Solved: Show that <1> = el'Tr = (l/'Tr) arctan (ylx) is
Chapter 18, Problem 18.1.9(choose chapter or problem)
Show that \(\Phi=\theta / \pi=(1 / \pi) \arctan (y / x)\) is harmonic in the upper half-plane and satisfies the boundary condition \(\Phi(x, 0)=1\) if x < 0 and 0 if x > 0, and the corresponding complex potential is \(F(z)=-(i / \pi) \mathrm{Ln} z\).
Text Transcription:
Phi = theta/pi = (1/pi) arctan (y/x)
Phi(x, 0) = 1
F(z) = -(i/pi) Ln z
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