Electric field line diagrams don't work

American Journal of Physics

Volumn 64, Issue 6, 1996, Pages 714-724

  Wolf, Alan ^a   Van Hook, Stephen J ^b   Weeks, Eric R ^b  

^a The Cooper Union for the Advancement of Science and Art   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030544345     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18237     Document Type: Article

References (19)

1. "No observable electromagnetic phenomenon can exist which involves two points in space, and which depends upon there being a continuous line of force joining the points. Such a phenomenon could contradict our postulate of the complete sufficiency of the local vector fields for describing local phenomena." Joseph Slepian, "Lines of Force in Electric and Magnetic Fields," Am. J. Phys. 19, 88 (1951).
2. Some texts demonstrate that field strength is quadratically related to field line density in the CFLD of an isolated point charge. Since these discussions are limited to the monopole, the reader may be left with the impression that the quadratic relationship, or some consistent relationship, holds in the case of more complex charge distributions.
3. Besides the inherent problems of CFLDs, such as limited spatial resolution, many of the CFLDs found in elementary texts are incorrectly drawn. See Leo Kristjansson, "On the drawing of lines of force and equipotentials," Phys. Teacher 23, 202-206 (1985).
4. The field lines for a dipole are determined analytically in Ref. 3, pp. 205-206.
5. Electric Field Plotter (Physics Academic Software), which employs an algorithm similar to the one described in Sec. III, produces CFLDs that exhibit equatorial clumping. More commonly, electric field plotters, such as EM Field (Physics Academic Software), only draw field lines through user-specified points in space, and therefore do not attempt to convey field strength through two-dimensional field line density.
6. There has been some confusion regarding the relationship between the magnitude of a point charge and the number of field lines it emits or absorbs in a two-dimensional field line diagram. Dennis E. Kelly, "Computing E-field Lines," Phys. Teacher 18, 463 (1980); Mario Iona, "Number of Lines of Force," Phys. Teacher 19, 354 (1981); Dennis E. Kelly, "A Common Misconception," Phys. Teacher 19, 463 (1981). The relationship must be a linear one. Consider two +1 charges, each emitting N field lines. When observed at a distance much larger than the separation between the charges, the total electric field must resemble that of a single +2 charge. Since 2N field lines are seen to originate from a charge of apparently doubled magnitude, the relationship between charge and number of field lines must be linear. This result holds in both two and three dimensions. The contrary result of Kelly and Iona, which would have the +2 charge emit √2N field lines, results from an incorrect comparison of uniform field line spacing in solid angle (in three dimensions) to uniform angular spacing within the plane.
7. There has been some confusion regarding the relationship between the magnitude of a point charge and the number of field lines it emits or absorbs in a two-dimensional field line diagram. Dennis E. Kelly, "Computing E-field Lines," Phys. Teacher 18, 463 (1980); Mario Iona, "Number of Lines of Force," Phys. Teacher 19, 354 (1981); Dennis E. Kelly, "A Common Misconception," Phys. Teacher 19, 463 (1981). The relationship must be a linear one. Consider two +1 charges, each emitting N field lines. When observed at a distance much larger than the separation between the charges, the total electric field must resemble that of a single +2 charge. Since 2N field lines are seen to originate from a charge of apparently doubled magnitude, the relationship between charge and number of field lines must be linear. This result holds in both two and three dimensions. The contrary result of Kelly and Iona, which would have the +2 charge emit √2N field lines, results from an incorrect comparison of uniform field line spacing in solid angle (in three dimensions) to uniform angular spacing within the plane.
8. There has been some confusion regarding the relationship between the magnitude of a point charge and the number of field lines it emits or absorbs in a two-dimensional field line diagram. Dennis E. Kelly, "Computing E-field Lines," Phys. Teacher 18, 463 (1980); Mario Iona, "Number of Lines of Force," Phys. Teacher 19, 354 (1981); Dennis E. Kelly, "A Common Misconception," Phys. Teacher 19, 463 (1981). The relationship must be a linear one. Consider two +1 charges, each emitting N field lines. When observed at a distance much larger than the separation between the charges, the total electric field must resemble that of a single +2 charge. Since 2N field lines are seen to originate from a charge of apparently doubled magnitude, the relationship between charge and number of field lines must be linear. This result holds in both two and three dimensions. The contrary result of Kelly and Iona, which would have the +2 charge emit √2N field lines, results from an incorrect comparison of uniform field line spacing in solid angle (in three dimensions) to uniform angular spacing within the plane.
