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The article is devoted to the substantiation of a technical solution to the problem of monitoring corrosion changes in the walls of oil and gas pipelines using the electromagnetic method of non-destructive testing. To conduct a machine experiment on the qualitative and quantitative assessment of the characteristics of the magnetic field of solenoids with different geometric characteristics, a model has been developed that allows determining the magnetic induction and vector potential of the magnetic field of the solenoid and to visualize individual projections of vectors. The dependence of the vector magnetic potential of the field induced in the transformer and the role of the magnetic circuit in which the control object performs on the geometric and electromagnetic properties of the control object is determined.