Let S be the surface shown in the following figure in the first octant in the xy-plane, and let 7 be a continuously differentiable vector field on R³ such that V x F = 2K on S. If the circulation of F is 12 around C₂, 157 around C³, and 14 around C4, determine the circulation of F around C₁. (Assume that the radii of C₂, C3, and C are equal to 1.) y 2 C₁ 48

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let S be the surface shown in the following figure in the first octant in the xy-plane, and let F be a continuously differentiable vector field on R³ such that V x F = 2K on S. If the circulation of
F is 12π around C₂, 157 around C3, and 147 around C₁, determine the circulation of F around C₁. (Assume that the radii of C₂, C3, and C₁4 are equal to 1.)
y
4
3
2
1-
C₂
C3
S
2
C₁
4
C₁
X
Transcribed Image Text:Let S be the surface shown in the following figure in the first octant in the xy-plane, and let F be a continuously differentiable vector field on R³ such that V x F = 2K on S. If the circulation of F is 12π around C₂, 157 around C3, and 147 around C₁, determine the circulation of F around C₁. (Assume that the radii of C₂, C3, and C₁4 are equal to 1.) y 4 3 2 1- C₂ C3 S 2 C₁ 4 C₁ X
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