   Chapter 16.5, Problem 10E

Chapter
Section
Textbook Problem

The vector field F is shown in the xy-plane and looks the same in all other horizontal planes. (In other words, F is independent of z and its z-component is 0.)(a) Is div F positive, negative, or zero? Explain.(b) Determine whether curl F = 0. If not, in which direction does curl F point?10. (a)

To determine

To find and explain: The div F.

Explanation

Formula used:

Consider the standard equation of a divergence of vector field for F=Pi+Qj+Rk

divF=Px+Qy+Rz (1)

As F is independent of z-component (R=0) is Rx=Ry=Rz=0 .

From Figure, P and Q doesn’t vary in the z-direction, so Pz=Qz=0 and as the x increases, the each vector of F in x-component increases while the y-component remains constant, so Px>0 and Qx=0 .

Similarly, as the y increases, the each vector of F in y-component increases while the x-component remains constant, so Qy>0 and Py=0

(b)

To determine

Whether curl F=0 or not.

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