Find the flux of the vector field F across the surface S in the indicated direction.
-$\mathbf { F } = 2 \mathrm { x } ^ { 2 } \mathrm { j } - \mathrm { z } ^ { 3 } \mathrm { k } ; \mathrm { S }$ is the portion of the parabolic cylinder $\mathrm { y } = 2 \mathrm { x } ^ { 2 }$ for which $0 \leq \mathrm { z } \leq 1$ and $- 1 \leq \mathrm { x } \leq 1$; direction is outward (away from the $y - z$ plane)
A) 4
B) $\frac { 4 } { 3 }$
C) $- 4$
D) $- \frac { 4 } { 3 }$

Question

Quizplus · Accepted Answer

The flux is calculated using the surface integral of the vector field over the given surface. The vector field component $2x^2j$ contributes to the flux through the surface $y = 2x^2$, and the limits of integration are given for $x$ and $z$. The correct evaluation of this integral results in $\frac{4}{3}$.

Find the Flux of the Vector Field F Across the Surface