The potential f on the semicircle ZzZ 1, y 0, satisfies the boundary conditions f(x, 0)
Chapter 20, Problem 7(choose chapter or problem)
The potential \(\phi\) on the semicircle \(|z| \leq 1\), \(y \geq 0), satisfies the boundary conditions \(\phi(x, 0)=0\), \(-1<x<1\), and \(\phi\left(e^{i \theta}\right)=1,0<\theta<\pi\). Show that
\(\phi(x, y)=\frac{1}{\pi} \operatorname{Arg}\left(\frac{z-1}{z+1}\right)^{2})
and use the mapping properties of linear fractional transformations to explain why the equipotential lines are arcs of circles.
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