The solution of the boundary-value problem of magnetostatics for a circular ferromagnetic cylinder with a longitudinal sectorial cutout is described. The external primary magnetic field is orthogonal to the cylinder and directed at arbitrary azimuth relative to the cutout. A system of algebraic equations for finding the amplitudes of azimuthal expansions of the spatial distribution of the secondary field of the outer and sectorial partial regions of the cylinder is obtained by the method of rearrangement of functions.

1. Dzhala, R.M.; Dzhala, V.R.; Ivasiv, I.B.; Rybachuk, V.G.; Uchanin, V.M. Electrophysical methods of non-destructive testing of defect in structural elements. Technical diagnostics of materials and constructions: Reference manual. Nazarchuk, Z.T., Ed.; Volume IV. Prostir-M, 2018.

2. Bakunov, A.S.; Gorkunov, E.S.; Shcherbinin, V.E. Magnetic control. Kluev, V.V., Ed.; Spectrum, 2015. (In Russian).

3. Slesarev, D.A.; Abakumov, A.A. Processing and representation of information in the MFL method of non-destructive testing. Defectoscopy. 2013, 9, 3-9. (In Russian). https://doi.org/10.1134/S106183091309009X

4. Troitsky, V.A. Monitoring of technical condition of trunk pipelines. Techn. diagnostics and non-destructive testing. 2016, 3, 29-39. (In Ukrainian).

5. Krapivsky, E.I.; Demchenko, N.P. Geophysical methods of diagnostics of the technical condition of underground pipelines: A manual. Ukhta: UTTU, 2002. (In Russian).

6. Dzhala, R.M.; Dzhala, V.R.; Melnyk, M.I.; Horon, B.I.; Senyuk, O.I. Influence of the pipe defects on its magnetic field. Information Extraction and Process. 2018, 46 (122), 5-10. https://doi.org/10.15407/vidbir2018.46.005

7. Dzhala, R.M. Taking into account finite conductivity of longitudinal-slit cylinder. Information Extraction and Processing. 1982, 66, 66-72. (in Russian)

8. Dzhala, R.M. Longitudinally slotted cylindrical shield with finite thickness and electrical conductance. Soviet Journal of Communications Technology & Electronics. 1985, 30, 1-7.

9. Hrinchenko V., Vovk I. Wave problems of scattering of sound on elastic surfaces. Naukova Dumka, 1986. (in Russian)

10. Stratton, J. Electromagnetic Theory. McGraw Hill, 1948.

11. Smyte, W.R. Static and dynamic electricity. McGraw Hill, 1950.

12. Govorkov, V.A. Electrical and magnetic fields. GEI, 1960. (In Russian).

13.Nikolsky, V.V. Electrodynamics and the propagation of radio waves. Nauka, 1973. (In Russian).

14. Dikmarova, L.P.; Dzhala, R.M.; Kornienko, V.Yu. Metallic pipeline in the magnetic field of the Earth. Selection and processing of information, 1991, 6 (82), 67-70. (In Ukrainian).

15. Dzhala, R.M. Electromagnetic survey and control of corrosion of pipelines. Mechanics of fracture and strength of materials: References. manual. Panasyuk, V.V. Ed.; V.5: Non-destructive testing and technical diagnostics.; Nazarchuk, Z.T. Ed. Karpenko Physico-Mechanical Institute of the NAS of Ukraine, 2001. Part. 5. 263-330. (In Ukrainian).

16. Bland, D. Solutions of Laplace's equation. London: Routlegde& Kegan Paul Ltd, 1961. https://doi.org/10.1007/978-94-011-7694-1

17. Dwight, H.B. Tables of Integrals and Other Mathematical Data, 3rd Ed. The Macmillan Company. 1957.