If $\int_{S} \vec{F} \cdot \overrightarrow{d A}=0$ , then $\vec{F}$ is perpendicular to the surface S at every point.

Question

Quizplus · Accepted Answer

The integral $\int_{S} \vec{F} \cdot \overrightarrow{d A}=0$ means that the net flux of $\vec{F}$ through the surface $S$ is zero. This does not necessarily imply that $\vec{F}$ is perpendicular to $S$ at every point; it could mean that the flux entering and exiting the surface balances out.

If ∫SF⃗⋅dA→=0\int_{S} \vec{F} \cdot \overrightarrow{d A}=0∫S​F⋅dA=0 , Then F⃗\vec{F}F Is Perpendicular to the Surface S at Every Point

If $\int_{S} \vec{F} \cdot \overrightarrow{d A}=0$ , Then $\vec{F}$ Is Perpendicular to the Surface S at Every Point