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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
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?

9. images

(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, the x-component of each vector is 0 (P=0) , hence Px=Py=Pz=0

and Q dec

(b)

To determine

Whether curl F=0 or not.

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Chapter 16 Solutions

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