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Electromagnetic conic sections
1.Jason W. Dunn and Julius Barbane, “One model for an integrated math/physics course focusing on electricity and magnetism and related calculus topics,” Am. J. Phys. 68, 749–757 (2000).
2.Tevian Dray and Corinne A. Manogue, “The vector calculus gap: ” PRIMUS 9, 21–28 (1999).
3.For the record, while a traditional course in multivariable or vector calculus will certainly discuss polar, cylindrical, and spherical coordinates, vectors will most likely be expressed exclusively in terms of their rectangular components.
4.Tevian Dray and Corinne A. Manogue, “Using differentials to bridge the vector calculus gap,” College Math. J. (to appear).
5.H. M. Schey, div, grad, curl, and all that, 3rd ed. (Norton, New York, 1997).
6.David J. Griffiths, Introduction to Electrodynamics, 3rd ed. (Prentice-Hall, New York, 1999).
7.Mary L. Boas, Mathematical Methods in the Physical Sciences, 2nd ed. (Wiley, New York, 1983).
8.One plate is in fact sufficient. The advantage of two plates is that the field vanishes outside the capacitor.
9.We use φ rather than θ for compatibility with our later examples, and rather than to avoid confusion with spherical coordinates.
10.A spheroid is an ellipsoid with two axes of the same length.
11.It is instructive to consider this latter example as a “stretched out” point charge.
12.Philip M. Morse and Herman Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Chap. 5.
13.A similar statement can be made in three dimensions, using quaternions in place of the complex numbers.
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