The Development of Maxwell’s Displacement Current Concept

Krishnasamy T. Selvan

Department of Electrical and Electronic Engineering Faculty of Engineering

University of Nottingham Malaysia Campus Jalan Broga, Semenyih 43500

Selangor Darul Ehsan, Malaysia Email: Krishnasamy.Selvan@nottingham.edu.my

Abstract− In this tutorial presentation, the development of the concept of Maxwell’s displacement current, acknowledged as one of the greatest innovations in the history of science, is traced. The presentation of this concept as an innovation that resulted from an intensive and interesting research process is believed to help in facilitating discussions on academic qualities in students that are increasingly being considered important.

I. INTRODUCTION One of the missions of educational institutions is to ‘promote intellectual development’ of students, desirably helping with their ‘developmental progression’ in which they ‘gradually relinquish their belief in the certainty of knowledge and the omniscience of authorities and take responsibility for their own learning.’ This would entail, among others, helping with the development in students of the qualities of intellectual curiosity and openness to alternative ideas [1]. There are difficulties with working towards this mission in the traditional approach of engineering education [2]. Alternative approaches are therefore desired. It is in this background that this tutorial presentation, prepared drawing from, and based on the teaching-in-context approach discussed in, a recent article on the topic by the author [3], aims to trace the development of Maxwell’s displacement current concept in historical context. The presentation in this way of the concept, which is one of the most profound innovations in the history of science, is believed by the author to offer scope to engage students in discussions on attributes considered necessary in modern education. Besides, as a reviewer of [3] pointed out, ‘the historical context of the fundamental discoveries and of the analyses and conjectures that brought them together into a coherent theory is important to learning and understanding a subject’ and is ‘inspiring.’ The above being the motivation for the presentation, this paper outlines the core ideas involved. In Section II, the development of the displacement current concept is traced. Section III suggests an outline for discussing the concept with students. In Section IV, some of the responses from students

and staff on lectures based on the teaching-in-context approach are given. In Section V, some academic reflections are shared. Section VI concludes the paper.

II. DEVELOPMENT OF DISPLACEMENT CURRENT CONCEPT

The context for the development of the concept of displacement current was the belief held by the seventeenth century scientists, and shared by Maxwell at the beginning of his research, that a medium was necessary for explaining physical phenomena. In his mechanical model, Maxwell employed the hypothesis of molecular vortices, which formed the context for the initial formulations of ‘two major innovations in (his) electromagnetic theory – the displacement current and the electromagnetic theory of light’ [4]. Recognizing that the Ampere’s law did not hold for open circuits, Maxwell added a term that he called displacement current to make its applicability general. Interestingly, the concept and meaning of this term have been ‘the source of significant controversy and − particularly among students − confusion for years... Questions related to the relationship between the displacement current and an electric current, and to whether or not the displacement current produces a magnetic field, continue to be debated today in the literature’ [5].

III. PRESENTING THE CONCEPT TO STUDENTS Given the above, how do we as educators present the displacement current concept to students? As the reviewer of [3] pointed out, since ‘it is undoubtedly the case that the historical context of the fundamental discoveries and of the analyses and conjectures that brought them together into a coherent theory…can be inspiring,’ we can accommodate as much contextual information as possible in our teaching. Alternatively, as further stated by the reviewer, as the development of displacement current concept ‘is complex and subject to much seemingly contrary discussion’, we can edit the reality ‘to make it a better story, (which) is easier to tell and has more immediate impact while the reality may be much less clear and full of debate.’ This author prefers the former approach and believes that such an approach is consistent with the objectives of ‘student-centred teaching,’ a term rather

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popular in modern educational literature [6]. Besides, there are other academic benefits with this approach [7, 8, 9]. While there might be several approaches to presenting the concept in context, a suggested approach is as follows [3]:

- Discuss the development of displacement current in context

- Discuss its importance and consequences - Present the positive as well as negative criticism of

the term and the method of its development, without taking sides

- Infer from the discussions the unavoidable variety in perspectives in the pursuit of science

The author has used a presentation material, available online [10], for discussing the displacement current concept with his students following the above outline.

IV. WHAT STAFF AND STUDENTS SAID

The following are some of the comments, paraphrased in some cases, from colleagues and students on the author’s lectures following the teaching-in-context approach:

- I found that presenting material in historical context was a particularly refreshing approach to present the material for this subject which can be rather abstract and mathematical. This approach could stimulate student interest.

