In Cartesian coordinates, a vector field takes the form F = 2rzi+2yzj + (x² + y²) k throughout the whole of three-dimensional space. (a) Find the divergence and curl of F in Cartesian coordinates. (b) Use Procedure 1 of Unit 9 to express F in cylindrical coordinates (r, o, z). (c) Use your answer to part (b) to calculate the divergence and curl of F in cylindrical coordinates. Comment on the agreement with part (a)..
In Cartesian coordinates, a vector field takes the form F = 2rzi+2yzj + (x² + y²) k throughout the whole of three-dimensional space. (a) Find the divergence and curl of F in Cartesian coordinates. (b) Use Procedure 1 of Unit 9 to express F in cylindrical coordinates (r, o, z). (c) Use your answer to part (b) to calculate the divergence and curl of F in cylindrical coordinates. Comment on the agreement with part (a)..
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 11E
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Transcribed Image Text:In Cartesian coordinates, a vector field takes the form
F = 2xzi+2yzj + (x² + y²) k
throughout the whole of three-dimensional space.
(a) Find the divergence and curl of F in Cartesian coordinates.
(b)
Use Procedure 1 of Unit 9 to express F in cylindrical coordinates
(r, o, z).
(c) Use your answer to part (b) to calculate the divergence and curl of F in
cylindrical coordinates. Comment on the agreement with part (a).
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