Exact Formulas for Magnetic Field Strength inside and outside a Homogeneous Ellipsoidal Magnet Placed in an External Field Homogeneous in Magnet Vicinity

• Published in: Russian journal of nondestructive testing Vol. 58; no. 2; pp. 118 - 129
• Main Authors: Dyakin, V. V., Kudryashova, O. V., Raevskii, V. Ya
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-02-2022; Springer Nature B.V
• Subjects: Characterization and Evaluation of Materials; Chemistry and Materials Science; Circular cylinders; Electromagnetic Methods; Elliptic functions; Field strength; Magnetic fields; Magnetostatics; Materials Science; Mathematical analysis; Structural Materials; ellipsoidal magnet; basic equation of magnetostatics; direct problem; magnetic nondestructive testing
• ISSN: 1061-8309; 1608-3385
• DOI: 10.1134/S1061830922020048

We consider a direct problem of magnetostatics, i.e., calculation of the strength of the resulting magnetic field inside and outside a homogeneous magnet in the form of an arbitrary ellipsoid placed in the region of uniformity of an external magnetic field. The final formulas are given for calculating the indicated strength containing elementary functions or incomplete elliptic integrals. Based on these formulas, formulas for the intensity are obtained for the “limit” cases of a magnet of the indicated shape—a finite thickness plate, an infinite circular cylinder and a cylinder with an elliptical cross section, a ball. A comparison is made with a number of known formulas for these cases.