E1. Consider the vector field in spherical coordinates, F(r) = 6n (a) Find the closed line integral around path C that is a circle of radius s in the x-y plane and centered on the origin. f. F. dl (b) Find the surface integral of curl Fover the hemispheric surface, H, enclosed by C: V x F. da (c) Find the surface integral of curl Fover the circular disk area, D, enclosed by C. (d) Demonstrate that for both surfaces H and D that Stoke's theorem works.
E1. Consider the vector field in spherical coordinates, F(r) = 6n (a) Find the closed line integral around path C that is a circle of radius s in the x-y plane and centered on the origin. f. F. dl (b) Find the surface integral of curl Fover the hemispheric surface, H, enclosed by C: V x F. da (c) Find the surface integral of curl Fover the circular disk area, D, enclosed by C. (d) Demonstrate that for both surfaces H and D that Stoke's theorem works.
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Transcribed Image Text:E1. Consider the vector field in spherical coordinates, F(r) = n
(a) Find the closed line integral around path C that is a circle of radius s in the x-y plane and
centered on the origin.
$. F. dl
(b) Find the surface integral of curl F over the hemispheric surface,H, enclosed by C:
V X F. da
(c) Find the surface integral of curl F over the circular disk area, D, enclosed by C.
(d) Demonstrate that for both surfaces H and D that Stoke's theorem works.
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