Average circulation Let S be a small circular disk of radius Rcentered at the point P with a unit normal vector n. Let C be theboundary of S.a. Express the average circulation of the vector field F on S as asurface integral of ∇ x F.b. Argue that for small R, the average circulation approaches(∇ x F) | P ⋅ n (the component of ∇ x F in the direction of nevaluated at P) with the approximation improving as R → 0.
Average circulation Let S be a small circular disk of radius Rcentered at the point P with a unit normal vector n. Let C be theboundary of S.a. Express the average circulation of the vector field F on S as asurface integral of ∇ x F.b. Argue that for small R, the average circulation approaches(∇ x F) | P ⋅ n (the component of ∇ x F in the direction of nevaluated at P) with the approximation improving as R → 0.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 60E
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Average circulation Let S be a small circular disk of radius R
centered at the point P with a unit normal
boundary of S.
a. Express the average circulation of the vector field F on S as a
surface integral of ∇ x F.
b. Argue that for small R, the average circulation approaches
(∇ x F) | P ⋅ n (the component of ∇ x F in the direction of n
evaluated at P) with the approximation improving as R → 0.
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