Asymptotic behavior of the inductance coefficient for thin conductors
Rachid St. Touzani, Youcef Amirat · 2002
We study the asymptotic behavior of the inductance coefficient for a thin toroidal inductor whose thickness depends on a small parameter ε > 0. We give an explicit form of the singular part of the corresponding potential u ε which allows to construct the limit potential u (as ε → 0) and an approximation of the inductance coefficient L ε . We establish some estimates of the deviation u ε - u and of the error of approximation of the inductance. We show that L ε behaves asymptotically as ln ε, when ε → 0.