Calculation of two-point resistances for conducting media needs regularization of Coulomb singularities
Department of Physics - Laboratoire PIMENT, University of La Réunion, Le Tampon, France
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Accepted: 8 August 2019
Published online: 11 November 2019
The definition of the electrical resistance between two arbitrary points of a conducting d -dimensional medium is clarified and we show that the calculation of such two-point resistances in the ideal case needs the regularization of Coulomb singularities located at current input and output points. The case of 2 -dimensional media stands apart from other dimensionality because of the scale invariance of the fundamental solution for the Laplacian operator on the plane. The regularization of logarithmic Coulomb singularities implies that the resistance between two arbitrary points is an indeterminable constant conventionally chosen as zero.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2019