Let F(x,y) = ( P(x,y), Q(x,y)) be a vector field that is continuously differentiable along the closed smooth curve C : x2+y2 = 1. Moreover let
-F(x,y) = F( -x, -y)≠ 0 and
P(x,y) = -P(-x,y) and Q(x,y) = Q(-x,y).
Determine all the possible values of the circulation around C, and argue why flux across C is non zero.
Circulation = ∫CF. T ds , T tangent vector
Flux = ∫CF. N ds , N normal vector
The Attempt at a Solution
I'm not quite sure where to begin . Do we parametrize C by r(t) = (cos t, sin t) 0≤ t≤ 2[itex]\pi[/itex], and then use the definitions of flux and circulation?