Asymptotic behaviour of the inductance coefficient for thin conductors

Abstract

We study the asymptotic behaviour of the inductance coefficient for a thin toroidal inductor whose thickness depends on a small parameter \eps>0. We give an explicit form of the singular part of the corresponding potential u\ue which allows to construct the limit potential $u$ (as \eps\to 0) and an approximation of the inductance coefficient L\ue. We establish some estimates of the deviation u\ue-u and of the error of approximation of the inductance. We show that L\ue behaves asymptotically as \ln\eps, when \eps\to 0