Some geometrical features of fields

Abstract

There are many ways of demonstrating electric and magnetic fields for introductory physics students, but in most instances only qualitative features of fields are treated. Sometimes, a student may be misled into believing that the electric field produced in a shallow electrolytic tank by two small electrodes is the same as the field produced by two equal and opposite charges (or by a bar magnet) in free space. In this paper we show how some quantitative, but purely geometrical, features of field lines can be used to distinguish between these two cases. Equations are derived for field lines and radii of curvature of field lines for several idealized cases. We show that the radius of curvature of a field line is a unique and distinguishing feature of each of the four charge configurations treated. These purely geometrical criteria are applied to two typical experimental field plots to characterize them and to show that experimental constraints introduce departures from theoretical models.