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?
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?
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: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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