A 1D approximation is the basis of the impedance boundary condition (IBC). We review the use of the IBC conditions and present the errors which occur if those approximations are not checked. For an edge in the transverse electric case, we propose a modified surface impedance that we derive with the exact 2D analytical solution of the electromagnetic problem, and we compare it with the classical impedance and with another solution proposed in publication. We show that this impedance is not always necessary. This study can be used to model induction devices, such as a plasma torch.
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Aymard et al. (1997) studied this question.