Question

Consider an annulus with inner radius a and outer radius b. Suppose u satisfies the Laplace equation and the boundary conditions: u(a,θ)=5cos(2θ) on the inner ring and u(b,θ)=-10sin(θ) on the outer ring. Find a solution for u(r,θ). (Hint: break this into two problems: i) where u=5cos(2θ) on the inner ring and zero on the outer and ii) where u=-10sin(θ) on the outer ring and zero on the inner.)

Answer 1

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