This description of the EMI Movies CD is adapted from a paper by Ruth Chabay and Bruce Sherwood presented at the International Conference on Undergraduate Physics Education, at the University of Maryland, 1996 July 30-August 3.

3D VISUALIZATION OF FIELDS

The abstract nature of a vector field makes this concept difficult for beginning students, who often have difficulty visualizing fields throughout space. A common student error involves thinking imprecisely of "the field" rather than of the field vector at a particular location in space. Time-varying fields offer an additional challenge, since both the magnitude and direction of the field at a given location can change with time. Students' difficulties are most acute in the domain of magnetism. Magnetic fields point in unexpected directions, which can be determined only by invoking vector cross products. Ordinary two-dimensional diagrams offer little support for three-dimensional reasoning about fields, and even the use of perspective in static images is usually not sufficient.

To address these difficulties, very short QuickTime movies have been created to provide dynamic 3-D images of electric and magnetic fields throughout a region of space, using a simple vector representation. If the fields of interest are not changing with time, camera motion is used to provide a sense of depth. The dynamic quality of the images gives a much richer view than is possible with a single still image.

For example, one of the movies shows the magnetic field at selected locations in space around a proton moving at constant velocity across the screen. The three-dimensional pattern of the magnetic field is clearly illustrated, and one can observe how the magnitude of magnetic field at each location changes with time.

Another movie demonstrates in detail how to use the right hand to determine the direction of the magnetic field at a location above a moving proton. (This movie was created at the request of students, who often struggle with this procedure.) In the ordinary application of the right-hand rule, the projecting thumb is naturally located near the source charge, not near the field location of interest. This reinforces students' tendency to think vaguely of "the field" rather than the field at a specific location. To dramatize the important issue concerning the field due to what charge at what location, at the end of the movie the thumb detaches from the computer-drawn hand and moves to the field location.

Other movies illustrate field configurations that figure prominently in introductory E&M courses, such as the electric field of a dipole, the electric field of a uniformly charged plate, and the magnetic field of a current-carrying wire. Importantly, field vectors are depicted not only at locations where students can easily calculate the field (e.g. on the axis perpendicular to a uniformly charged disk), but also at locations where the field is difficult to calculate analytically (e.g. near the edge of a charged disk). This provides an opportunity for discussion of the range of validity of common approximations, and offers visual answers to common student questions such as "How close to the center of the disk must I be?"

CHOICE OF REPRESENTATION

An important pedagogical decision was the use of a field vector representation rather than field lines. Since the movies are short, and little time is spent on them in class, in order for students to benefit from them it is important that they utilize the representation that is most familiar to students and requires the least mental effort to interpret. Although students can be taught to understand and use field lines, this is not a trivial undertaking, and requires a significant investment of time and effort on the part of both instructors and students. Students of E&M are at least somewhat familiar with vectors because they have used vectors in introductory mechanics courses. Furthermore, there are a number of common misconceptions and confusions about field lines which do not arise when the vector representation is used (for example, the belief that field lines are lines of constant field magnitude).

USE IN LECTURES

Chemists and molecular biologists routinely use three-dimensional molecular modeling tools in their research, so it has been natural for them to take these tools into the classroom to help students with three-dimensional visualization. Such tools are not a routine part of most physics research, and perhaps for this reason have not played a major role in teaching. We have used these movies for several years as lecture-demonstration devices in a new electricity and magnetism course that is part of the calculus-based introductory physics sequence.

In our classes, including large lectures, the movies are projected from a computer onto a screen at the front of the classroom. Projection equipment varies; some lecture rooms have resident computers and color video projectors, while in other rooms we must bring a laptop computer and an LCD projection panel. The movies have no audio tracks or canned explanations, so an instructor's commentary is an important accompaniment. We have found that a useful technique is to ask students to predict what they should see in a particular situation, then show a movie and discuss it. In this way, we use the movies to stimulate and motivate discussion of conceptual issues. Students have generally been enthusiastic about the movies, and have reported that they found them helpful.