8. A vector field F is given in cylindrical polar coordinates by F(p₁6, 2) == cos(7²)₂ Find the outward flux of F across the curved surface of a cylinder of radius a and height h located with its centre at the origin and its axis on the z axis. Find also the outward flux of F across the plane end faces of the cylinder. What is the next outward flux of F across the whole cylinder?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 98E
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8. A vector field F is given in cylindrical polar coordinates by
F(p, Ó, z) = ª cos (7²)p
ㅠ
P
Find the outward flux of F across the curved surface of a cylinder of radius
a and height h located with its centre at the origin and its axis on the z axis.
Find also the outward flux of F across the plane end faces of the cylinder.
What is the next outward flux of F across the whole cylinder?
Transcribed Image Text:8. A vector field F is given in cylindrical polar coordinates by F(p, Ó, z) = ª cos (7²)p ㅠ P Find the outward flux of F across the curved surface of a cylinder of radius a and height h located with its centre at the origin and its axis on the z axis. Find also the outward flux of F across the plane end faces of the cylinder. What is the next outward flux of F across the whole cylinder?
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Wouldn't the sin(pi*h/2a) cancel eachother out ? In teas of being 2sin ? 

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