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.
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 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 ∇ 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.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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