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 at P? Explain. div(F) is --Select--- because the vectors that start near P are -Select--- (b) Determine whether curl(F) = 0. If not, in which direction does curl(F) point at P? O curl(F) + 0. At P the curl(F) points in the direction of positive x. O curl(F) + 0. At P the curl(F) points in the direction of negative x. O curl(F) + 0. At P the curl(F) points in the direction of positive y. O curl(F) + 0. At P the curl(F) points in the direction of negative y. O curl(F) + 0. At P the curl(F) points in the direction of positive z. O curl(F) # 0. At P the curl(F) points in the direction of negative z. O curl(F) = 0 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.) (a) Is div(F) positive, negative, or zero at P? Explain. div(F) is --Select--- because the vectors that start near P are -Select--- (b) Determine whether curl(F) = 0. If not, in which direction does curl(F) point at P? O curl(F) + 0. At P the curl(F) points in the direction of positive x. O curl(F) + 0. At P the curl(F) points in the direction of negative x. O curl(F) + 0. At P the curl(F) points in the direction of positive y. O curl(F) + 0. At P the curl(F) points in the direction of negative y. O curl(F) + 0. At P the curl(F) points in the direction of positive z. O curl(F) # 0. At P the curl(F) points in the direction of negative z. O curl(F) = 0 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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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 z-component is 0.)
(a) Is div(F) positive, negative, or zero at P? Explain.
div(F) is --Select--- because the vectors that start near P are -Select---
(b) Determine whether curl(F) = 0. If not, in which direction does curl(F) point at P?
O curl(F) + 0. At P the curl(F) points in the direction of positive x.
O curl(F) + 0. At P the curl(F) points in the direction of negative x.
O curl(F) + 0. At P the curl(F) points in the direction of positive y.
O curl(F) + 0. At P the curl(F) points in the direction of negative y.
O curl(F) + 0. At P the curl(F) points in the direction of positive z.
O curl(F) + 0. At P the curl(F) points in the direction of negative z.
O curl(F) = 0
those that end near P.
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