New Formulas for Mutual Inductance and Axial Magnetic Force Between a Thin Wall Solenoid and a Thick Circular Coil of Rectangular Cross-Section

• Published in: IEEE transactions on magnetics Vol. 47; no. 8; pp. 2034 - 2044
• Main Authors: Babic, Slobodan, Sirois, Frédéric, Akyel, Cevdet, Lemarquand, Guy, Lemarquand, Valérie, Ravaud, Romain
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-08-2011; Institute of Electrical and Electronics Engineers
• Subjects: Coils; Cross-disciplinary physics: materials science; rheology; Electronic mail; Exact sciences and technology; Finite element methods; Inductance; Magnetic force; Magnetic forces; Materials science; Maxwell's coils; mutual inductance; Newman's formula; Other topics in materials science; Physics; Software; Solenoids; Coils; Newman's formula; Inductance; mutual inductance; Magnetic force; Maxwell's coils; Magnetic properties
• ISSN: 0018-9464; 1941-0069
• DOI: 10.1109/TMAG.2011.2125796

This paper presents new analytic formulas for determining the mutual inductance and the axial magnetic force between two coaxial coils in air, namely a thick circular coil with rectangular cross-section and a thin wall solenoid. The mutual inductance and the magnetic force are expressed as complete elliptical integrals of the first and second kind, Heuman's Lambda function and one well-behaved integral that must be solved numerically. All possible singular cases are automatically handled by the proposed formulas. The results of the work presented here have been verified by the filament method and previously published data. The new formulas provide a substantially simple alternative over previously published approaches, which involve either numerical techniques (finite element method, boundary element method, method of moments) or other semianalytic or analytic approaches.