1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

11.11 • SOURCES AND SINKS 509

Figure 11.103

6. T he complex potential F (z) = !. determines an electrostatic field that is referred
   z
   to as a dipole.

(a) Show that

F(z) = lim log(z)-log(z -a)

a- 0 a

and that a dipole is the li miting case of a source and sink.

(b) Show that the lines of flux of a dipole are circles that pass through the

origin, as shown in Figure 11.104.

y

Figure 11.104