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.) 0 1 t 1 t G (a) Is div(F) positive, negative, or zero at PP Explain div(P) is negative because the vectors that start near P are shorter than (b) Determine whether curl(F) = 0. If not, in which direction does curl(F) point at curl(F) 0. At P the curi(F) points in the direction of positive x. curi(F) 0. At P the curi(F) points in the direction of negative x. curi(F) 0. At P the curi(F) points in the direction of positive y curi(F) 0. At P the curi(P) points in the direction of negative y ✔those that end near P.
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.) 0 1 t 1 t G (a) Is div(F) positive, negative, or zero at PP Explain div(P) is negative because the vectors that start near P are shorter than (b) Determine whether curl(F) = 0. If not, in which direction does curl(F) point at curl(F) 0. At P the curi(F) points in the direction of positive x. curi(F) 0. At P the curi(F) points in the direction of negative x. curi(F) 0. At P the curi(F) points in the direction of positive y curi(F) 0. At P the curi(P) points in the direction of negative y ✔those that end near P.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please help solve part b
Transcribed Image Text: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 -component is 0.)
1
f
1 1
(a) Is div(F) positive, negative, or zero at PP Explain.
div(P) is negative because the vectors that start near P are shorter than
(b) Determine whether curl(F) = o. If not, in which direction does curl() point at
curl(F) 0. At P the curi(F) points in the direction of positive x.
curi(F)-0. At P the curi(F) points in the direction of negative x
curi(F)-0. At P the curi(F) points in the direction of positive y
curi(F) 0. At P the curi() points in the direction of negative y
curi(F)-0. At the curl(P) points in the direction of positive z.
curi(F)-0. At the curl(F) points in the direction of negative z.
curi(F) = 0
✔those that end near P.
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