B. Let S be the part of the sphere r +y + z2 = 4 located above the plane z 0, oriented at the point (0, 0, 2) by the unit normal vector i=k. Note that CE is not a closed surface. Let F %3D also be the defined vector field by F(z, y, z) = [r + exp(Vy? +2?)]i+ [y +exp(v+22)]j+2 + exp(v+y²)] , %3D where exp stands for the exponential function. Calculate the flux of F through S.
B. Let S be the part of the sphere r +y + z2 = 4 located above the plane z 0, oriented at the point (0, 0, 2) by the unit normal vector i=k. Note that CE is not a closed surface. Let F %3D also be the defined vector field by F(z, y, z) = [r + exp(Vy? +2?)]i+ [y +exp(v+22)]j+2 + exp(v+y²)] , %3D where exp stands for the exponential function. Calculate the flux of F through S.
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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![3. Let S be the part of the sphere +y + z² = 4 located above the plane z 0, oriented at
the point (0, 0, 2) by the unit normal vector n= k. Note that CE is not a closed surface. Let F
also be the defined vector field by
F(z, y, 2) = [r +exp(Vy? +2?)]i+ [v + exp(v2 + z²)] j +[z + exp{/2
where exp stands for the exponential function.
Calculate the flux of F through S.
is pronortional to the square of the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc17eb80e-e601-466c-970a-ea037a1c5193%2Fd5404f3e-b17f-4d29-b99c-3f10576847c7%2F0vbs9yv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Let S be the part of the sphere +y + z² = 4 located above the plane z 0, oriented at
the point (0, 0, 2) by the unit normal vector n= k. Note that CE is not a closed surface. Let F
also be the defined vector field by
F(z, y, 2) = [r +exp(Vy? +2?)]i+ [v + exp(v2 + z²)] j +[z + exp{/2
where exp stands for the exponential function.
Calculate the flux of F through S.
is pronortional to the square of the
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