Consider the vector field Fˆ(x, y, z) = (y/(x^2 +y^2) i - (x/(x^2 +y^2)j (a) compute the curl (b) ) If Fˆ were conservative, what would be the value of the line integral closed integral C(Fˆ · dr ˆ) where C is the unit circle x^2 + y^2 = 1 in the xy-plane? Explain (c) Compute the line integral in part (b) directly (d) From part C, why doesn't it contradict the test for a coservative vector field?
Consider the vector field Fˆ(x, y, z) = (y/(x^2 +y^2) i - (x/(x^2 +y^2)j (a) compute the curl (b) ) If Fˆ were conservative, what would be the value of the line integral closed integral C(Fˆ · dr ˆ) where C is the unit circle x^2 + y^2 = 1 in the xy-plane? Explain (c) Compute the line integral in part (b) directly (d) From part C, why doesn't it contradict the test for a coservative vector field?
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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Consider the
Fˆ(x, y, z) = (y/(x^2 +y^2) i - (x/(x^2 +y^2)j
(a) compute the curl
(b) ) If Fˆ were conservative, what would be the value of the line
closed integral C(Fˆ · dr ˆ) where C is the unit circle x^2 + y^2 = 1 in the xy-plane? Explain
(c) Compute the line integral in part (b) directly
(d) From part C, why doesn't it contradict the test for a coservative vector field?
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