Does the vector field plotted below appear to be conservative? 1.0 0.5- 0.0- %3D -0.5 -1.0b -1.0 -0.5 0.0 0.5 1.0 Select one: a. No b. Yes

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Does the vector field plotted below appear to be conservative?
1.0
0.5F
0.0 -
-0.5
-1.0
-1.0
-0.5
0.0
0.5
1.0
Select one:
a. No
b. Yes
Transcribed Image Text:Does the vector field plotted below appear to be conservative? 1.0 0.5F 0.0 - -0.5 -1.0 -1.0 -0.5 0.0 0.5 1.0 Select one: a. No b. Yes
Expert Solution
Step 1 Introduction

Graphically, a vector field is conservative if it has no tendency to ``swirl around.'' If it did swirl, then the value of the line integral would be path dependent. A conservative vector field has the direction of its vectors more or less evenly distributed.A conservative vector field is a vector field which is the gradient of a function, known in this context as a scalar potential. Conservative vector fields have the following property: The line integral from one point to another is independent of the choice of path connecting the two points; it is path-independent.

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