2003/03/01 by Robert A. Schill · 1 citation
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · Materials Science · Mathematics · #Geomagnetism and Paleomagnetism Studies #Solar and Space Plasma Dynamics #Magnetic Properties and Applications #Gauss #Current (fluid) #Helmholtz free energy #Magnetic field #Current loop #Loop (graph theory) #Closed loop #Computer science #Relation (database) #Physics #Field (mathematics) #Magnetostatics #Identity (music) #Mathematical analysis #Mathematics #Pure mathematics #Quantum mechanics
paper · doi:10.1109/tmag.2003.808597
openalex publication_date 2003/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This paper presents a general theory for the fields generated by a circular current loop and compares it with existing theories. The existing, general, closed solution for the vector magnetic field may be expressed in a number of seemingly different but equivalent forms. These relations offer alternative closed-form solutions that may find various applications, including the characterization of Helmholtz coils. The paper provides alternative closed forms in both spherical and cylindrical coordinate systems. It employs Gauss's magnetic law to show that the alternative closed form is self-consistent and correct and also shows agreement with well-known solutions. Finally, it develops a new (or not readily found) tabulated mathematical identity.