Compute the flux of the vector field F = 2x²y²zk through the surface S which is the cone √² + y² : =z, with 0≤ z < R. oriented downward. (a) Parameterize the cone using cylindrical coordinates (write as theta). x(r, 0) = y(r, 0) = z(r, 0) = H with

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Compute the flux of the vector field F = 2x²y²zk through the surface S which is the cone √² + y² : =z, with 0≤ z < R. oriented downward.
(a) Parameterize the cone using cylindrical coordinates (write as theta).
x(r, 0) =
y(r, 0) =
z(r, 0) =
H
with
and
<r<
<O<
(b) With this parameterization, what is the downward normal vector n? (This vector should not be a unit vector.)
n =
(c) Find the flux of through S.
flux =
Transcribed Image Text:Compute the flux of the vector field F = 2x²y²zk through the surface S which is the cone √² + y² : =z, with 0≤ z < R. oriented downward. (a) Parameterize the cone using cylindrical coordinates (write as theta). x(r, 0) = y(r, 0) = z(r, 0) = H with and <r< <O< (b) With this parameterization, what is the downward normal vector n? (This vector should not be a unit vector.) n = (c) Find the flux of through S. flux =
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