Let r = (x2+y2)1/2. Figure 20.10 shows the vector fieldrA(yi + xj ) for r = 0 and A = 1
Chapter 20, Problem 33(choose chapter or problem)
Let r = (x2+y2)1/2. Figure 20.10 shows the vector fieldrA(yi + xj ) for r = 0 and A = 1, 2, and 3.The vector fields are shown in the xy-plane; they have noz-component and are independent of z.(a) Show that curl(rA(yi +xj )) = (2+A)rAk forany constant A.(b) Using your answer to part (a), find the directionof the curl of the three vector fields for A =1, 2, 3.(c) For each value of A, what (if anything) does your answerto part (b) tell you about the sign of the circulationaround a small circle oriented counterclockwisewhen viewed from above, and centered at (1, 1, 1)?Centered at (0, 0, 0)?
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