Electric field line diagrams don’t work

Abstract

Electric fields produced by coplanar point charges have often been represented by field line diagrams that depict two-dimensional slices of the three-dimensional field. Serious problems with these ‘‘conventional’’ field line diagrams (CFLDs) have been overlooked. Two of these problems, ‘‘equatorial clumping’’ and ‘‘false monopole moment,’’ occur because a two-dimensional slice lacks information vital to the accurate representation of an inherently three-dimensional field. Equatorial clumping causes most CFLDs to exhibit unphysical behavior such as irregular spacing between field lines terminating on negative charges. CFLDs can also mistakenly indicate that a neutral charge distribution has a significant monopole moment. Such phenomena make the visual estimation of local field strengths impossible and render CFLDs of little utility for representing three-dimensional fields. While these ‘‘projection’’ problems can be avoided by using two-dimensional field line diagrams to represent two-dimensional (1/r) electric fields, or by using three-dimensional field line diagrams to represent three-dimensional fields, other forms of distortion generally remain.

A Look into Students' Interpretation of Electric Field Lines

“…Electric field line diagrams are, without doubt, visually attractive for students who are learning about electric fields, but this feature does not mean that they are useful for concept understanding. In the late 90's, Wolf, Van Hook and Weeks (1996) stated that electric field line diagrams do not work, because even when they correctly indicate the direction of the field, they fail to accurately report its magnitude. They made their case by finding that there is no possible relationship that satisfies both linear and quadratic relations between density and strength, they also note that the problems presented by electric field lines diagrams can easily be avoided by using vector representation of the electric field, although it is less aesthetic (Wolf, Van Hook & Weeks, 1996).…”

“…In the late 90's, Wolf, Van Hook and Weeks (1996) stated that electric field line diagrams do not work, because even when they correctly indicate the direction of the field, they fail to accurately report its magnitude. They made their case by finding that there is no possible relationship that satisfies both linear and quadratic relations between density and strength, they also note that the problems presented by electric field lines diagrams can easily be avoided by using vector representation of the electric field, although it is less aesthetic (Wolf, Van Hook & Weeks, 1996). In agreement with Wolf, Van Hook and Weeks (1996), Chabay and Sherwood (2006) emphasize that at an introductory level there are not many problems in which the field lines are absolutely necessary, and understanding this representation requires a long investment of time; instead, vectors may allow both 2D and 3D representation without as much investment since students should be familiar with the use of vectors.…”

“…As the findings in the present study suggest, the use of electric field line diagrams carries misconceptions in the understanding of the electric field. Teaching how to draw and interpret electric field line diagrams correctly would need a large investment of time both for professors and students (Chabay & Sherwood, 2006); and at a certain degree, it would render unfruitful, since the magnitude of the field cannot be accurately interpreted from the electric field line diagram alone (Wolf, Van Hook & Weeks, 1996).…”

Graphical representations of vector functions in upper-division E&M

“…This led to a comparison of how the two representations handle the magnitude of the field. With field lines, the density of the lines represents magnitude (the closer the lines are to each other, the larger the magnitude of the field -though the exact relationship only works if the lines are drawn in a 3D space [5]); in the vector representation, the arrows' lengths represent the magnitude of the field. This student's suggestion may indicate not understanding that the vectors in the vector representation come from an arbitrary sampling of points.…”

Quantitative analysis of the electric dipole on finite sized graphite sheets

“…In addition to edge effects, another problem with a qualitative comparison between theory and experiment is that the PASCO manual that comes with the device shows a twodimensional cross section of a three-dimensional dipole plot. 4 There are several methods of calculating the voltage contours on the sheet. Three will be discussed in the followingthe method of images, the discrete Laplace method, and the boundary value problem method.…”