BOUNDARY CONDITIONS FOR THIN IMPERFECT CONDUCTORS AND INSULATORS*
D Hurley · Geophysical Prospecting · 1975
Abstract Consider a thin, plane, finite sheet of material of thickness 2t whose electrical resistivity is σ2. It is surrounded by a medium of resistivity σ1 in which there is an electric field whose length scale is L. We consider the limit t/L→ o with , or fixed. In the former case the sheet is an imperfect conductor and it is shown that it may be modelled by a surface on which the boundary condition is , where φ and Z are the (nondimensional) electrical potential and distance measured normal to the surface, and the subscripts + and − denote values on either side of the surface. In the latter case the sheet is an imperfect insulator and the boundary condition is