1. Consider the vortex field F(z.y) = 4+ 2+ {a) Recall that back in Week 7, we have computed its circulation along a circle C;

1. Consider the vortex field F(z.y) = <__13f l> 4+ 2+ {a) Recall that back in Week 7, we have computed its circulation along a circle C; of radius K centered at the origin, oriented counter-clockwise. Take a few minutes to review how to perform this computation. (b) Let C be the unit circle centered at (2,0}, oriented counter-clockwise. What is the circulation of the vortex field F along C,7 In other words, find sz F - dr. (c) Let Cy be the smooth, simple path around the origin in the xy-plane, oriented counter-clockwise, as shown in the picture below. Use Green's Theorem to eval- uate the circulation of F along C;. Cy Hint: Consider a small circle centered at the origin, small enough so that it lies completely inside the region bounded by C;. Let D he the region bounded by the two curves and apply the general form of Green's Theorem