Date of Award
Summer 8-22-2025
Level of Access Assigned by Author
Open-Access Thesis
Degree Name
Master of Arts (MA)
Department
Mathematics
First Committee Advisor
Matthew Hernandez
Second Committee Member
Neel Patel
Third Committee Member
Peter Stechlinski
Abstract
This study presents a closed-form analytical model for the magnetic field around two perfectly conducting, undeformable cylinders as they converge toward one another. By treating the exterior region as an incompressible, irrotational potential fluid, we reformulate the field problem in terms of a complex potential. A suitably chosen conformal map transforms the narrowing gap into a parallel-strip domain, enabling an explicit representation via elliptic functions. The derived complex potential remains well–behaved for all separations down to contact. We evaluated and visualised our models using Python. The closed-form model offers a fast, robust tool for exploring magnetic interactions in closely spaced conductor geometries.
Recommended Citation
Ilung, Gideon, "Magnetic Fields Between Two Converging Cylinders Using Elliptic Functions" (2025). Electronic Theses and Dissertations. 4289.
https://digitalcommons.library.umaine.edu/etd/4289
Authorization Form for Deposit of Student Research to Digital Commons