Remarks on Selecting Length of Cylindrical Sample to Determine Magnetic Properties of its Material

When experimentally studying magnetic properties of the ferromagnetic materials, preferences are often given to a more convenient method involving the use of sufficiently long cylindrical samples with the L length and the D diameter placed in the solenoid field as an alternative to the method based on using classical samples of the toroidal shape (to exclude manifestations of the demagnetizing factor). Currently, required justification is practically missing for specific values of the relative L/D length, which would indicate such [L/D] values (for L/D ≥ [L/D]), at which magnetic properties of a sample (already long enough) correspond to magnetic properties of its material. While the existing recommendations such as [L/D] = 50 are postulated, let us note that relevant experimental studies of magnetic properties of the cylindrical samples with the L/D parameter targeted variation were not made. An attempt was made to fill this gap. For cylindrical steel samples with the different L/D values (from 1 to 50), families of the B magnetic induction and of the μ permeability field dependencies were obtained experimentally using the ballistic method. The sought [L/D] values were determined from the B and μ dependencies on the L/D by the junction abscissa of the ascending and self-similar branches. It was established that in the accepted field strength in the range of H = 0.94--54.2 kА/m magnetizing field, the [L/D] parameter is a variable substantially depending on H (and/or μ). It varies from [L/D] = 10--15 at H = 54.2 kA/m (μ = 30) to [L/D] = 50--60 at H = 4.7 kA/m (μ = 270). And at H < 4.7 kA/m, [L/D] > 50--60, i.e., more than is commonly believed. Thus, it was stated that the data on magnetic properties obtained when using even long samples (L/D = 50) and declared as data on the magnetic properties of the corresponding material, are only close to those with H < 4.7 kA/m. Phenomenological expressions were obtained for the [L/D] determination: exponential with the H argument and logarithmic with the μ argument

The study was carried out with financial support of the RFBR and the London Royal Society (project no. 20-52-10006); Ministry of Education and Science of the Russian Federation within the framework of the State Assignment in the field of science (project no. 0706-2020-0024); grant of the President of the Russian Federation for state support of young scientists (project MK-807.2020.8)

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