Surface integrals of vector fields Find the flux of the

Chapter 11, Problem 43E

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QUESTION:

Find the flux of the following vector fields across the given surface with the specified orientation. You may use either an explicit or parametric description of the surface.

\(\mathbf{F}=\langle 0,0,-1\rangle\) across the slanted face of the tetrahedron\(z=4-x-y\) in the first octant; normal vectors point in the positive z-direction.

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QUESTION:

Find the flux of the following vector fields across the given surface with the specified orientation. You may use either an explicit or parametric description of the surface.

\(\mathbf{F}=\langle 0,0,-1\rangle\) across the slanted face of the tetrahedron\(z=4-x-y\) in the first octant; normal vectors point in the positive z-direction.

ANSWER:

Solution 43E

Step 1:

Given that

F = 〈0, 0. −1〉 across the slanted face of the tetrahedron z =4 − x −y in the first octant; normal vectors point in the positive z-direction.

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