How and why does the text differ from traditional texts?

Why change?

When I first began teaching electricity and magnetism, I decided to divide questions on the final exam into two sections: easy conceptual questions and more difficult problem questions. I was quite surprised by the results: students invariably did better on the problems than the conceptual questions. Eventually I came to understand that students learned how to work problems without really understanding what they were doing.

I was curious what other students’ experiences had been in similar courses, so I talked with a number of professionals: people in science, engineering, and computer science. No matter where the students went to school, I almost invariably got the same feedback. Students learned to “get by” by memorizing how to do problems, but they felt like they never really understood the course material. And students in advanced courses in electricity and magnetism added that their introductory course wasn’t very useful because they couldn’t relate their earlier course to the new material they were learning.

As I looked over the pedagogy of the existing texts, a key problem became obvious: Texts rely heavily on mathematics to teach concepts. That works fine for professors who already understand the mathematics and its implications, but it doesn’t work for students.

Over many years, I have developed a course that presents concepts first and then translates the concepts into mathematical forms afterwards. The range of topics is nearly identical to traditional texts, but the approach is not. There are a few differences in content, however. I have invented a few concepts to help fill the conceptual gaps and I have emphasized some concepts that I feel are particularly important.

With these changes in the course, I have found that students perform about the same on problems as in the past, but that almost all students finish the course with a fairly solid conceptual understanding of electricity and magnetism.

Added concepts

            The Thread Model. The latest concept I have added to the course is the model of threads and stubs. Threads and stubs don’t take the place of anything in a traditional text, they simply fill some voids. This model is used to explain why electromagnetic phenomena operate on a fundamental level and it draws connections between different concepts. I use the model primarily to introduce Coulomb’s law, the magnetic field and the Lorentz force law, induced fields, and radiation. A typical text, for example, treats the magnetic field as an experimental fact and offers no explanation as to why it exists. However, once I have introduced concepts with the thread model, I develop the subject using the traditional concepts of field, field lines, and Maxwell’s equations. At the end of the course you will be fully conversant in all the traditional concepts of electricity and magnetism. Threads and stubs provide a conceptual framework, but traditional ideas are the end product.

            Field Contours. Another concept that is not used in most texts is field contours. This is a geometrical model that is used to visualize line integrals in much the same way that field lines are traditionally used to visualize flux integrals. Electric field contours are the equipotential surfaces treated in traditional texts. We extend the idea to magnetic fields as well, however. Field contours are closely related to 2-forms that you may encounter in advanced courses in electricity and magnetism from the electrical engineering department.

            Differential Operators. As a natural outgrowth of fluxes and line integrals, we define divergence and curl and then write Maxwell’s equations in differential form. I have done this to provide a connection with advanced courses in electricity and magnetism which use the differential form of Maxwell’s equations rather than the integral form that is introduced in this text as well as traditional texts. I only very briefly discuss differential operators, however.

            Relativity. I include a very short discussion of relativity to emphasize its intimate connection to electromagnetic theory. I feel that after a century of relativity, we ought to include it in the mainstream of our physics courses rather than relegate it to a sidebar. But the discussion is extremely brief.

Shifts of Emphasis

            Studying Electricity and Magnetism Together. Traditional texts spend quite a while discussing electric fields and then more briefly develop magnetic fields afterwards. It works better pedagogically, however, to develop concepts of both fields at the same time. The similarities and differences can be more easily compared, so that concepts relating to both fields reinforce each other. In traditional courses, the treatment of the two types of fields is far enough apart that the distinctions tend to become muddy.

            Radiation and Electromagnetic Waves. Electromagnetic radiation and electromagnetic waves are very important in today’s society and need more than the cursory and misleading introduction given to them in traditional texts.

            Applications. We spend a while learning about house wiring and radio communication in order to see how elements of the course apply to everyday life. They also serve as a review of some basic ideas at the end of the course.

What’s Missing?

            If I add things that are not in traditional courses, then it seems that something must be taken out. Surprisingly enough, a concept-first approach is quite efficient, so I don’t take much out. What I sacrifice is primarily:  1) some (not all) long and involved problems in direct integration to find fields and 2) Kirchoff’s law problems that require the solution of systems of linear equations. (I teach you how to set up the equations, but we don’t solve them.) To keep the workload reasonable, I assign fewer homework problems than many classes, but I use Mastering Physics to make the assigned problems more useful pedagogically.