Complex Analysis: Theory and Applications · Problem 3.3.13

Sequences, Series, and Fractals — Howell & Matthews

Mathematics — Complex Analysis · dipole-field

Problem

The function

F(z) = \dfrac{1}{z}

is used to determine a field known as a dipole. (a) Express

F(z)

in the form

F(z) = \phi(x,y) + i\psi(x,y)

. (b) Sketch the equipotentials

\phi = 1, \dfrac{1}{2}, \dfrac{1}{4}

and streamlines

\psi = 1, \dfrac{1}{2}, \dfrac{1}{4}