Average circulation Let S be a small circular disk of radius R centered at the point P with a unit normal vector n . Let C be the boundary of S . a. Express the average circulation of the vector field F on S as a surface integral of ▿ × F. b. Argue that for small R, the average circulation approaches (▿ × F)| p ·n (the component of ▿ × F in the direction of n evaluated at P ) with the approximation improving as R→ 0.
Average circulation Let S be a small circular disk of radius R centered at the point P with a unit normal vector n . Let C be the boundary of S . a. Express the average circulation of the vector field F on S as a surface integral of ▿ × F. b. Argue that for small R, the average circulation approaches (▿ × F)| p ·n (the component of ▿ × F in the direction of n evaluated at P ) with the approximation improving as R→ 0.
Solution Summary: The author explains the average circulation of the vector field F on S as a surface integral of nablatimes F.
Average circulation Let S be a small circular disk of radius R centered at the point P with a unit normal vectorn. Let C be the boundary of S.
a. Express the average circulation of the vector field F on S as a surface integral of ▿ × F.
b. Argue that for small R, the average circulation approaches (▿ × F)|p·n (the component of ▿ × F in the direction of n evaluated at P) with the approximation improving as R→0.
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