9. θ is the polar angle in the plane of the CFLD measured counterclockwise down from the y axis. φ is the azimuthal angle in the xz plane. This coordinate system is most convenient for discussing collinear charge distributions along the y axis.
10. The sign-reversed (-2, +4, -2) quadrupole provides further evidence that equatorial clumping misrepresents local field strength. Sign reversal, whose only impact on the electric field is a global reversal of its direction, should not alter the relative spacing of field lines in a CFLD. Since the sign-reversed version of Fig. 6 must show uniform spacing of the outgoing field lines on the +4 charge, equatorial clumping does not show the invariance under charge reversal that would be expected of a true field property.
11. Phillip M. Rinard, Delbert Brandley, and Keith Pennebaker, "Plotting Field Intensity and Equipotential Lines," Am. J. Phys. 42, 792-793 (1974).
12. 0 to a value very close to 0, producing an apparently divergent field line that eventually reappears at the opposite end of the diagram and terminates on a negative charge.
13. Edwin A. Abbot, Flatland: A Romance of Many Dimensions by a Square (Seeley & Co., London, 1884). For a more technical discussion of two-dimensional science, see A. K. Dewdney, The Planiverse: Computer Contact with a Two-dimensional World (Poseidon, New York, 1984). While this article was in press, the authors were made aware of the recent note of T. E. Freeman, "One-, two-, or three-dimensional fields?," Am. J. Phys. 63, 273-274 (1995). Freeman shows a field line diagram with a false monopole moment and correctly observes that the distortion would disappear in a two-dimensional universe.
14. Edwin A. Abbot, Flatland: A Romance of Many Dimensions by a Square (Seeley & Co., London, 1884). For a more technical discussion of two-dimensional science, see A. K. Dewdney, The Planiverse: Computer Contact with a Two-dimensional World (Poseidon, New York, 1984). While this article was in press, the authors were made aware of the recent note of T. E. Freeman, "One-, two-, or three-dimensional fields?," Am. J. Phys. 63, 273-274 (1995). Freeman shows a field line diagram with a false monopole moment and correctly observes that the distortion would disappear in a two-dimensional universe.
15. Edwin A. Abbot, Flatland: A Romance of Many Dimensions by a Square (Seeley & Co., London, 1884). For a more technical discussion of two-dimensional science, see A. K. Dewdney, The Planiverse: Computer Contact with a Two-dimensional World (Poseidon, New York, 1984). While this article was in press, the authors were made aware of the recent note of T. E. Freeman, "One-, two-, or three-dimensional fields?," Am. J. Phys. 63, 273-274 (1995). Freeman shows a field line diagram with a false monopole moment and correctly observes that the distortion would disappear in a two-dimensional universe.
16. Boundary clumping can be avoided in a distribution with one negative and several positive charges by reversing the sign of each charge. A form of boundary clumping can be seen in charge distributions containing a single positive charge, but the problem originates solely from numerical errors that are easily avoided.
17. The problem of distributing points uniformly on a sphere is discussed in the Internet document sphere.faq, produced by Dave Rusin. The document is located at: http://www.math.niu.edu:80/∼rusin/papers/spheres/sphere.faq. Uniform tilings are not achieved on golf balls or geodesic domes which either employ multiple tiling elements or contain defects at the north pole or at the equatorial "weld" line.
18. Refercnce 13 describes methods of obtaining nearly uniform distributions of an arbitrary number of points on the surface of a sphere.
19. If field line diagrams are seen as primarily serving visualization and pedagogic purposes (rather than serving as a practical research/design tool) it may be time to reevaluate their pedagogic worth. Tornkvist et al. suggest that, independent of any imperfections that may be present in CFLDS, students often misinterpret these diagrams. S. Tornkvist, A. Petterson, and G. Transtromer, "Confusion by representation: On students' comprehension of the electric field concept," Am. J. Phys. 61, 335-338 (1993).