(Solution) - A rectangular pipe running parallel to the z axis -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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A rectangular pipe, running parallel to the z-axis (from ? ? to + ?), has three grounded metal sides, at y = 0, y = a, and x = 0. The fourth side, at x = b, is maintained at a specified potential V0(y).
(a) Develop a general formula for the potential within the pipe.
(b) Find the potential explicitly, for the case V0(y) = V0 (a constant).