volumes. Based on the appearing (and then measured) ponderomotive force impacting the sample, the method allows accurate determining of single particles magnetic susceptibility by using the data of the sample represented by a conglomerate of the particles of such a fraction. In addition, it is mentioned that to date there is still a great gap in the methodology of the Faraday method as there are no exact recommendations on choosing both the form of the polar pieces of the Faraday balance and the positioning of the sample (the location of the working zone) in the interpolar area. Owing to these drawbacks, the well-known and long-time used Faraday method cannot be considered substantiated to a satisfactory degree. Thus, in our point of view, the treatment of the results obtained earlier with the help of the method should be cautious. In our work, we experimentally defined and substantiated an approach to identifying a working (local) zone, viz. the zone with stable values of the magnetic force factor -the product of the field intensity and induction by its gradient. The approach features the relative phenomenological analysis and is exemplified by polar pieces of non-traditional spherical form. It has been demonstrated that in order to state the fact of mere existence of this zone (and its location) in the interpolar area, the coordinate (usually nonlinear one) characteristic of intensity or induction, which is obligatorily obtained in an experiment, should have an inflexion, which guarantees a functionally extreme view of the following coordinate characteristics both of the gradient and that of the force factor. We also established the coordinates and the length of the working zone in a specific interpolar area.

-The paper demonstrates that when defining the content of ferroimpurities in the analyzed media by magnetic control based on measuring the ferroimpurities masses m, which are extracted from the media sample step-by-step, it is crucial to define a functional view of the obtained dependence m on the operation order number n. It allows receiving additional forecast data m by extrapolating this dependence. With corresponding calculations being done, it enables determining the sought total mass of ferroimpurities (including their residual mass). We consider alternate solutions of practical tasks which yield magnetic control results in case of linear and piecewise-linear views (in semi-logarithmic coordinates) of the control mass-operational characteristics.

-The paper observes matter about identification of zone with a stable value of gradient in Faraday's balance. This matter is solved by purpose obtained coordinate characteristics of magnetic field induction between pole pieces of such balance. The paper shows that such identification may be quite effective when given characteristic (usually it is non-linear and doesn't yield to desired linear even local approximation) is curly, i.e. has an inflection. It is possible to make a linear approximation of rather shortly characteristic's region, i.e. establish a stable values of induction pole gradient. It is also possible to get visualized extremum view of gradient induction characteristic: in the vicinity of its extremum gradient value are relatively stable.

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