Use the Divergence Theorem to calculate the flux of the vector fields F₁ = -7zi+7ck and F₂ = −7zi + (5y+7)j + 7æk through the surface S given by the sphere of radius a centered at the origin with outwards orientation. Be sure that you are able to explain your answers geometrically. With W giving the interior of the sphere, Is F₁· dà = Swdv = [ and Ss F₂ · dà = Sw|dv = [
Use the Divergence Theorem to calculate the flux of the vector fields F₁ = -7zi+7ck and F₂ = −7zi + (5y+7)j + 7æk through the surface S given by the sphere of radius a centered at the origin with outwards orientation. Be sure that you are able to explain your answers geometrically. With W giving the interior of the sphere, Is F₁· dà = Swdv = [ and Ss F₂ · dà = Sw|dv = [
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 32E
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![Use the Divergence Theorem to calculate the flux of the vector fields F₁ = −7zi + 7xk and F₂ = −7zi + (5y + 7)j +7ck through the surface S given by the sphere of radius a
centered at the origin with outwards orientation. Be sure that you are able to explain your answers geometrically.
With W giving the interior of the sphere,
Ss F₁ · dà = SwdV =
and
√s F₂ · dà = Sw|dv=
Ss
dV](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdbd5786d-c03d-4368-809a-5f6317a6d7c8%2F3e7e31ba-7728-4c23-b410-569c982d08c5%2F78ktju_processed.png&w=3840&q=75)
Transcribed Image Text:Use the Divergence Theorem to calculate the flux of the vector fields F₁ = −7zi + 7xk and F₂ = −7zi + (5y + 7)j +7ck through the surface S given by the sphere of radius a
centered at the origin with outwards orientation. Be sure that you are able to explain your answers geometrically.
With W giving the interior of the sphere,
Ss F₁ · dà = SwdV =
and
√s F₂ · dà = Sw|dv=
Ss
dV
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