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The electrostatic potential satisfies Laplace’s equation ∇^{2}u = 0 in any region free of charges. Also the heat equation u_{t} = c^{2 }∇^{2}u reduces to Laplace’s equation if the temperature u is time-independent (“steady-state case”). Using (20), find the potential (equivalently: the steady-state temperature) in the disk r < 1 if the boundary values are (sketch them, to see what is going on).

u (1, θ) = 400 cos^{3} θ

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