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Unformatted text preview: 27 Gauss’s Law Recommended class days: 2 Background Information Gauss’s law is a notoriously difficult topic for students. As an example, the tutorials designed by Lillian McDermott’s group at the University of Washington have been highly successful at improving success rates, typically to 80%, on topics known to cause student difficulties. But on the topic of Gauss’s law, the success rate on exam questions was still < 20% after a Gauss’s law tutorial. I’m not aware of any research on the specific topic of Gauss’s law, but several things seem to contribute to its difficulty: • Only a minority of students have yet reached vector integrals in their calculus course. For the large majority, this is new and frightening math that obscures the physical concepts of electric and magnetic fields. • Gauss’s law requires reasoning on the basis of symmetry. As important as this is, it requires a sophisticated level of conceptual ability. Few students have ever used this kind of reasoning, and few will master it in the short time available. • The use of Gauss’s law presupposes a basic understanding of electric fields. However, many students learned of electric fields only a few days earlier. They are confronting serious miscon- ceptions about the basic properties of charges and electric forces, and few yet have much of an idea about what a field even is. For most, their physical understanding is not at the level where Gauss’s law becomes an appropriate tool. All in all, the evidence suggests that a vector-integral approach to fields is simply beyond the capability of nearly all students in introductory physics. We can also inquire as to the purpose of teaching Gauss’s law in an introductory class. It can hardly be considered a practical tool for doing field calculations. Neither does it produce any important results that we can’t arrive at through superposition. Gauss’s law is vitally important in a more advanced treatment of electromagnetic fields, but that doesn’t justify its inclusion in an introductory course. Ultimately, Gauss’s law is deemed to be an important statement about the basic characteristics of electric fields. However, the significance of such a statement is apparent only to students who are at a point in their intellectual development to understand and appreciate it. The evidence is that only a small minority of students in a typical introductory physics class have reached this point. I do not include Gauss’s law in my own course. I feel I can make much better use of those two days by giving more attention to other topics. Nonetheless, I recognize that many instructors feel strongly that Gauss’s law is an important topic. For them, I’ve written this chapter with an emphasis on the symmetry issues and mathematical issues that are barriers to student understanding of Gauss’s law, topics that are glossed over as “obvious” in most textbooks....
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- Spring '10
- Electrostatics, Electric charge, Gauss’s Law