- The interesting stories from the history made us understand the meaning of each contributing term of Maxwell’s equations. The instructor also led us towards ongoing discussions and articles regarding the concept of displacement current.

- Historical contents and anecdotes are interesting. Relaxes the learning atmosphere.

- Please add historical notes wherever necessary. We like to hear those, and I should mention this…this kind of content is very rare in other modules.

- Historical review…gives a very good reason for why we learn this module.

Several colleagues from outside the author’s university, with whom the materials have been shared, also expressed the view that the approach could be interesting and useful in motivating student interest.

V. SOME REFLECTIONS One of the chief concerns relating to the teaching-in-context approach in general could be the limited time available for lectures and the fairly vast syllabus to cover. The reviewer of [3] expressed this concern quite aptly: ‘In a busy course on EM theory, any attention paid to the

displacement current as an example of the creative process will be necessarily limited and tend towards the tabloid version. There is too little time to enter the broader debate.’

While this could of course be an issue particularly under certain situations – for example when the course is examined by a person other than the lecturer – it is the author’s view that, wherever possible, teaching scientific processes is much more important than just covering facts. As stated earlier, such an approach would be consistent with fundamental educational objectives. For, an instructor’s role extends beyond inculcating basic knowledge in students: they should be helped in recognizing that ‘all knowledge and attitudes must be viewed in context’ [11]. Besides, ‘the goal of teaching is not to cover material but to uncover it’ [12]. Another concern may relate to the level of student interest in the approach. While no approach can ever be appealing to an entire class, we can always find students that appreciate, and derive perceived benefits from, the teaching-in-context approach [8, 9].

VI. CONCLUSION The concept of Maxwell’s displacement current was considered in the background of teaching-in-context approach. The presentation of this concept as a scientific process resulting in what is one of the most profound innovations could have desirable academic benefits.

REFERENCES

[1] R.M. Felder and R. Brent, “The intellectual development of science and

engineering students. Part 2: Teaching to promote growth,” Journal of Engineering Education, Oct. 2004, pp. 279-291.

[2] R.M. Felder, D.R. Woods, J.E. Stice and A. Rugarcia, “The future of engineering education II. Teaching methods that work,” Chemical Engineering Education, vol. 34, no. 1, 2000, pp. 26-39.

[3] K.T. Selvan, “A revisiting of scientific and philosophical perspectives on Maxwell’s displacement current,” IEEE Antennas and Propagation Magazine, vol. 51, no. 3, June 2009, pp. 36-46.

[4] D.M. Siegel, Innovations in Maxwell’s Electromagnetic Theory, New York, Cambridge University Press, 1991.

[5] R. Stone, “Editor’s comments,” IEEE Antennas and Propagation Magazine, vol. 51, no. 3, June 2009.

[6] R.M. Felder and R. Brent, “The intellectual development of science and engineering students. Part 2: Teaching to promote growth,” Journal of Engineering Education, Oct. 2004, pp. 279-291.

[7] K.T. Selvan, “Engineering education: Presentation of Maxwell’s equations in historical perspective and the likely desirable implications,” IEEE Antennas and Propagation Magazine, Vol. 49, No. 5, October 2007, pp. 155-160.

[8] K.T. Selvan, “K.T. Selvan and L. Ellison, “Incorporation of Historical Context into Teaching: Student Perception at The University of Nottingham Malaysia Campus,” IEEE Antennas and Propagation Magazine, Vol. 49, No. 5, October 2007, pp. 161-162.

[9] K.T. Selvan, “Integration of historical content into engineering teaching: Possible benefits and perceptions,” Proceedings of the IEEE Applied Electromagnetics Conference, Calcutta, India, December 2007.

[10] http://www.nottingham.ac.uk/ggiemr/publications/Krishnasamy2009.pdf [11] A. Rugarcia, R.M. Felder, D.R. Woods and J.E. Stice, “The future of

engineering education. I. A vision for a new century,” Chemical Engineering Education, vol. 34, no. 1, 2000, pp. 16-25.

[12] R.M. Felder, J.E. Stice, and A. Rugarcia“The future of engineering education. VI. Making reform happen,” Chemical Engineering Education, vol. 34, no. 3, 2000, pp. 208-215.