(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known dataI need to solve the Laplace equation, u_rr + (1/r)u_r + (1/r^2)u_{theta}{theta} = 0,

on a circular wedge with radius R, angle {alpha}, where u(r,0) = 0, u(R,{theta}) = 0, and

u(r,{alpha}) = 50.

2. Relevant equations

3. The attempt at a solutionSeparate variables - u(r,{theta}) = P(r)Q({theta}), and we have the equations

Q'' + (k^2)Q = 0, (r^2)P'' + rP' - (k^2)P = 0, where k is a constant. Q_n = Asin(n{theta})+Bcos(n{theta}), P_n = C(r^n).

Since u(r,0) = 0, B = 0. Now, since u(R,{theta}) = 0, this must mean R^n = 0, hence

R = 0, so u = 0 for all r, {theta}. Is this reasoning correct?

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# Homework Help: Laplace Equation - Wedge

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