On the inductance of a Möbius strip

Abstract

The work is devoted to the calculation of the self-inductance of the Möbius strip (MS), assuming that a self-contained surface current flows on its surface. Subsequently, the vector potential corresponding to this situation is expressed in cases where: (a) the surface current is constant (b) the surface current is inversely proportional to the length of the line along which it flows. The self-inductance of the MS is determined by the integration of the vector potential. From the derived relations, the inductance of the MS is determined by computer simulation at different values of the ratio of width and radius of the MS. The reference value to the results for MS is the calculated and shown inductance of the cylindrical surface with a surface current flowing around the circumference of its shell. In conclusion, simple relations are derived that enable quick calculation of the inductances of both the MS and the cylindrical surface from their geometrical parameters. The article is intended for students of mathematical-physical and technical faculties as well as for graduates of these faculties dealing with the issue of (meta) materials.