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Compute the flux of the vector field F = 5x³y²zk through the surface S which is the cone (a) Parameterize the cone using cylindrical coordinates (write as theta). x(r,0) = y(r, 0) = z(r, 0) = with and ≤rs

Compute the flux of the vector field F = 5x³y²zk through the surface S which is the cone (a) Parameterize the cone using cylindrical coordinates (write as theta). x(r,0) = y(r, 0) = z(r, 0) = with and ≤rs

Advanced Engineering Mathematics
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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Compute the flux of the vector field F = 5x³y²zk through the surface S which is the cone (a) Parameterize the cone using cylindrical coordinates (write 0 as theta). x(r, 0) = y(r, 0) z(r, 0): = with and ≤rs <O< (b) With this parameterization, what is dA? dà = (c) Find the flux of F¹ through S. flux = x² + y² = z, with 0 ≤ z ≤ R, oriented downward.
Transcribed Image Text:Compute the flux of the vector field F = 5x³y²zk through the surface S which is the cone (a) Parameterize the cone using cylindrical coordinates (write 0 as theta). x(r, 0) = y(r, 0) z(r, 0): = with and ≤rs <O< (b) With this parameterization, what is dA? dà = (c) Find the flux of F¹ through S. flux = x² + y² = z, with 0 ≤ z ≤ R, oriented downward.
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