2. (28 marks) Consider the boundary value problem 1 1 r p2 V(a,0) = 0 lim V(r,0) = Cr cos e 7?(rV=)r + y2 sing(sin ØVo)

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2 28 Marks Consider The Boundary Value Problem 1 1 R P2 V A 0 0 Lim V R 0 Cr Cos E 7 Rv R Y2 Sing Sin Ovo 1 (364.47 KiB) Viewed 20 times

2. (28 marks) Consider the boundary value problem 1 1 r p2 V(a,0) = 0 lim V(r,0) = Cr cos e 7?(rV=)r + y2 sing(sin ØVo) = 0 = a<r < oo, 0 <O<a 2 p2 )o 0, = no where a > 0 and C # 0 are real constants. Find V(r, 6). = > The Legendre polynomials Pn(2x) for n = 0, 1, 2, 3 are: Po(x) = 1, P1(x) = x, P2(x) = (3x2 – 1)/2, = = P3(x) = (5x² – 3x)/2, = |2 <1