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HW5 - Φ θ = 0 = 0 and Φ θ = ψ = V in polar...

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MEEN 634/489, Fall 2008 Dynamics and Modeling of Mechatronic Systems Problem Set #5 Issued: Monday, October 13, 2008 Due: Friday, October 24, 2008 Reading assignment: WM, pages 188 233 Problem 1. WM, 5.1 Problem 2. WM, 5.3 Hint 1: Conductance 1 / resistance. Hint 2: Begin with the Poisson’s equation, 2 Φ = ρ / ε 0 . What is the charge density ρ in the volume between the pair of highly conducting plates? Find the electric potential Φ ( θ ) that satisfies the Poisson’s equation and the two boundary conditions,
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Unformatted text preview: Φ ( θ = 0) = 0, and Φ ( θ = ψ ) = V in polar coordinates. (Is Φ a function of r as well with the assumptions given in Fig. 5P.3b? Think about the electric potential inside a parallel plate capacitor.) Then, find the electric field E = −∇Φ in polar coordinates. Problem 3. WM, 5.6 Do by linearization. Problem 4. WM, 5.6 Do by potential wells. Problem 5. WM, 5.8 Problem 6. WM, 5.11...
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