Elsevier, Nonlinear Analysis: Theory, Methods and Applications, 5(47), p. 3295-3305
DOI: 10.1016/s0362-546x(01)00446-1
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We consider the inductance coefficient for a thin toroidal inductor whose thickness depends on a small parameter $\eps>0$. An explicit form of the singular part of the corresponding potential $u\ue$ is given. This 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. The main result shows that $L\ue$ behaves asymptotically as $\ln\eps$, when $\eps\to 0$.