Recognition and conversion of electric field representations: The case of electric field lines

We conducted a study with introductory and upper-division physics students in a Mexican university to learn how students independently recognize the electric field’s main characteristics in the electric field lines diagram and as a source or target representation in conversion processes. We used the theory of registers of semiotic representations and a phenomenographic approach as a framework to analyze data. The recognition and conversion abilities were explored through interpretation and construction tasks. We identified students’ main difficulties in recognition and conversion in the interpretation and construction tasks. In conversion processes, we found that when the electric field lines diagram is the source representation, students do not interpret the field lines’ density as the magnitude of the electric field. The difficulties of interpretation that arise in these conversion processes depend partially on the target representation. We also found that constructing electric field lines is especially difficult for students at both introductory and upper-division levels. Most students would prefer to draw vector field plots instead. We recommend that electricity and magnetism teachers and researchers be aware of the difficulties that the recognition and conversion in interpretation and construction tasks may represent for their students in understanding the electric field concept.

Figure 1

Main concepts of the theory of registers of semiotic representations and their connections.

Figure 2

Item Q1.1 targets the recognition of the magnitude and direction of the electric field in the electric field lines diagram.

Figure 3

Items Q1.2 and Q2.2 have the objective of conversion from the electric field lines diagram to the vector field plot or the algebraic notation, respectively.

Figure 4

Item Q2.1 targets the recognition of the electric field and the application of the superposition principle in the electric field lines diagram.

Figure 5

Expected construction of the electric field lines (blue) in item Q2.1. (a) Corresponds to the expected answer in Q2.1 (a), and (b) is the expected answer in Q2.1 (b).

Figure 6

Item Q1.3 aims to convert from the algebraic notation to the electric field lines diagram.

Figure 7

Item Q2.3 aims to convert from the vector field plot to the electric field lines diagram.

Figure 8

Expected construction of the electric field lines (blue) in conversion items. (a) Corresponds to the expected answer in Q1.3, and (b) is the expected answer in Q2.3.

Figure 9

Examples of (a) recognition of magnitude and direction of the electric field lines diagram and (b) difficulty of recognition “Magnitude: increases with radius”.

Figure 10

Example of the complete construction of an electric field lines diagram for items (a) Q2.1 (a), (b) Q2.1(b), (c) Q1.3, and (d) Q2.3.

Figure 11

Drawing (a) shows an example of the difficulty “Identified only outer region” in item Q2.1 (a), while drawing (b) shows an example of the same difficulty in Q2.1 (b). Drawing (c) shows an example of the “Difficulty with field lines density” in item Q2.3. Drawing (d) shows an example of the difficulty “Joined vectors in a continuous line” in item Q2.3. Drawing (e) shows an example of the “Difficulty with field lines density” in item Q1.3.

Figure 12

Examples of the difficulty of “Drew vector field plot” in the different items. The drawing in (a) corresponds to item Q2.1 (a), in (b) with item Q2.3, and in (c) with item Q1.3.