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Unformatted text preview: ing the integral computation)
p. 916 #7 (use z ) and #8 (use H-1)
Change-of Reference: At this point, we abandon Zill’s book (since it is inadequate) and
go to Erwin Kreyzsig, Advanced Engineering Mathematics, 8th Edition, Wiley.
28 9. Complex Potentials (Based on Kreyszig)
The electrostatic force of attraction between charged objects is the gradient of an
electrostatic potential function ∞ that satisfied Laplace's equation.
(A) Find the potential ∞ between two parallel plates extending to infinity, which are kept
at potentials ∞1 and ∞2 respectively.
Solution: This is just Dirichlet's problem. If the parallel plates are vertical, we can take
the vertical axis to be the y-axis with the lower plate x = 0, and take
∞ = ∞1 + (∞2 - ∞1)
where h is the distance between the plates. A complex potential function corresponding
o the real potential function ∞(z) is an analytic function F(z) = ∞(z) + i§(z). Notice that
∞ and § are conjugate harmonic functions.
In this exa...
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