Find the Flux of the Curl of Field F Through

Multiple Choice

Find the flux of the curl of field F through the shell S.
- $\mathbf { F } = 5 \mathrm { y } \mathbf { i } + 2 \mathrm { x } \mathbf { j } + \cos ( \mathrm { z } ) \mathbf { k } ; \mathrm { S } : \mathbf { r } ( \mathrm { r } , \theta ) = 2 \sin \varphi \cos \theta \mathbf { i } + 2 \sin \varphi \sin \theta \mathbf { j } + 2 \cos \varphi \mathbf { k } , 0 \leq \theta \leq 2 \pi$ and $0 \leq \varphi \leq \frac { \pi } { 2 }$

A) $- 24 \pi$
B) $24 \pi$
C) $- 12$
D) $- 12 \pi$