3.9 Local Extension and Compression
The fields and charge distributions obtained in the previous section by one pair of
local forces can be used as building blocks for constructing more complicated
electric fields and charge distributions mechanically. As an example, consider an
unbounded rod under two local pairs of forces, one compressive and the other tensile
as shown in Fig. 3.14 [6].
The solution to this problem is similar to that in the previous section, with more
algebra because of more regions with different stresses, more undetermined constants, and more boundary and continuity conditions. The solution is not presented
here, and we show the results directly in Fig. 3.15 for two different values of n 0 . Our
main interest is in the big potential well with two small potential barriers in (c).
Fig. 3.13 Fields for different F. n 0 ¼ 10
21
m
À3
. (a) Effective polarization charge density ρ
P
. (b)
Electron concentration perturbation Δn. (c) Electric potential φ. (d) IÀV curve. V ¼ φ(L )Àφ(ÀL ).
I ¼ J
n
A
58
3 Extension of Rods