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Computing flux Use the Divergence Theorem to
Chapter 14, Problem 19E(choose chapter or problem)
Computing flux Use the Divergence Theorem to compute the net outward flux of the following fields across the given surfaces S.
\(\mathbf{F}=\langle x, 2 y, z\rangle\); S is the boundary of the tetrahedron in the first octant formed by the plane x + y + z = 1.
Text Transcription:
F = langle x, 2y, z rangle
Questions & Answers
QUESTION:
Computing flux Use the Divergence Theorem to compute the net outward flux of the following fields across the given surfaces S.
\(\mathbf{F}=\langle x, 2 y, z\rangle\); S is the boundary of the tetrahedron in the first octant formed by the plane x + y + z = 1.
Text Transcription:
F = langle x, 2y, z rangle
ANSWER:Solution 19E
In this problem we have to find the net outward flux of the following field across the given surface S.
The given function in vector form
F(x,y,z)=x i +2 y j +z k,
As we know the divergence theorem
F·n dS =
div F dV
Step 1:
Calculate divergence of F
div F =x +
2y +
z
=1+2+1
= 4
Step2:
Calculate the boundary
Now we will consider the boundary of the tetrahedron in the first octant formed by the plane