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?

Question

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?

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