Visualization of electric field lines in an engineering education context Renato G. Sousa, Paulo J.V. Garcia, Vítor Marinho Faculdade de Engenharia, Universidade do Porto 4200-465 – Porto, Portugal pgarcia@fe.up.pt Ana Mouraz Centro de Investigação e Intervenção Educativas Faculdade de Psicologia e de Ciências da Educação da Universidade do Porto 4200-135 – Porto, Portugal anamouraz@fpce.up.pt Abstract— The electromagnetic theory presents a unifying explanation of electric and magnetic phenomena underlying our technological society. It is a fundamental physical theory taught in engineering schools at university level. In this theory the electromagnetic field is a vector field permeating space. An important aspect relating to students difficulties and misconceptions is the difficulty in visualizing vector fields. With the goal of enhancing student understanding and studying student engagement we have developed high quality 3D visualizations of electromagnetic situations. These make use of accurate computation of the field lines, together with realistic rendering using the open source software Blender. We present examples of electrostatic situations with both an assessment of the student understanding and an evaluation of the students’ perceptions of the importance of the visualizations. Complex interplay between visualization specific issues and the abstract notion of the field is identified in the students’ conceptions. It is found that the visualizations are not used as substitutes of other learning resources. They are perceived as allowing a quick access to content and prompting motivation. The adequacy of the visualization to the subject content as well as the capacity to use it as self-assessment is valued by the students. Keywords—electric field, 3D visualization, students’ beliefs and misconceptions, students’ attitudes and perceptions I. INTRODUCTION A field is a scalar, vectorial or higher dimensional (e.g. tensor) quantity that is defined in every point of space. Fields are central quantities in engineering: the temperature distribution is a scalar field; the velocity of a fluid is a vector field; the stress distribution a tensor field. In this paper we focus on the electric field, in the context of a “Physics II” course. This course (with different designations) takes place in all engineering degrees in our School of Engineering, typically in the 1 st semester of the 2 nd year. For many students it presents the first systematic contact with the concept of vector field and with the difficulties in understanding this abstract concept and in visualizing it. This difficulty is enhanced by an incomplete understanding of the notion of vector. The visualization dimension is very important in engineering education, where the vast majority of engineering students are visual learners (e.g. [1]). The visualization of fields is a research topic in the computing sciences; however we focus on a specific kind of visualization – the field line, and its interaction with student learning. The field line concept is introduced in pre-university physics education and ubiquitous in university physics textbooks. There are more advanced visualization concepts but their introduction often requires costly software packages, the climbing of usability learning curves and adaptation to new visualization concepts. A. The electrostatic field and field lines The electrostatic field in free-space is completely described by Maxwell’s equations for electrostatics. These prescribe the rotational and divergence of the electrostatic field ( ܧ ሬ Ԧ ) ׏ ሬ ሬ Ԧ ൈ ܧ ሬ Ԧ ൌ 0 ሬ Ԧ (1) ׏ ሬ ሬ Ԧ ܧ· ሬ Ԧ ൌ ߝ/ߩ ଴ (2) where ߩis the volume density of electric charge and ߝ ଴ the permittivity of free-space. The situations presented in this paper consist of charge distributions with symmetry. The spatial regions considered for the electrostatic field are void of charge. One situation is that of a thin homogenous sheet of positive charge coplanar to the ݕݔplane. The planar and axial symmetry of the situation implies that ܧ ሬ Ԧ ൌ ܧሺݖሻ ෠ . Furthermore, outside the sheet no charge exists and the divergence is zero. This implies that the field is constant, more exactly ܧ plane ሺݖሻൌ൜ ܧ ଴ ݖ,൐0 െ ܧ ଴ ݖ,൏0 (3) where ܧ ଴ is a constant. Another situation is that of an infinite cylinder of charge, with a charge density that is function only of the cylindrical radius . This situation has cylindrical symmetry and the field is of the form ܧ ሬ Ԧ ൌ ܧሺሻ ො . Outside the cylinder no charge exists and the field has zero divergence. This implies that in this region ܧ cylinder ሺሻ ൌ ܧ ଴  బ  (4) 2013 1st International Conference of the Portuguese Society for Engineering Education (CISPEE) 978-1-4799-1221-6/13/$31.00 ©2013 IEEE