Page 40 - Engineering Electromagnetics, 8th Edition

22 ENGINEERING ELECTROMAGNETICS

D1.7. Given the two points, C(−3, 2, 1) and D(r = 5,θ = 20 , φ =− 70 ),
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◦
find: (a) the spherical coordinates of C;(b) the rectangular coordinates of D;
(c) the distance from C to D.
Ans. C(r = 3.74, θ = 74.5 , φ = 146.3 ); D(x = 0.585, y =−1.607, z = 4.70);
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6.29
D1.8. Transform the following vectors to spherical coordinates at the points
given: (a)10a x at P(x =−3, y = 2, z = 4); (b)10a y at Q(ρ = 5,φ = 30 ,
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z = 4); (c)10a z at M(r = 4,θ = 110 , φ = 120 ).
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Ans. −5.57a r − 6.18a θ − 5.55a φ ;3.90a r + 3.12a θ + 8.66a φ ; −3.42a r − 9.40a θ

REFERENCES
1. Grossman, S. I. Calculus.3d ed. Orlando, Fla.: Academic Press and Harcourt Brace
Jovanovich, 1984. Vector algebra and cylindrical and spherical coordinates appear in
Chapter 17, and vector calculus is introduced in Chapter 20.
2. Spiegel, M. R. Vector Analysis. Schaum Outline Series. New York: McGraw-Hill, 1959.
A large number of examples and problems with answers are provided in this concise,
inexpensive member of an outline series.
3. Swokowski, E. W. Calculus with Analytic Geometry.3d ed. Boston: Prindle, Weber, &
Schmidt, 1984. Vector algebra and the cylindrical and spherical coordinate systems are
discussed in Chapter 14, and vector calculus appears in Chapter 18.
4. Thomas, G. B., Jr., and R. L. Finney: Calculus and Analytic Geometry. 6th ed. Reading,
Mass.: Addison-Wesley Publishing Company, 1984. Vector algebra and the three
coordinate systems we use are discussed in Chapter 13. Other vector operations are
discussed in Chapters 15 and 17.

CHAPTER 1 PROBLEMS
1.1 Given the vectors M =−10a x + 4a y − 8a z and N = 8a x + 7a y − 2a z , find:
(a)a unit vector in the direction of −M + 2N;(b) the magnitude of 5a x +
N − 3M;(c) |M||2N|(M + N).
1.2 Vector A extends from the origin to (1, 2, 3), and vector B extends from the
origin to (2, 3, −2). Find (a) the unit vector in the direction of (A − B);
(b) the unit vector in the direction of the line extending from the origin to the
midpoint of the line joining the ends of A and B.
1.3 The vector from the origin to point A is given as (6, −2, −4), and the unit
vector directed from the origin toward point B is (2, −2, 1)/3. If points A
and B are ten units apart, find the coordinates of point B.