Let S be the surface shown in the following figure in the first octant in the xy plane, and let F(vector) be a continuously differentiable vector field on R 3 such that x F 2k on S If the circulation of F(vector) is 12 around C 2 , 15 around C 3 and 14 around C 4 , determine the circulation of F(vector) around C1 Assume that the radii of C 2 , C 3 and C 4 are My Notes equal to 1 ) C, C4

Question: Let S be the surface shown in the following figure in the first octant in the xy-plane, and let F(vector) be a continuously differentiable vector

Let S be the surface shown in the following figure in the first octant in the xy-plane, and let F(vector) be a continuously differentiable vector field on R ³ such that ∇ x F-2k̂ on S. If the circulation of F(vector) is 12π around C ₂, 15π around C ₃ and 14π around C ₄, determine the circulation of F(vector) around C1 Assume that the radii of C ₂, C ₃ and C ₄ are My Notes equal to 1.)

C, C4

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