At Q(1, 1), f>0, 8, > 0, and V· F>0. F = r?, y) Q(1, 1) V.F>0. for x>- V.F<0 for x<- 2 Figure 17.39
Divergence from a graph To gain some intuition about the divergence,
consider the two-dimensional
a. Without computing it, determine whether the two-dimensional divergence is positive or negative at the point Q(1, 1). Why?
b. Confirm your conjecture in part (a) by computing the two-dimensional divergence at Q. c. Based on part (b), over what regions within the circle is the divergence positive and over what regions within the circle is the divergence negative?
d. By inspection of the figure, on what part of the circle is the flux across the boundary outward? Is the net flux out of the circle positive or negative?
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