Chapter 17.2, Problem 58E

Circulation Consider the following vector fields F and closed oriented curves C in the plane (see figures).

a. Based on the picture, make a conjecture about whether the circulation of F on C is positive, negative, or zero.

b. Compute the circulation and interpret the result.

58. $F=\frac{\langle y,-2x\rangle }{\sqrt{4x^2+y^2}};$ C : $r(t)=\langle 2\cos t,4\sin t\rangle ,$ for 0 ≤ t ≤ 2π