Page 62 - Engineering Electromagnetics, 8th Edition

44 ENGINEERING ELECTROMAGNETICS

D2.7. Find the equation of that streamline that passes through the point
−8x 4x 2
5x
P(1, 4, −2) in the field E = (a) a x + a y ;(b)2e [y(5x +1)a x + xa y ].
y y 2
2
2
2
Ans. x + 2y = 33; y = 15.7 + 0.4x − 0.08 ln(5x + 1)
REFERENCES

1. Boast, W. B. Vector Fields.New York: Harper and Row, 1964. This book contains
numerous examples and sketches of fields.
2. Della Torre, E., and Longo, C. L. The Electromagnetic Field. Boston: Allyn and Bacon,
1969. The authors introduce all of electromagnetic theory with a careful and rigorous
development based on a single experimental law—that of Coulomb. It begins in Chapter 1.
3. Schelkunoff, S. A. Electromagnetic Fields.New York: Blaisdell Publishing Company,
1963. Many of the physical aspects of fields are discussed early in this text without
advanced mathematics.

CHAPTER 2 PROBLEMS

2.1 Three point charges are positioned in the x-y plane as follows: 5 nC at y = 5
cm, −10 nC at y =−5 cm, and 15 nC at x =−5 cm. Find the required x-y
coordinates of a 20-nC fourth charge that will produce a zero electric field at
the origin.
2.2 Point charges of 1 nC and −2nC are located at (0, 0, 0) and (1, 1, 1),
respectively, in free space. Determine the vector force acting on each charge.
2.3 Point charges of 50 nC each are located at A(1, 0, 0), B(−1, 0, 0), C(0, 1, 0),
and D(0, −1, 0) in free space. Find the total force on the charge at A.
2.4 Eight identical point charges of Q C each are located at the corners of a cube
of side length a, with one charge at the origin, and with the three nearest
charges at (a, 0, 0), (0, a, 0), and (0, 0, a). Find an expression for the total
vector force on the charge at P(a, a, a), assuming free space.
2.5 Let a point charge Q 1 = 25 nC be located at P 1 (4, −2, 7) and a charge
Q 2 = 60 nC be at P 2 (−3, 4, −2). (a)If = 0 , find E at P 3 (1, 2, 3). (b)At
what point on the y axis is E x = 0?
2.6 Two point charges of equal magnitude q are positioned at z =±d/2. (a)
Find the electric field everywhere on the z axis; (b) find the electric field
everywhere on the x axis; (c) repeat parts (a) and (b)if the charge at
z =−d/2is −q instead of +q.
2.7 A2-µC point charge is located at A(4, 3, 5) in free space. Find E ρ , E φ , and
E z at P(8, 12, 2).