Chapter 14.2, Problem 66E

Flux across curves in a vector field Consider the vector Field F = 〈y, x〉 shown in the figure.

a.    Compute the outward flux across the quarter circle C: r(t) = 〈2 cos t, 2 sin t), for 0 ≤ t ≤ π/2.

b.    Compute the outward flux across the quarter circle C: r(t) = 〈2 cos t, 2 sin t), for π/2 ≤ t ≤ π.

c.    Explain why the flux across the quarter circle in the third quadrant equals the flux computed in part (a).

d.    Explain why the flux across the quarter circle in the fourth quadrant equals the flux computed in part (b).

e.    What is the outward flux across the full circle?