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Unformatted text preview: 30 Potential and Field Recommended class days: 2 Background Information The primary difficulties that students have with the concept of potential were discussed in the last chapter. In particular, • Students have a very hard time understanding the relationship between E r and V . Standard numerical problems using the electric potential do little to build a conceptual understanding of what potential is all about. Students need ample opportunities to work with graphs, potential maps, and equipotential surfaces if they are to understand the links between field and potential. • Students view batteries as constant current sources rather than as sources of potential difference. To change this misconception requires both experimental evidence and a mental model of what a battery does. Chapter 29 introduced the concept of potential, and this chapter will now try to make the idea more “real” by linking it both to charges/fields and to batteries. Student Learning Objectives • To establish the relationship between E r and V . • To learn more about the properties of a conductor in electrostatic equilibrium. • To introduce batteries as a practical source of potential difference. • To find the connection between current and potential difference for a conductor. • To find the connection between charge and potential difference for a capacitor. • To analyze simple capacitor circuits. Pedagogical Approach As described in the last chapter, the concept of the electric potential is very difficult for most students to grasp. To deal with this, class time should focus on reasoning, qualitative understanding, and linking potential to more tangible quantities such as currents, charges, and fields. The compu- tational demands of this chapter are not hard, and students should have little difficulty with the numerical aspects of problem solving if they understand how the concepts are used. 30-1 30-2 Instructor’s Guide An important task is to establish the relationship between E r and V . Students need help and practice with: • Reading two-dimensional and three-dimensional graphs and maps of the potential. The analogy with topographic maps is helpful, but a surprising number of students are not familiar with and cannot read a topographic map. • Understanding equipotential lines and surfaces. • Recognizing that E r points “downhill” on a contour map and that the field strength E is the slope of the “potential hill.” • Recognizing that E r is always perpendicular to equipotential surfaces. • Understanding that ∆ V closed loop = 0. This is best approached with a wide variety of graphical and qualitative exercises. If students at your school start calculus concurrently with physics, there’s a good chance that they will not have reached multivariable calculus and partial derivatives. Although the textbook does give the components of E as partial derivatives of V , the basic mathematical statement is that the component of E r in the s-direction is...
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- Spring '10
- Electric Potential, Potential difference, Electric charge