Conjugate two-dimensional electric potential maps

Abstract

Two-dimensional electric potential maps based on voltage detection in conducting paper are common practice in many physics courses in college. Most frequently, students work on 'capacitor-like' geometries with current flowing between two opposite electrodes. A 'topographical' investigation across the embedding medium (map of equipotential curves) allows one to reassure a number of physical properties. This paper focuses on some less common configurations that bear pedagogical interest. We analyse 'open-geometries' with electrodes in the form of long strips with slits. They provide a natural groundwork to bring the student to complex variable methods. Aided by this, we show that shaping the conducting paper board one may analyse finite size effects, as well as some meaningful discontinuities in the measured potential. The concept of conjugate electric potentials is exploited. Equipotentials and electric field lines acquire interchangeable roles and may be obtained in complementary 'dual' experiments. A feasible theoretical analysis based on introductory complex variables and standardised numerics gives a remarkable quantification of the experimental results.