The z-axis runs down the center of an infinitely long heating duct with a square cross section. For a real metal duct (not a perfect conductor), the electrostatic potential (x, y) varies linearly along the side walls of the duct. Suppose that the duct corners at (a, 0) are held at potential +V and the duct corners at (0,a) are
Chapter 7, Problems #4
The z-axis runs down the center of an infinitely long heating duct with a square cross section. For a real metal duct (not a perfect conductor), the electrostatic potential φ(x, y) varies linearly along the side walls of the duct. Suppose that the duct corners at (±a, 0) are held at potential +V and the duct corners at (0,±a) are held at potential −V. Find the potential inside the duct beginning with the trial solution.
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