NUMERICAL-ANALYSIS OF CERTAIN SOLUTIONS OF LAPLACES-EQUATION TO CALCULATE THE OHMIC POTENTIAL DROP AFTER SCRIBING

The accuracy of certain solutions to Laplace's equation for various electrode geometries is examined and compared to the accuracy of new solutions based on a Taylor's series expansion. Whereas previous solutions are accurate only for cases where the counter-electrode is remotely placed from the working electrode, the new solutions are highly accurate for all values of relevant geometric parameters. In particular, for an electrode with a non-uniform current or uniform current distribution, the ohmic drop computed with an equation assuming an infinite spacing can deviate substantially from the correct potential drop for a counter-electrode near a working electrode. For the specific case of a rectangular electrode, the solution computed here provides a better fit to experimental data than available solutions in the literature. A direct benefit to the user of these results is the freedom from having to make the decision as to what constitutes a large enough separation (or spacing) between the working- and counter-electrodes. In addition, error bounds on the use of the new solutions are provided for the benefit of the user.