Misconceptions Encountering Introductory-Physics Students About Charges and Gauss s Law

Transcription

1 Misconceptions Encountering Introductory-Physics Students About Charges and Gauss s Law Nacir Tit*, Bashar Issa and Ihab Obaidat Department of Physics, United Arab Emirates University, UAE Abstract We discuss conceptual difficulties with charges and Gauss s law encountered by freshman students in introductory Electricity and Magnetism (E&M) course. Beyond the worldwide known problems due to both the inverse-nature of the problem and the inappropriate use of symmetry, our test results done on 366 freshman students show the origin of their struggle to stem from their confusion of electric field and electric flux. Quantitative understanding of the nature of difficulties is discussed and suggestions to partially lift some of the difficulties are suggested. Keywords: Electricity and magnetism, Charges, Gauss law, Flux, Electric field PACS: a, d, Fk (*) Corresponding Author: ntit@uaeu.ac.ae 1

2 1. Introduction Electromagnetic force is one of the basic forces in nature. Coulomb force is responsible for holding the atoms together, and thus of everything in our universe. Thus understanding electric field and force is essential for science and engineering students. At the United Arab Emirates University, students of the colleges of science and engineering are forced to take two introductory physics courses. The first one is about classical mechanics and the second one is about electricity and magnetism. The introductory electricity and magnetism course covers topics such as charges, electric field, Coulomb force, electric flux, Gauss Law, electric potential and potential energy, magnetic field, magnetic force, magnetic flux, and other related topics. The students are usually enrolled in small sections (not more than 30 students in a section). Usually, the department of physics offers about 10 sections per semester that are taught by several instructors. To the students this course is much more difficult than the introductory classical mechanics one because they have to learn about interactions that they do not experience in their daily life and about objects that they cannot see by eye. In addition the level of mathematics in this course is higher than that required in the classical mechanics course. Thus most of the students face difficulties in understanding several essential concepts in this course and at the same time face difficulties in solving problems. Most of the instructors have been noticing some misconceptions among students in this course over long time of teaching. Thus we decided to quantify some of these misunderstandings and misconceptions. This study involves 366 students who took the introductory electricity and magnetism course in two different semesters. The data was collected from 19 sections taught by 5 different instructors, who use different teaching methods and techniques. Gauss s law in electrostatics consists a whole chapter in introductory electricity and magnetism (E&M) course as well as consists one of the four laws of Maxwell. The E&M course is among core courses in physics and its concepts are very fundamental ones [1-2]. Having taught the course to freshman science and engineering students for many years, we observed that the students persist to have some difficulties in concept of charges and in the applications of Gauss s law. We focused to give a diagnostic exam for the problem. Gauss s law states that: E. da = Q (S) enc /ε 0, where S is a closed surface, ε 0 is dielectric permittivity of vacuum, and Q enc is the net charge enclosed in the closed surface S. While the students have been taught that the flux solely controlled by the charge inside S, the students still not clear about the electric field on the points located on S. The student leant that Gauss s law is useful to find the electric field, especially of continuous charge distributions having high symmetry (e.g., spherical, cylindrical and planar). Nevertheless, it has been mentioned to students that in order to use Gauss s law, one must: (1) be able to determine from the symmetry of the charge distribution both direction of E and on what variable(s) its magnitude depends upon; so that one can (2) create a Gaussian surface on whiche. da is known to be either constant or zero. Once such a Gaussian surface has been created, one can then (3) solve for E by pulling it out of the integral. Of course, the right-hand side is always easy to determine based on the symmetry considerations; so that one obtain one algebraic equation with basically one unknown, which is the strength of E. 2

3 In related investigations [3-5],it has been a common trend that undergraduate students persists to have difficulty with Gauss s law. While most of instructors do not expect that juniors taking an advanced course in electricity and magnetism [6] will have significant difficulties with Gauss s law. Rachel Pepper and coworkers [5] presented that even the best juniors still straggle with aspects of Gauss s law using evidence from the Colorado Upper-division Electrostatics (CUE) diagnostic [4]., exam questions and student interviews. Similar work was even done before in extended way by Singh [3], who carried out tests and student interviews in University of Pittsburgh on both undergraduate and graduate students. He came out with a conclusion that difficulties in Gauss s law applications are restrained among undergraduates. Among the main difficulties, of this latter category of students, is that they find it easy to memorize a collection of formulas for various charge distributions and do not bother with symmetry considerations [7-8]. Actually, most text-books do not sufficiently emphasize symmetry considerations or the chain of reasoning, required to decide whether or not Gauss s law is useful for calculating the electric field. In the present investigation, we developed both solving and multiple-choice questions to obtain a quantitative understanding of the nature of difficulties. The multiple-choice questions were done by calculus-based introductory physics course offered in second semester for both science and engineering students. Statistics of results are collected versus many years and from several instructors. The general trend revealed by statistics is that students do have a serious problem with electric field, which is of course very fundamental in deciding about the geometry of the Gaussian surface, in case of relevance of Gauss s law. In next section, we will discuss the results and last section will highlight our main concluding remarks. 2. Results and discussion The first chapter, in introductory E&M course, which all instructors taught to the students should concern Coulomb s law and the electric field. In this chapter, students are supposed to learn about the concepts of charge, interaction, charging a metallic ball by induction, the electric field, motion of a charged particle and rotation of electric dipole in a uniform electric field. We have prepared a multiple-choice question #1 shown in Appendix, to assess the understanding of students to the effect of electric field due to a positively charged insulating rod on a neutral metallic sphere held by an insulating string (see Fig.3). The question addressed to the students was when the rod moves closer toward the metallic ball, does this latter move or not? The statistics of answers of students are summarized in chart diagram and pie-diagram in Figure 1. While the correct answer is of course (a), most of students got wrong answers. Only 40% of the total number of students got the correct answer; most others, about 37%, have chosen answer (c) as they followed the figure without paying attention on the microscopic phenomena such as the electronic motion taking place in the metallic ball to screen the electric field and make E inside = 0 inside the metallic sphere. Assuming the rod has a positive charge, the side of the metal sphere which is closer to the rod will have extra negative charge whereas the farthest side will have extra positive charge. This displacement of charges will result in an attractive Coulomb force that is stronger than the repulsive one and thus leading to the displacement of the metal sphere to move closer to the rod. At this level, students seem not mastering the concept of electric interaction due to the field and the evidence of this misconception is that 60% got the incorrect answers. 3

