Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ , where $\mathbf { F } = ( x , y , z ) = y \mathbf { j } - z \mathbf { k }$ and S is the cube bounded by $x = \pm 1 , \quad y = \pm 1 , \quad z = \pm 1$ .
A) $16$
B)$8$
C) $- 8$
D) $1$
E) $32$
F) $4$
G) $- 4$
H)$0$

Question

Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ , where $\mathbf { F } = ( x , y , z ) = y \mathbf { j } - z \mathbf { k }$ and S is the cube bounded by $x = \pm 1 , \quad y = \pm 1 , \quad z = \pm 1$ .
A) $16$ 
B)$8$
C) $- 8$
D) $1$
E) $32$ 
F) $4$
G) $- 4$ 
H)$0$

Quizplus · Accepted Answer

The vector field $\mathbf { F } = ( x , y , z ) = y \mathbf { j } - z \mathbf { k }$ is incorrect as stated; it should be $\mathbf { F } = y \mathbf { j } - z \mathbf { k }$. The divergence of $\mathbf { F }$, $\nabla \cdot \mathbf { F } = 0$, indicates that the net flux through the surface of the cube is zero.

Evaluate ∬SF⋅dS\iint _ { S } \mathbf { F } \cdot d \mathbf { S }∬S​F⋅dS

Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$