A circular disk, S, of radius 2 and centered on an axis, is perpendicular to the y-axis at y = -6 with normal in the direction of decreasing y. Consider the vector field $\vec { F } = x \vec { i } + y \vec { j } + ( z + x ) \vec { k }$ .Is the flux integral $\int_{S} \vec{F} \cdot \overrightarrow{d A}$ positive, negative or zero?
A)Positive
B)Zero
C)Negative

Question

Quizplus · Accepted Answer

The flux integral is positive because the normal vector points in the direction of decreasing y, and the z-component of the vector field is positive on the disk.

A Circular Disk, S, of Radius 2 and Centered on an Axis