Students' understanding of the concept of the electric field through conversions of multiple representations

We conducted a study with introductory and upper-division level physics students in a Mexican and a Spanish university to learn how students recognize the main characteristics of the electric field in three of its more widely used representations, namely, algebraic notation, vector field plot, and electric field lines, and how the students do conversions of them. The students' abilities to recognize the three representations of the electric field and do conversions gave insight into their understanding of this concept. We used the theory of registers of semiotic representations as a framework to analyze the data. Our results showed that the direction of the conversion is an essential factor in determining the students' success in performing conversions of electrical field representations. We found close synergy between the vector field plot and the algebraic notation of the electric field. However, we found that the conversions that involve electric field lines do not present synergy. The electric field lines representation is especially difficult for students, both as a source and as a target representation, specifically, the interpretation and representation of the magnitude of the field through the density of field lines. We recommend that teachers and researchers of electricity and magnetism be more conscious of the difficulties that some conversion tasks may present to their students. We specifically invite instructors to be attentive to how they approach the representation of electric field lines and be explicit when performing conversions that involve electric field lines.