Let sigma denote the surface of a solid G with n the outward unit normal vector

Question

Let sigma denote the surface of a solid G with n the outward unit normal vector field to sigma. Assume that F is a vector field with continuous first-order partial derivatives on sigma. Prove that (curl F) ndS = 0 [Hint: Let C denote a simple closed curve on sigma that separates the surface into two subsurfaces sigma 1 and sigma 2 that share C as their common boundary. Apply Stokes' Theorem to sigma 1 and to sigma 2 and add the results.] The vector field curl(F) is called the curl field of F. In words, interpret the formula in part (a) as a statement about the flux of the curl field.

Explanation / Answer

hope this link helps. https://docs.google.com/viewer?a=v&q=cache:SzVUGDpTGo4J:math.harvard.edu/~ytzeng/worksheet/1130_sol.pdf+&hl=en&gl=in&pid=bl&srcid=ADGEESiN8E6eoQObDxg7KQgmsV3NbfsItA0GABKx8gUGGdWmTqTl2bX9ccy1N9du9RClsWhgfgsQFHbW_UD-XIjYgDg_d8Bwo9rf3JFAtbuYuMmq8EIPIGGzr6QZ08OnhDG3M2WgUOdN&sig=AHIEtbS-fRWMvk1BkVyk15PRaj3VEJSOxA

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