Let F = (x, y², z²). (a.) Let E be bounded below by xy-plane and above by the sphere x2 + y² +2²= 1. Find the flux of Ethrough E by direct calculation. Notice the boundary of É consists of the spherical shell as well as the downward oriented unit-disk on the xy-plane. (b.) Calculate the flux of F through E using the Divergence Theorem.
Let F = (x, y², z²). (a.) Let E be bounded below by xy-plane and above by the sphere x2 + y² +2²= 1. Find the flux of Ethrough E by direct calculation. Notice the boundary of É consists of the spherical shell as well as the downward oriented unit-disk on the xy-plane. (b.) Calculate the flux of F through E using the Divergence Theorem.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let F= (x, y², z²).
(a.) Let E be bounded below by xy-plane and above by the sphere x² + y² + 2² = 1. Find the flux of Ethrough
E by direct calculation. Notice the boundary of É consists of the spherical shell as well as the downward
oriented unit-disk on the xy-plane.
(b.) Calculate the flux of F through E using the Divergence Theorem.
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