If $\vec { F}$ is a constant vector field and S₁ and S₂ are oriented rectangles with areas 3 and 15 respectively, both orientated with the vector $\overrightarrow { { i } } ,$ is it true that $\int _ { S _ { 2 } } \vec { F } \cdot \vec { d A } = 5 \oint _ { S _ { 1 } } \vec { F } \cdot \vec { d A }$ ?

Question

Quizplus · Accepted Answer

The surface integral of a constant vector field over a surface depends on the dot product of the vector field with the surface's normal vector and the surface's area. Since both surfaces are oriented with the same vector, the integrals are proportional to their areas, not a factor of 5.

If F⃗\vec { F}F Is a Constant Vector Field and S1 and S2 Are

If $\vec { F}$ Is a Constant Vector Field and S₁ and S₂ Are