1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

11.6 • Two-DIMENSIONAL ELECTROSTATICS 463

y

v

w =S(t.)

x

"

Figure 11.38 The potentials </> and 4'.

-------~EXERCISES FOR SECTION 11.6

1. Find the electrostatic potential </> (x, y) between the two coaxial cylinders r = 1
   and r = 2 that has the boundary values shown in Figure 11.39:

cf>(x, y) = 100

cf>(x, y) = 200

y

Figure 11.39

when lzl = 1,

when lzl = 2.

2. Find the electrost atic potential cf>(x,y) in the upper half-plane Im(z) > 0 that
   satisfies the boundary values shown in Figure 11.40:

cf> (x, O} = 100,

<f>(x, O} = 0,

<f>(x, O} = -100

y

;=- 100 ;=O

Figure 11.4 0

for x > l ;

for -1<x<1;

forx<-1.