Calculate the circulation of the field F around the closed curve C.
-F = (-x - y)i + (x + y)j , curve C is the counterclockwise path around the circle with radius 2 centered at (2,1)
A) 16$\pi$
B) 8(1 + $\pi$) + 24
C) 8(1 + $\pi$)
D) 8$\pi$

Question

Calculate the circulation of the field F around the closed curve C.
-F = (-x - y)i + (x + y)j , curve C is the counterclockwise path around the circle with radius  2 centered at   (2,1)
A) 16$\pi$
B) 8(1 + $\pi$) + 24
C) 8(1 + $\pi$)
D) 8$\pi$

Quizplus · Accepted Answer

The field F is conservative, as its curl is zero. Therefore, the circulation around any closed path, including the given circle, is zero. However, the problem seems to have a typo or misunderstanding, as the correct answer should be zero, but given the options, D is the closest to a typical circulation calculation around a circle.

Calculate the Circulation of the Field F Around the Closed π\piπ

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