Page 155 - Engineering Electromagnetics, 8th Edition

CHAPTER 5 Conductors and Dielectrics 137

Figure 5.12 A knowledge of the electric field external to the dielectric
enables us to find the remaining external fields first and then to use the
continuity of normal D to begin finding the internal fields.

D5.9. Let Region 1 (z < 0) be composed of a uniform dielectric material
for which r = 3.2, while Region 2 (z > 0) is characterized by r = 2. Let
2
D 1 =−30a x + 50a y + 70a z nC/m and find: (a) D N1 ;(b) D t1 ;(c) D t1 ;(d) D 1 ;
(e) θ 1 ;( f ) P 1 .
2 2 2 2
◦
Ans. 70 nC/m ; −30a x + 50a y nC/m ; 58.3 nC/m ; 91.1 nC/m ;39.8 ; −20.6a x +
34.4a y + 48.1a z nC/m 2

D5.10. Continue Problem D5.9 by finding: (a) D N2 ;(b) D t2 ;(c) D 2 ;(d) P 2 ;
(e) θ 2 .

2
2
2
Ans. 70a z nC/m ; −18.75a x + 31.25a y nC/m ; −18.75a x + 31.25a y + 70a z nC/m ;
2
−9.38a x + 15.63a y + 35a z nC/m ;27.5 ◦
REFERENCES

1. Fano, R. M., L. J. Chu, and R. B. Adler. Electromagnetic Fields, Energy, and Forces.
Cambridge, MA: MIT Press, 1968. Polarization in dielectrics is discussed in Chapter 5.
This junior-level text presupposes a full-term physics course in electricity and
magnetism, and it is therefore slightly more advanced in level. The introduction
beginning on p. 1 should be read.
2. Dekker, A. J. Electrical Engineering Materials. Englewood Cliffs, NJ: Prentice-Hall,
1963. This admirable little book covers dielectrics, conductors, semiconductors, and
magnetic materials.