4 Figure-1: Statistics of answers of 366 students to question #1 about the electric field. Question #2 dealt with the concept of electric flux. Students are supposed to know that the flux depends solely on the net charge inside the Gaussian surface. This question is made very simple to assess freshman students of a general-physics level course. The correct answer is of course (b) and most of students, about 65%, got it right. Yet, regardless of how simple the question is, about 35% still have confusion and doubts about the right-hand side of Gauss s law. Having faith in Gauss s law, the flux is supposed to be independent of shape and size (geometry) of the Gaussian surface. Within this basic concept, students are still straggling and do mistakes. It is worth mentioning that these results are independent of the instructor and the method of teaching, since as it has been mentioned in the introduction that the students were taught by 5 instructors with different teaching approaches. Thus more attention should be paid in conveying the concepts and principles of this course to students. Several methods are suggested to minimize these misunderstandings and misconceptions. Along the line of resolving the difficulties, we further suggest:(a) to form groups of 2-4 students in each section and assign a major project about these topics, (b) provide more online practice on these topics, (c) make students responsible and aware that rigorous calculations of electric fields due to continuous charge distributions will be in regular tests with certainty. Figure-2: Statistics of answers of 366 students to question #2 about Gauss s law. 4

5 3. Conclusion Throughout this investigation, it has been demonstrated that freshman students persist to straggle with the fundamental concepts of charges, field, and Gauss s law. In our diagnosis of possible sources of their troubles, we discovered their overlook to the geometry of the Gaussian surface and confusion of visualization of electric field due to continuous charge distribution to be the main sources of students difficulties. Definitely, instructors have partial responsibility in giving more practices to students on broader range of problems of calculating the electric fields for continuous charge distributions as well as making student ready and responsible for that part as to be included in tests. Besides, in the chapter of Gauss s law, more practice is recommended to show students cases where Gauss s law is not appropriate to find the strength of electric field and contrast the other cases, which have high symmetry of charge distributions, for which Gaussian surfaces exist to be used and Gauss s law efficiently applies to get the electric field (direction and strength). Acknowledgments The authors are indebted to thank UPAR (grant #31S169) and UAEU-Research-center fund (grant # 31R068) for continuous support. 5

6 Appendix: The Multiple-Choice Questions Chose the correct answer for the following questions: Question #1: A charged insulating rod held near an uncharged metal ball as shown in the figure below (Fig.3). What will be the response of the ball? (a) It will move toward the rod. (b) It will move away from the rod. (c) It will not move at all. (d) We do not have enough information erofeb retfa Figure-3 Question #2: Which spherical Gaussian surface has the largest flux? (a) Surface A. (b) Surface B. (c) They have the same flux. (d) Not enough information to decide. Figure-4 6

7 REFERENCES [1] H.D. Young and R.A. Freedman, University Physics with Modern Physics, 13-Ed (Pearson, 2014). [2] R.A. Serway and J.W. Jewett, Physics for Scientists and Engineers, 9-th Ed (Belmont,CA, USA, 2014) [3] C. Singh, Am. J. Phys. 74 (2006) [4] S. Chasteen and S. Pollock, Trapping into Junior s Understanding of E&M: The Colorado Upper- Division Electrostatics (CUE) Diagnostic, in AIP PERC Proc (2009) [5] R.E. Pepper, S.V. Chasteen, S.J. Pollock, and K.K. Perkins, AIP-Conf. Proc (2010) 245. [6] D.J. Griffiths, Introduction to Electrodynamics, 3-Ed (Prentice Hall, 1999). [7] A. Hekkenberg, Adressing Misconceptions about Electric and Magnetic Fields: A Variation Theory Analysis of a Lecture s Learning Space, Master Thesis (Utrecht University, the Netherlands, 2012). [8] R. Rathore, IOSR-J. Appl. Phys. 8 (2016)