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 3 centered at (3, 6)
A) $18 ( 1 + \pi ) + 108$
B) $18 \pi$
C) $36 \pi$
D) $18 ( 1 + \pi )$

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 3 centered at (3, 6) 
A) $18 ( 1 + \pi ) + 108$
B) $18 \pi$
C) $36 \pi$
D) $18 ( 1 + \pi )$

Quizplus · Accepted Answer

The field F is conservative, and the circulation of a conservative field around a closed curve is zero. However, the field can be rewritten as F = (-1, 1) x (x, y), which is a constant vector field rotated by 90 degrees. The circulation around a circle of radius 3 is given by the line integral of the tangential component, which is $18 \pi$.

Calculate the Circulation of the Field F Around the Closed 18(1+π)+10818 ( 1 + \pi ) + 10818(1+π)+108

Calculate the Circulation of the Field F Around the Closed $18 ( 1 + \pi ) + 108$