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Unformatted text preview: 34 Electromagnetic Fields and Waves Recommended class days: 3 Background Information There’s little research on student difficulties with the more technical and mathematical aspects of electromagnetism. In an investigation of light waves, McDermott’s group at the University of Washington found that students often interpret a “picture” of a light wave as if the wave has spatial extent, like a water wave. Thus a light wave that is “too big” for an aperture is truncated as it passes through. If you ask whether or not it is possible for a light wave with wavelength λ to pass through an aperture of width a < λ , many students reply “No, because it won’t fit through the opening if λ is less than a .” These responses suggest that most students do not have a correct mental image of an electromagnetic wave and cannot interpret the standard textbook picture of a transverse electromagnetic wave. A study of students’ organization of knowledge in the domain of electromagnetism (Bagno and Eylon, 1997) found that most students—at the end of instruction—could not identify the main ideas of electromagnetism (a large fraction identified Ohm’s law as one of the most important ideas), nor could they identify what the primary equations (Maxwell’s equations and the Lorentz force law) tell us. While students may become adept at manipulating equations, for most it is a mathematical “game” with little or no connection to physical phenomena. Student Learning Objectives • To understand that electric and magnetic fields are interdependent. There’s just a single electromagnetic field that presents different faces, in terms of E r and , B r to different observers. • Electromagnetic fields obey four general laws, called Maxwell’s equations. • Electromagnetic fields can exist without source charges or currents in the form of a self- sustaining electromagnetic wave. • Maxwell’s equations predict that all electromagnetic waves travel at the same speed. • Electromagnetic waves can be polarized. Pedagogical Approach Chapter 34 assumes that you’ve covered Gauss’s law and Ampère’s law. Much of this chapter is fairly standard. Earlier chapters emphasized electric and magnetic phenomena and a conceptual understanding of electric and magnetic fields. Now it’s time for mathematical sophistication. 34-1 34-2 Instructor’s Guide The one non-standard topic in this chapter is the Galilean field transformation for electric and magnetic fields. The magnetic force F qv B = × r r r is a velocity-dependent force, and better students are often troubled by recognition that velocity depends on the choice of reference frame. By ignoring this issue, most textbooks present electromagnetism in an outdated 19th century mode.ignoring this issue, most textbooks present electromagnetism in an outdated 19th century mode....
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- Spring '10
- Magnetic Field, Maxwell’s equations