Let S be the level surface g(x, y, z) = 4 where g(x, y, z) = x4 + y® + 32º. Let F be the vector field Vg ||V9||' F = and let G be the vector field G = Vg × (0,0,3). (a) Show that the flux of F through S is equal to the surface area of S (up to a sign). (b) Compute the flux of G through S. Hint: Your answers should not be long!
Let S be the level surface g(x, y, z) = 4 where g(x, y, z) = x4 + y® + 32º. Let F be the vector field Vg ||V9||' F = and let G be the vector field G = Vg × (0,0,3). (a) Show that the flux of F through S is equal to the surface area of S (up to a sign). (b) Compute the flux of G through S. Hint: Your answers should not be long!
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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How to solve a or b
second picture is definition
Transcribed Image Text:Let S be the level surface g(x, y, z) = 4 where g(x, y, z) = x4 + y® + 32º. Let F be the vector field
Vg
||V9||'
F =
and let G be the vector field G = Vg × (0,0,3).
(a) Show that the flux of F through S is equal to the surface area of S (up to a sign).
(b) Compute the flux of G through S.
Hint: Your answers should not be long!
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Suppose
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