C potential in an angular region here we have two

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Unformatted text preview: ing the integral computation) #5, 6, Hand In: 2 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. Examples (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 x ∞ = ∞1 + (∞2 - ∞1) h 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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This document was uploaded on 03/20/2014 for the course MATH 144 at Hofstra University.

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