Page 143 - Engineering Electromagnetics, 8th Edition

CHAPTER 5 Conductors and Dielectrics 125

Figure 5.7 (a)A given charge configuration above an infinite conducting plane may
be replaced by (b) the given charge configuration plus the image configuration, without
the conducting plane.
charges. The radial vector from the positive line charge to P is R + = 2a x − 3a z ,
while R − = 2a x + 3a z . Thus, the individual fields are

ρ L 30 × 10 −9 2a x − 3a z
E + = a R+ = √ √
2π 0 13 13
2π 0 R +
and
30 × 10 −9 2a x + 3a z
E − = √ √
2π 0 13 13
Adding these results, we have
−9
−180 × 10 a z
E = =−249a z V/m
2π 0 (13)
This then is the field at (or just above) P in both the configurations of Figure 5.8, and
it is certainly satisfying to note that the field is normal to the conducting plane, as it
2
must be. Thus, D = 0 E =−2.20a z nC/m , and because this is directed toward the
2
conducting plane, ρ S is negative and has a value of −2.20 nC/m at P.

Figure 5.8 (a)A line charge above a conducting plane. (b) The conductor is
removed, and the image of the line charge is added.