Let S be the disk enclosed by the curve C: r(t) = (cost, cos q sin t, sin q sin t), for 0 ≤t≤2, where π is a fixed angle. By introducing the variable r, this surface can be parameterized as 2 Osos S = {(r cost, r cos q sin t, r sin q sin t): 0 ≤r≤1, 0≤t<2} with the normal vector n = (0, - Φ Use Stokes' Theorem and a surface integral to find the circulation on C of the vector field F = (-z,0,x) as a function of p. For what value of op is the circulation a maximum? - r sin ,r cos q).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
Let S be the disk enclosed by the curve C: r(t) = (cost, cos q sint, sin q sin t), for 0≤t≤ 2, where
π
is a fixed angle. By introducing the variable r, this surface can be parameterized as
2
0≤ps.
S = {(r cos t,rcos o sin t, r sin q sin t): 0≤r≤ 1, 0≤t<2} with the normal vector n = (0, -r sin p,r cos p).
Use Stokes' Theorem and a surface integral to find the circulation on C of the vector field F = (-z, 0, x) as a
function of p. For what value of op is the circulation a maximum?
The circulation on C is. (Type an exact answer, using as needed.)
Transcribed Image Text:Let S be the disk enclosed by the curve C: r(t) = (cost, cos q sint, sin q sin t), for 0≤t≤ 2, where π is a fixed angle. By introducing the variable r, this surface can be parameterized as 2 0≤ps. S = {(r cos t,rcos o sin t, r sin q sin t): 0≤r≤ 1, 0≤t<2} with the normal vector n = (0, -r sin p,r cos p). Use Stokes' Theorem and a surface integral to find the circulation on C of the vector field F = (-z, 0, x) as a function of p. For what value of op is the circulation a maximum? The circulation on C is. (Type an exact answer, using as needed.)
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