Chapter 15.8, Problem 18ES

(a) 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

${\displaystyle \underset{\sigma }{\iint }\text{(curlF}}).\text{n }ds=0$

(b) The vector field curl (F) is called curl field of F. In words, interpret the formula in part (a) as a statement about the flux of the flux of the curl field.